ETD vs OTC Counterparty Risk and Capital Requirements for Exchange Traded Derivatives

Transcription

1 ETD vs OTC Counterparty Risk and Capital Requirements for Exchange Traded Derivatives Marco Bianchetti a,1, Mattia Carlicchi a,2, Federico Cozzi a,3, Leonardo Recchia a, Andrea Spuntarelli b,4 a Financial and Market Risk Management, Intesa Sanpaolo, Milan, Italy, b Internal Validation, Intesa Sanpaolo, Milan, Italy. First version: 24 th September 2014; last revision 17 September 2018 Abstract It is common belief that Exchange Traded Derivatives (ETDs), e.g. Futures and Futures Options, are collateralized plain vanilla financial instruments carrying low counterparty risk and capital requirements with respect to corresponding Over The Counter Derivatives (OTCs). In this paper we discuss techniques to compute counterparty risk exposures for ETD portfolios, both computationally efficient and compliant with regulatory requirements. We compare a number of sample ETDs and OTCs, and we show how the different collateralisation rules may lead to high exposure spikes. We also find that ETDs exposures may be, in some cases, larger than the corresponding OTCs exposures. Finally, we show that the capital requirements generated by ETDs under the Internal Model Method (IMM) may be larger than those under Current Exposure Method (CEM). These findings may have important consequences for financial institutions holding large ETDs portfolios. Keywords: ETD, exchange traded derivatives, OTC, Over The Counter, derivatives, FRA, Futures, counterparty risk, exposure, collateral, CSA, margin, capital, Internal Model Method, IMM, Current Exposure Method, CEM, Risk Weighted Assets, RWA, Exposure at Default, EAD. JEL Classifications: C15, G12, G13, G32 Acknowledgements and disclaimer: the authors gratefully acknowledge fruitful interactions with many colleagues in Risk Management, Internal Validation and Trading Desks. The views and the opinions expressed here are those of the authors and do not represent the opinions of their employers. They are not responsible for any use that may be made of these contents. No part of this material is intended to influence investment decisions or promote any product or service. 1 Corresponding autor, marco.bianchetti[at]intesasanpaolo.com 2 Present affiliation: MSCI, Milan, Italy 3 Present affiliation: Risk Management, Unicredit, Milan, Italy 4 Present affiliation: Internal Validation, Banco Popolare, Milan, Italy Page 1 of 33

2 Table of Contents 1. Introduction ETDs and OTCs OTC Market ETD Market Credit Risk Mitigation Regulatory Requirements ETDs Margination Rules Futures Options on Stock-Index Options on Futures ETD Portfolios and Risk Measures Computation ETD vs OTC Portfolios Counterparty risk measures ETD exposure computation ETD time simulation grid Numerical Results Interest Rate Futures Option on Stock-Index Option on Interest Rate Futures OTC vs ETD in a real framework Capital Simulation Exposure At Default Risk Weights Capital Requirements Conclusions References Page 2 of 33

3 1. Introduction The financial crisis that began in August 2007 had many consequences and changed the counterparty and credit risk perception of interbank market institutions. The bankruptcy of Lehman Brothers in September 2008 demonstrated that even big financial institutions, considered risk-less until then, can default and the paradigm to big to fail (or to big to be allowed to fail ) has been abandoned. Since then, counterparty risk, related to the possibility that a counterparty can default and be unable to fulfil its obligations, became one of the most important financial risks to be considered when dealing with Over The Counter Derivatives (OTCs). International regulators and financial institutions focus on how to effectively manage and reduce counterparty risk. In the market, we can identify two main practices that can lead to the mitigation of counterparty risk: the usage of bilateral collateralization mechanisms and the recourse to Central Counterparties (CCPs), considered less risky than financial institutions. Indeed, CCPs (i.e. Euronext, Eurex, ICE, CME, LCH, etc.) reduce the market systemic risk and prevent domino-effect in case of market turmoil through over-collateralisation mechanisms and a loss-mutualisation system. Hence, the risk management regulation of OTCs tends to be more severe due to an higher perception of their counterparty risk. As reported by ISDA (2013a), the amount of collateral posted for non-cleared OTC transactions increased of 18.4% compound annual growth rate between 2002 and In 2012 the 87% of collateral agreements were regulated under ISDA dispositions (i.e. Credit Support Annex, CSA). In this paper we focus our attention on the counterparty risk generated by Exchange Traded Derivatives (ETDs). These are plain vanilla financial products, such as Futures, Option on Futures and Option on Stock-Index, quoted and traded on an exchange that regulates all the features of the margination mechanism and the settlement of these instruments. Traditionally, ETDs are believed to generate a small, if not negligible, counterparty risk, due to their margination mechanism and to small default probability of exchanges, see e.g. Bates and Craine (1999). Actually a few CCPs defaulted in the past years: for example, the Hong Kong Futures Exchange defaulted after the market crash in 1987 because of high concentration of brokers with no position limits, and the government supported bank bailout. Others were close to default, such as CME and OCC in 1987, BM&F in In more recent times concerns were raised about the actual systemic default risk of CCPs generated by increasing volumes of ETDs concentrated in a few large CCPs. See e.g. Knott and Mills (2003), Litke (2013), Brigo and Pallavicini (2013) for more information and discussion. We discuss techniques to compute counterparty risk exposures for ETD portfolios, both computationally efficient and compliant with regulatory requirements. We show how the different margination and collateralisation rules that characterize ETDs and OTCs respectively may lead to high exposure spikes at instruments maturity. We also find that, in some cases, ETDs may carry more counterparty risk than the corresponding OTCs. Furthermore, we show that the capital requirements generated by ETDs under the Internal Model Method (IMM) may be much larger than those under Current Exposure Method (CEM). The paper is organized as follows. In section 2 we review the ETD and OTC markets, and we report an overview of the different regulatory capital requirements that regulates ETDs and OTCs transactions. We consider both in-force regulations and upcoming proposals. In section 3 we describe in detail the margination mechanisms that characterized ETDs, with a particular focus on their implications for counterparty risk reduction. In particular, we analyse the differences between the CSA collateralization mechanism of interest rate Forward Rate Agreement (FRA) and the margin mechanism of interest rate Futures. In section 4 we describe the multi-factor, multi-step Monte Carlo simulation for counterparty credit risk, and we propose an efficient implementation specific for ETDs, consistent with the regulatory framework of section 2 and with the margination rules of section 3. We also discuss typical ETDs and OTCs portfolios. In section 5 we present our numerical results. In particular we focus on Future on Interest Rates, Option on Interest Rate Futures and Option on Stock-Index instruments, and we analyse the different Mark-to-Future Page 3 of 33

4 profiles between ETDs and OTCs. In section 6 we report the differences in capital requirements between Internal Model Method (IMM) and standard method (CEM, Current Exposure Method). Conclusions are drawn in section ETDs and OTCs 2.1. OTC Market OTC counterparties trade tailor made derivatives with a large variety of features (payoff, maturity, size, etc.), thus generating the global OTCs market summarized in Figure 1. Since trading OTCs generates credit exposure, OTC counterparties may subscribe bilateral collateral agreements, typically under ISDA Master Agreement with Credit Support Annex (CSA). In Figure 2 we show the size of collateral in circulation in the non centrally cleared OTCs market. We may notice the sharp increase in collateralization at the onset of the credit crunch crisis in , and the subsequent decline in due to market contraction. Figure 1: size of the global OTCs market as of end of Source: Bank for International Settlements (2013) Page 4 of 33

5 Figure 2: size of collateral in circulation (USD billions) in the non centrally cleared OTCs market. Source: ISDA (2013a) ETD Market Counterparties also trade derivatives via derivatives exchanges, thus generating the global ETDs market summarized in Table 1. We notice the predominance of interest rate ETDs in terms of outstanding amount (65 USD trillions). Contrary to OTCs, ETDs are highly standardized contracts in terms of underlying, maturity, size, etc. A derivatives exchange is a regulated market, where counterparties trade such contracts, acting as an intermediary to all transactions. Exchanges provide also clearing services of the listed ETDs (i.e. margination) using an internal clearing house. All the exchanges counterparties are registered clearing members of the exchange s clearing house. ETDs are typically used to hedge the short term (delta and vega) risk generated by OTCs portfolios. Amounts outstanding Turnover Contracts outstanding Turnover USD Bln Futures Options Futures Options Futures Options Futures Options All markets 25,933 38,695 1,415, , ,208 3,913 Interest Rate 24,210 32,797 1,244, , , Currency ,871 3, , Equity Index 1,482 5, , , ,407 2,936 Table 1: ETDs market, outstanding notional amount (cols. 2-3) in USD billions, number of outstanding contracts (cols. 6-7) in millions. Also, turnover 2013 data are reported (cols. 4-5 and 8-9, respectively). Source: Bank for International Settlements Page 5 of 33

6 2.3. Credit Risk Mitigation Exchanges centralize and standardize derivatives transactions, thus allowing higher reduction of credit exposures by netting between multiple counterparties, requiring initial margin and collateral deposits, providing a guarantee fund, independent valuation of trades and collateral, and monitoring the credit worthiness of the clearing firms. We show in Figure 3 a graphical representation of the ETD and OTC collateral mechanics. Figure 3: graphical comparison of collateral mechanics for ETDs (right) and OTCs (left). In Table 2 we compare the main features that regulate the margination and collateral mechanism of ETDs and OTCs. The first main difference between the two cases is the instrument s payoff, which is settled daily through variation margin cash flows or at contract maturity, respectively. The second difference that we observe is related to the absence of a threshold for ETDs that implies that daily variations of the MtM of the contracts are fully margined, regardless of their magnitude. Instead, collateralized OTCs may prescribe a threshold that represents the amount of MtM that is excluded from collateralization, thus increasing counterparty exposure. Another relevant aspect that has to be considered in evaluating counterparty risk is the margin frequency. According to ISDA (2013a), only the 48.4% of the OTCs (in terms of trade volume) are reconciled with daily margin frequency (73.9% if we restrict to large firms portfolios). Regarding ETDs, clearing houses always adopt a daily margin frequency, which can be even intraday in some circumstances. Hence, ETDs usually present a lower counterparty exposure than OTCs. Indeed, the higher the margination frequency, the higher the probability that the MtM of the trade is covered by collateral, the lower the probability of loss in case of counterparty s default. Both ETDs and OTCs also require the identification of a valuation agent that is in charge to provide a fair evaluation of the MtM of the contract for margination purposes. In the case of OTCs the valuation agent is defined by the two counterparties. If they disagree on the fair MtM a dispute resolution procedure begins. This can considerably delay the contract s margination, leaving part of the contract s MtM uncollateralized. For all ETDs the valuation agent is represented by the exchange itself and, since the MtM is identified by market quotations, there is no room for any disputes. Dealing with OTCs, counterparties usually define the nature of collateral they agree to exchange. As reported by ISDA (2013a), 79.5% of the overall collateral amount is in cash, 11.6% is represented by government securities, and 8.9% by other assets. In the ETDs market the counterparty can choose between securities and cash, even if cash is mandatory for certain types of margin, such as the Variation Margin. However, the market practice is to use cash for all the daily margination requirements. Page 6 of 33

7 OTCs ETDs Payoff Settlement At Maturity. Daily settlement through Variation Margin cash flows. Threshold Applicable. Not applicable. Margin Frequency Agreed by the counterparties. 48.4% of OTCs are reconciled on a daily basis. Daily. Valuation Agent Agreed by the counterparties. Clearing house. Collateral/Margin Type Use of collateral, Rehypothecation Type of agreement Transaction Account Agreed securities and cash. Cash covers the 79.5% of OTC collateral amount. Use of collateral and rehypothecation is possible if agreed by counterparties. Considering large firms, 82% of collateral is eligible to be re-used by the receiver. Bilateral (87.8%) or unilateral (12.2%). Identified by the two counterparties. Eligible securities and cash. Cash is mandatory for Variation Margin transactions. No use or re-hypothecation of eligible margin assets by clearing members. Use of delivered cash by the clearing house. Multilateral (CCP vs Margin Members). Held at the Clearing House, clearing members should post enough cash to cover margin variations. Independent Amount Minimum Transfer Amount, Rounding Applicable. Applicable. Applicable. Applicable. Table 2: comparison between ETDs and OTCs collateral mechanisms. Source: ISDA (2013a). An important difference between ETDs and OTCs may be the use and re-hypothecation of collateral. In the OTC market 82% of the collateral is eligible to be re-used (re-hypothecated) by the receiver counterparty. This practice is very common since it reduces funding costs and it prevents the increase of high quality collateral prices due to high demand. However, if we consider the possibility of default of the counterparty receiving assets that were previously posted as collateral, the right of re-hypothecation can increase the counterparty systemic risk of the market. Even ETDs allow the re-hypothecation, but only the clearing house can actually re-use the margins received from the clearing members. Further, CCPs operate under multilateral agreements that have the aim of reducing the systemic risk of the market and avoid the possibility that a default of a relevant participant can create a domino-effect, perturbing all the financial markets. On the other hand, most of the collateral agreements of the OTC market are bilateral and it would be impossible to segregate the consequences of a counterparty default. Page 7 of 33

8 The comparison between ETDs and OTCs shows that the counterparty risk associated to these financial instruments is different and depends on the details of the margination mechanism. We argue that ETDs generally present lower counterparty exposure than OTCs, thanks to the different nature of the payoff, characterized by daily settlement, and to more stringent margin dispositions Regulatory Requirements The capital requirements related to ETDs and OTCs are regulated, for European financial institutions, by the Regulation (EU) No 575/2013 (European Parliament and the Council, 2013), commonly known as Capital Requirement Regulation IV (CRR IV). The CRR IV transposes within the European financial market the global standards on bank capital of the Basel III agreement of the Bank for International Settlements (BIS, 2011). Thanks to their peculiar characteristics (reported in section 2.3), ETDs are subject to special capital requirements. In particular, thanks to their daily margination, Article 285 of the CRR IV on Exposure value for netting sets subject to a margin allows a 10 days margin period of risk (MPOR) for the counterparty exposure calculation. Instead, OTCs, under certain circumstances, can be penalised with a MPOR that can exceed 20 days. We remind that the MPOR is defined by the CRR IV as the time period from the most recent exchange of collateral covering a netting set of transactions with a defaulting counterparty until the transactions are closed out and the resulting market risk is re-hedged, as depicted in Figure 4. Figure 4: picture of the margin period of risk (MPOR) definition. In addition, capital requirements for CCPs benefit of a risk weight of 2% (Article 306, CRR IV) applied to exposure values. The 2% risk weight refers just to qualifying CCPs meeting the Principles for financial market infrastructures (BIS-IOSCO, 2012) published by the BIS and by the International Organization of Securities Commissions (IOSCO). Qualifying CCPs are recognised according to Regulation (EU) No 648/2012 of the European Parliament and the Council (2012). The competent authority for the recognition within the European market is the European Securities and Market Authority (ESMA). For non-qualifying CCPs the risk weight is assigned according to the Standardised Approach (Article 306, CRR IV). 3. ETDs Margination Rules Exchange Traded Derivatives are characterized by a daily margination (or clearing) procedures that consist in a daily exchange of cash flows between the clearing member and the clearing house of the exchange, based on the daily settlement price of the product. The daily settlement price represents the reference Mark-to-Market (MtM) value of the financial instrument and it is determined by the exchange according to the pricing methodologies adopted. The margination cash flows are given by the daily variation of the settlement price, and by margin adjustments parameterized on worst case scenarios of the underlying risk factors. Page 8 of 33

9 The aim of the margination mechanisms is to reduce both the liquidity and the counterparty risk of these instruments. Indeed, the margin cash flows represent the daily settlement of the payoff for the majority of ETD typologies and prevent P&L accumulation over the life of the contract. In fact, at the start of a trading day and after the daily margination the MtM of an ETD is null, thus its volatility and counterparty risk exposure are determined by the price variations occurring during a trading day. Moreover, certain ETDs, such as Options on Futures, are characterized by forward premia and, hence, they do not require any upfront liquidity. The dynamics of initial margins may influence the price of the ETDs, as discussed by some authors, see e.g. Cont et al (2011), Leippold and Su (2011), Cont and Kokholm (2012), Brigo and Pallavicini (2014), Green and Kenyon (2014). In the following sections we report in detail the margination rules of the most common ETDs according to Eurex Clearing (2014) practices and discuss their effects on the counterparty risk Futures Futures products are the most widespread ETDs and they represent one of the most liquid instruments in the market. Futures are contracts in which two counterparties agree at time t to buy or sell a certain asset Y at maturity T > t at a given price. According to, e.g., Bjork (2006), Futures are financial instruments characterized by the following features: o o o o they are standardized products traded through an exchange; at any time t during the life of the contract there is a quoted Futures price in the market, denoted by f(t; T, Y); in particular f(t; T, Y) at day close time t represents the daily settlement price of the Futures; during a certain time interval (s, t] the holder receives/pays a cash flow, called Variation Margin (VM), equal to the difference f(t; T, Y) f(s; T, Y), scaled by the notional of the contract and other parameters depending on the underlying of the contract; at any time t the premium to enter into a Futures contract is equal to zero. Considering the Eurex Clearing (2014) margination rules, Futures are regulated by three types of margin: o o o Variation Margin (VM): it represents the daily settlement of Futures payoff and it is given by f(t i ; T, Y) f(t i 1 ; T, Y), Additional Margin (AM): it is the margin that hedges the tail risk of the Futures and it is determined considering stressed market scenarios of the underlying risk factor; Futures Spread Margin (FSM): it concerns spread strategies on the same delivery month and it is computed on the netted position. When applicable, it substitutes the more expensive Additional Margin. The VM represents the most important feature of Futures and it distinguishes the trading of these instruments with respect to other similar products. In order to ensure the daily settlement of the VM, the clearing member holds a margin account at the clearing house where it maintains a minimum cash amount the clearing house can recur to in case of default of the clearing member, or in case of unexpected market shocks. All the cash flows related to Futures positions are settled through the margin accounts held at the clearing house. Interest Rate Futures vs Forward Rate Agreements (FRAs) In particular, Interest Rate Futures and Forward Rate Agreements (FRAs) are financial products that allow to fix in t the future interest rate that will prevail on time interval [T 1, T 2 ], with t < T 1 < T 2. At inception both instruments are in equilibrium and therefore they are worth zero. Looking at the details of the collateralization and margin procedures, discussed in general in section 2.3 and Table 2, we stress in this case the different payoffs of the two instruments. In fact, the payoff of a Page 9 of 33

10 standard FRA bought in t 0 on the interbank rate L x (T 1, T 2 ) for the time interval [T 1, T 2 ] with tenor x (e.g. x = 1M, 3M, 6M, 12M) is settled in T 2 and it is given by 5 FRA Std (T 2 ; L x (T 1, T 2 ), K, ω) = Nω[L x (T 1, T 2 ) K]τ x (T 1, T 2 ), (1) where N is the notional of the contract, ω = +/ 1 for a payer/receiver FRA (referred to the fixed leg), τ x (T 1, T 2 ) is the year fraction of the time interval [T 1, T 2 ], L x (T 1, T 2 ) is the underlying interest rate fixed at time T 1 prevailing on the time interval [T 1, T 2 ] paid by the floating leg, and K is the rate paid by the fixed leg. The price of the FRA contract at time t < T 1 is given by FRA Std (t; L x (T 1, T 2 ), K, ω) = P(t; T 2 )E t Q T2 [FRA Std (T 2 ; L x (T 1, T 2 ), K, ω)] = NP(t; T 2 )ω {E t Q T2 [L(T 1, T 2 ) K]} τ x (T 1, T 2 ) = NP(t; T 2 )ω[f x (t; T 1, T 2 ) K]τ x (T 1, T 2 ), (2) where F x (t; T 1, T 2 ) = E t Q T2 [L x (T 1, T 2 )], with F(T 1 ; T 1, T 2 ) = L x (T 1, T 2 ), is the FRA rate and it represents the expected value in t of the underlying interest rate L x (T 1, T 2 ), E t Q T 2 denotes the expectation in t under the discounting measure Q T2 associated to the discounting Zero Coupon Bond P(t; T 2 ). F x (t; T 1, T 2 ) is a martingale under the T-forward measure Q T2, F x (t; T 1, T 2 ) = E t Q T2 [F x (u; T 1, T 2 )], t < u < T 1 < T 2. (3) The equilibrium FRA rate in t, denoted by R FRA Std (t; T 1, T 2 ), is defined as the FRA fixed rate that makes null the FRA present value, FRA Std (t; L x (T 1, T 2 ), K, ω) = NP(t; T 2 )ω[f x (t; T 1, T 2 ) K]τ x (T 1, T 2 ) = 0, K = R FRA Std (t; T 1, T 2 ) = F x (t; T 1, T 2 ). (4) The Interest Rate Futures price is quoted in 100 minus rate terms and it reflects the market consensus on the future fixing of the underlying rate. For example, the price in t of a Futures on Euribor 3M fixed in T 1 and maturing in T 2 is given by 100 minus the market expectation on the 3M European interbank rate f(t; T 1, L 3M (T 1, T 2 )) = 100{1 E t Q B [L 3M (T 1, T 2 )]}, (5) where E t Q B is the expected value under the risk-neutral measure QB associated to the bank account B(t), and L 3M (T 1, T 2 ) is the Euribor 3M interest rate for the period [T 1, T 2 ]. For example, if the expected value for L 3M (T 1, T 2 ) is equal to 0.275%, then the price of the corresponding Futures will be = The market quotation of the Futures price depends on the Futures rate R x Fut (t; T 1, T 2 ), R x Fut (t; T 1, T 2 ) = E t Q B [L x (T 1, T 2 )] = E t Q B [F x (T 1 ; T 1, T 2 )] (6) According to Brigo and Mercurio (2006), the Interest Rate Futures contracts gives to the owner at the last settlement date T 1 the payoff 5 The standard FRA and the market FRA have different payoffs, see e.g. refs. Ametrano and Bianchetti (2013, Bianchetti and Morini (2013). Page 10 of 33

11 Futures(T 1 ; L x (T 1, T 2 ), ω) = Nω[1 L x (T 1, T 2 )], (7) where ω = +/ 1 for a long/short Futures contract. The fair price of the contract at time t is given by Futures(t; L x (T 1, T 2 ), ω) = E t Q B {Nω[1 L x (T 1, T 2 )]} = Nω{1 E t Q B [L x (T 1, T 2 )]} = Nω[1 R x Fut (t; T 1, T 2 )], (8) under the risk-neutral measure Q B. To price an Interest Rate Futures contract, we need to compute the Futures rate R x Fut (t; T 1, T 2 ). Considering equation (6), since F x (t; T 1, T 2 ) is not a martingale under the risk-neutral measure Q B, such computation requires the adoption of a model for the dynamics of F x (t; T 1, T 2 ). In general, we obtain that the Futures rate is given by the corresponding FRA rate corrected by a convexity adjustment R x Fut (t; T 1, T 2 ) = E t Q T2 [L x (T 1, T 2 )] + CA(t; T 1 ) = F x (t; T 1, T 2 ) + CA(t; T 1 ), (9) where CA(t; T 1 ) is the convexity adjustment term and it depends on the particular model adopted and it contains, in general, the model s volatility and correlations. Equation (9) shows that the FRA rate and Futures rate on the same underlying interest rate differ only for the convexity adjustment that comes from the different probability measure of the expected values. The daily settlement of the payoff in t i is given by the Variation Margin and it is represented by the difference between the two consecutive settlement prices scaled by the notional amount and the year fraction, VM(t i ; T 1, T 2 ) = Nω [f (t i ; T 1, L x,j (T 1, T 2 )) f (t i 1 ; T 1, L x,j (T 1, T 2 ))] τ x (T 1, T 2 ). (10) Due to the daily settlement of the payoff through the Variation Margin, the Futures contract implies that for each day till the maturity date the holder enters in a Futures at the start of the trading date and regulates his position at the end of the session. Hence, the exposure to the CCP corresponds to the daily variations of the Futures market quote that still has to be settled. We can argue that in the case of Futures the counterparty risk reduction is embedded in the financial instrument, and the counterparty exposure is directly decreased with the Variation Margin that reduces the MtM of the contract. In the case of the FRA, the counterparty risk exposure is mitigated only through a separate collateral agreement between the two counterparties. As we report in section 5.1, the counterparty exposure of these two instruments can considerably differs at the maturity of the contracts, due to operational aspects that govern the two different credit risk mitigation mechanisms Options on Stock-Index The product types that can be traded with exchanges include also Options on Stock-Index. These are traditional-style options on equity stocks or indexes quoted in the market and regulated by the clearing house of the exchange. ETD Options on Stock-Index are usually European Call and Put option that can be bought (long position) or sold (short position) between clearing members through the exchange. The buyer of the option pays up front the premium to the seller. In the case of a Call option, if the buyer exercises his right the seller has to fulfil his obligation and deliver the underlying asset at the strike price. In the case of a Put option, if the buyer exercises his right the seller of the option has to acquire the underlying asset at the strike price. Since premia of Options on Stock-Indexes are paid up front, the buyer doesn t have to face any additional obligations except the premium amount already paid. In fact, if the market goes against him, the option is out-of-the-money (OTM) and he does not exercise his right, but if the option goes Page 11 of 33

12 in-the-money (ITM) he can exercise the option and gain the profits. For this reason, no margin is required to the buyer of an option and the clearing house does not perceive any counterparty exposure risk. However, the buyer perceives counterparty risk exposure towards the clearing house. On the other hand, the seller of an option remains obliged to fulfil his obligation until the maturity of the option. The seller receives the premium up front, but he is asked to post margin at the clearing house on the basis of the option MtM in order to ensure the fulfilment of his obligations. Short Options on Stock-Indexes are daily margined and the margin types for these instruments are the following: o o Premium Margin (PM): it is based on the difference between the current daily settlement price of the option and the one of the previous trading date. The premium margin amount posted by the seller at the clearing house is aligned with the (negative or zero) MtM of the short option. Additional Margin (AM): similarly to Futures, Additional Margin covers unexpected losses that can occur due to adverse changes of the market dynamics. At the end of the trading date, the amount of margin due to or received from the clearing house is given by the sum of the Premium Margin and variations of the Additional Margin. Even if the long option positions do not require any margin, the clearing house recognizes a theoretical credit to the buyer that can be used to reduce the margin due on ETDs with the same underlying instruments (i.e. DJ EuroStoxx 50, DAX, FTSE MIB, etc.). The buyer cannot dispose directly of the margin credit associated to the options. At the maturity or exercise of the option, the clearing house returns to the seller the whole margin amount that has been posted during the life of the contract. Unlike the Variation Margin, the Premium Margin is not considered in the settlement of the option s payoff. We observe that, under certain assumptions on CSA dispositions, the margination mechanism associated to Options on Stock-Index can be considered as a CSA one-way agreement of an OTC option Options on Futures Options on Futures are ETDs contingent on Futures contracts of several asset classes. These financial products give to the buyer the right of buy (Call) or sell (Put) the reference asset (the underlying Futures) at a given price. Generally, Option on Futures are American style option, and can be exercised before the final maturity. The main characteristic of these options is that the premium is paid forward by the buyer, at maturity or when the option is actually exercised. For these reasons the Premium Margin associated to the Options on Stock-Index of section 3.2 does not apply. At maturity or exercise the buyer of the option has to pay the relevant premium that prevails in the market. The seller of the option does not receive the premium until exercise or maturity, and, since he cannot reinvest the amount, usually a higher premium is asked to cover the opportunity loss. If the option is exercised he has to deliver the underlying Futures or fulfil the cash settlement. Unlike Options on stock- Index, the clearing house does not require the posting of any Premium Margin to the seller of the option. Both the buyer and the seller of forward premium options benefit from a liquidity advantage if compared to traditional-style options, in fact they don t required liquidity commitment to enter the contract. These options are usually referred to as Futures-style option because of the similarity with the margination rules with Futures products. Indeed, the daily changes of the settlement option premium are settled each day during the life of the contract through the Variation Margin. The margin types that apply to Option on Futures are those of the Futures except the Futures Spread Margin. Page 12 of 33

13 4. ETD Portfolios and Risk Measures Computation 4.1. ETD vs OTC Portfolios We show in Figure 5 a real example of ETDs portfolio representing a typical ETD component of the trading book of a generic financial institution. The portfolio presents an average maturity of 10 months, reflecting the short maturity of the most widespread ETDs in the market. The characteristic stepwise shape is due to the standardized nature of ETDs: the sharp jumps occur on the relevant maturities (3M, 6M, 1Y and so on). We also observe that 80% of the instruments expire within the first year, leaving alive just 30% of the initial notional. Just one ETD contract has a maturity beyond 5 years. The portfolio expires completely after 12Y. A 5-year horizon allows to cover 99.8% of the notional amount and 98.7% of the trades. The instruments considered, i.e. Interest Rate Futures, Option on Stock-Index, Option on Interest Rate Futures, cover all the typologies of ETDs. In order to appreciate the different characteristics of ETD and OTC portfolios, we show in Figure 5 also a typical OTC portfolio, containing tens of thousands of instruments over all asset classes, both exotics and plain vanillas, with maturities extending to over 50 years. The smoother decay of the OTC portfolio is due to the higher differentiation of OTCs in terms of maturity. Figure 5: comparison between two typical OTC and ETD sample portfolios. OTC portfolios may have maximum maturity exceeding 50 years, while ETD portfolios are typically short-lived Counterparty risk measures There is a variety of risk measures that can be defined to describe the counterparty risk of a derivative portfolio. The basic building blocks for the construction of counterparty risk measures are the mark to future and the collateral of the portfolio of trades existing between two counterparties, for which there exist netting or collateral agreements. The mark to future at time t s, denoted by MtF(t s ), is nothing else than the mark to market of the portfolio computed at a future date t s > t 0, including all the portfolio cash flows occurring at t t s, discounted at t s. We stress that MtF(t s ) is not discounted at t 0 (it is not a present value at time t 0 ). Page 13 of 33

14 The computation of future portfolio values requires the generation of future values of the underlying risk factors, also called risk factors scenarios. Thus MtF(t s ) must be actually seen as a distribution of future portfolio values at time t s. The collateral at time t s, denoted by C(t s ), is the collateral amount or the premium margin amount exchanged between the two counterparties at time t s, in case of collateralized OTCs and short ETD Options on Stock-Indexes. Since the margination is based on the value of the portfolio, we have, ignoring thresholds and minimum transfer amounts, C(t s ) = MtF(t s Δt MPOR ), (11) where Δt MPOR takes into account the time distance between the margin call and the actual collateral exchange, or margin period of risk. We stress that such features of the collateral balance introduce a path dependency in the problem. The difference between the mark to future and the collateral, E(t s ) = MtF(t s ) C(t s ), (12) is called Exposure at time t s. We notice that the exposure is actually a distribution of undiscounted future values, and may assume both positive and negative values. At this point counterparty risk measures may be defined. One of the most important measures is the Expected Exposure (EE), given by the following formula EE(t 0, t s ) = E t0 P {Max[MtF(t s ) C(t s ), 0]}, (13) where E t0 P denotes the expectation at time t 0 under the probabilistic measure P. Thus, the EE represents the mean expected gain at a future time t s, which is at risk in case of default of the counterparty. In the case of Futures instruments, the EE in t s coincides with the Variation Margin if positive. Clearly there exist a corresponding Negative Expected Exposure (NEE) linked to the negative side of the exposure, NEE(t 0, t s ) = E t0 P {Min[MtF(t s ) C(t s ), 0]}, (14) representing the mean expected gain at a future time t s, which is at risk for the counterparty in case of default of ourselves. Another common risk measure is the Potential Future Exposure at quantile (PFE ), defined as the -quantile of the distribution of the exposure, PFE(t s, α) = Q α {Max[MtF(t s ) C(t s ), 0]}, (15) representing the expected gain at confidence level (e.g. 95%). Furthermore, since the previous risk measures assume no portfolio rollover in the time interval [t 0, t s ], we define also effective measures, such as Effective Expected Exposure (Eff EE) and Effective Potential Future Exposure (Eff PFE), as the non-decreasing EE and PFE. Finally, we may define average measures, such that the weighted average of the Eff EE and Eff PFE in the relevant time horizon (e.g. 1Y for the Eff EPE, full netting set life for the Eff PFE), called Eff EPE and Mean Eff PFE. More details can be found e.g. in refs. Gregory (2012) and Pykhtin (2009). Page 14 of 33

15 4.3. ETD exposure computation In order to effectively compute the exposure of ETD portfolios for counterparty risk purposes, one must compute the mark to future and collateral profiles in equation (12), considering the regulatory dispositions introduced in section 2.4 and taking into account the different margination mechanism associated to different products, reviewed in section 3. In order to compute exposure profiles, we use a multi-factor, multi-step Monte Carlo (MC) simulation for counterparty credit risk. In this simulation framework each risk factor is simulated over many MC scenarios on a time grid of future dates t s = {t 1,, t Ns } through appropriate stochastic dynamics calibrated to historical market data. Then, the portfolio MtF MtF j (t s ), collateral amount C j (t s ) and exposure MtF j (t s ) C j (t s ) are computed according to the contractual netting and collateral rules on each scenario and each time simulation step. Finally, the Expected Exposure is obtained using the approximate expression N MC EE(t s ) 1 Max[E N j (t s ), 0] = 1 Max[MtF MC N j (t s ) C j (t s ), 0], MC j=1 N MC j=1 t s = {t 1,, t Ns } (16) where N MC is the number of MC scenarios, N s is the number of time simulation steps. The most important parameters of the simulation framework controlling the performance are the number of risk factors, the number of MC scenarios N MC and the number and time distribution of time simulation steps N s. These parameters require a careful fine tuning to balance the overall performance of the simulation with, respectively, the most representative risk factors, the statistics (MC error), and the time sampling of the future dynamics of the portfolio. Typical settings for large OTC portfolios with many counterparties consist of a few hundreds of risk factors, a few thousands MC scenarios, and a few hundreds of time simulation dates ETD time simulation grid The number and the distribution of the time simulation dates t s in equation (16) used in practical MC simulation are the most important parameters in the time simulation of exposures. An important optimisation of the time simulation grid can be achieved by optimising its linear density to match the short-term horizons of regulatory risk measures (one year) and the decreasing cash flow density of typical portfolios (see section 4.1 above). Practitioners usually set shorter lagged time steps in the short term, and less time steps in the medium and long terms, with longer and possibly increasing time lags. Furthermore, since the CRR IV prescribes a margin period of risk of 10 days both for ETDs and the safest collateralized OTCs (see section 2.4), the simulation framework would require, in principle, a second time grid for the collateral computation, with a 10-days time lag with respect to the portfolio simulation grid. In practice, this solution doubles the computational effort required by the simulation and may be unfeasible for real, large portfolios of OTCs. Many different approaches have been proposed in literature in order to approximate the MtF between two fully evaluated time steps (see, e.g., Phyktin, 2009 and references therein). The Brownian Bridge method is one of the most used techniques for its simplicity, since it allows to reasonably estimate the MtF between two time steps through a stochastic interpolation, avoiding an additional full revaluation of the portfolio. Contrary to OTC portfolios, typical ETD portfolios constitute a few distinct netting sets, characterised by pure ETDs, short-dated, highly standardised plain vanilla instruments, subject to fixed 10-days regulatory MPOR. Moreover, except for the Option on Stock-Index, ETDs present uniform margination mechanisms that do not require the differentiation of simulation settings on the basis of different contractual dispositions like for OTCs. Page 15 of 33

16 Following the considerations above, we conclude that the counterparty risk simulation framework for ETD portfolios may be conveniently separated from the one used for OTCs and configured with specific simulation settings. In particular the time simulation grid for ETDs may be chosen to be regularly 10-days spaced, such that to avoid the approximation introduced by Brownian Bridge techniques. This is the main finding of this section. 5. Numerical Results In this section we report the numerical results of Mark to Future (MtF) and Expected Exposure (EE) simulations of some ETD products and of the corresponding OTCs. In particular, for each instrument, we show the MtF simulation results including the applicable margination mechanisms, and we analyse the implications on the counterparty exposure in terms of EE. The ETD products that we consider are those introduced in section 3. All the MtF and EE simulations of ETDs and OTCs are based on the same simulation, with 2048 MC scenarios, 10 days MPOR, and the 10 days time simulation grid discussed in section. In the MtF simulation we consider only Variation Margin and Premium Margin, since they depend on contracts prices only Interest Rate Futures In this section we report the numerical results of MtF and EE simulation for ETD Interest Rate Futures and OTC FRA contracts on the same underlying rate. In order to compare the different exposures, we have to consider instruments that present the same sensitivity to the underlying. For this reason, we compute the MtF profiles of a long Interest rate Futures and of a short FRA, since both the positions present a negative sensitivity on the underlying rate. For a long Interest Rate Futures with maturity T 1 on the underlying interbank rate L x (T 1, T 2 ), the MtF at time step t s > t 0 on MC scenario j is given by the Variation Margin MtF j Fut (t s ) = { N [f (t s; T 1, L x,j (T 1, T 2 )) f (t s 1 ; T 1, L x,j (T 1, T 2 ))] τ x (T 1, T 2 ), t 0 < t s T 1, j = {1,.., N Mc } 0, t s > T 1. (17) The MtF in t s is proportional to the Variation Margin accumulated (and not liquidated) during the margin period of risk [t s 1, t s ]. For a short payer FRA with maturity T 1 on L x (T 1, T 2 ), the MtF at time step t s > t 0 on MC scenario j is given by MtF j FRA (t s ) = { NP j(t s ; T 2 )[K F x,j (t s ; T 1, T 2 )]τ x (T 1, T 2 ), t 0 < t s T 1, j = {1,.., N Mc } 0, t s > T 1. (18) At inception the MtFs are equal to zero since both contracts are in equilibrium. Figure 6 shows the resulting MtF distributions for a long Interest Rate Futures and a payer FRA. We observe that the two instruments present similar mean values, with small MtFs, but the FRA distribution shows much more variance, at any future time step, w.r.t. the ETD distribution. This is explained as a consequence of the margination mechanism embedded in the Futures payoff, which avoids the accumulation of profits and losses and reduces the MtF volatility. Page 16 of 33

17 Figure 6: MtF distributions in terms of mean, 5% and 95% percentile of a long Interest Rate Futures (continuous lines) and of a payer FRA (dotted lines) on Euribor 3M with maturity date in 3 years and 3 months, notional 1 Mln. Valuation date 31/12/2013. Figure 7 shows the Expected Exposure (EE) profiles computed for a long position on an Interest Rate Futures, for a collateralized payer FRA and for an uncollateralized payer FRA. We observe that the higher EE profile is associated to the uncollateralized FRA, while the Futures and the collateralized FRA lead to the same EE profile, except at maturity when the EE of the collateralized FRA shows a large peak. These two features of the EE profiles can be explained as follows. In general, during the life of the contracts, the presence of collateral sensibly reduces the exposure with respect to the uncollateralized case. The 10 days margin period of risk assumed in these calculations means that, at any future date during the contract s life, the collateral has been margined 10 days before. In other words, in the calculation of EEs, we look at adverse scenarios with increasing MtF, in which the counterparty stops to margin collateral, defaults, and we must close out the position (see Figure 4) with insufficient received collateral (in case of positive MtF) or too much posted collateral (in case of negative MtF). In these scenarios, the loss suffered by the surviving counterparty amounts to the difference between the netting set value at the close out date and the collateral value 10 days before. In formulas MtF j (t s ) > MtF j (t s 1 ), C j (t s ) = MtF j (t s 1 ), E j (t s ) = MtF j (t s ) MtF j (t s 1 ) > 0, (19) where we remind that, in our computational framework described in the previous section 4.4, the time simulation step is equal to the 10 days MPOR (t s t s 1 = 10 days). Furthermore, looking more closely at the EEs around the maturity date with the aid of the inset (figure A inside Figure 7), we observe that the EE of the collateralized FRA peaks exactly at the time step just after the maturity date. This spike is due to the different schedules for payoff and collateral settlements. In fact, the payoff is settled at maturity, while the collateral is margined at the following margination date. Hence, in the scenarios with negative MtF at maturity, one must deliver immediately the payoff amount to the counterparty and wait for the release of the collateral amount at the next margination date. Within this time window, one is exposed to the possible default of the Page 17 of 33

18 counterparty, in which case the loss amounts to the total collateral balance. In formulas, given the instruments maturity T M date such that t M 1 < T M < t M, we have t = t M 1 MtF j (t M 1 ) < 0, C j (t M 1 ) = MtF j (t M 2 ), t = t M : MtF j (t M ) = 0, C j (t M ) = MtF j (t M 1 ) < 0, E j (t M ) = C j (t M ) > 0, t = t M+1 : MtF j (t M+1 ) = 0, C j (t M+1 ) = MtF j (t M ) = E j (t M+1 ) = 0. (20) We stress that the final peak in the exposure of the collateralized FRA is not an artefact of the simulation but represents a real counterparty risk that our simulation setting, with regular 10 days spaced time steps, is able to capture. The only approximation is given by the bracketing precision of the instruments maturity T M date within the time interval [t M 1 ; t M ]. This approximation could be improved with a finer time simulation grid, with no significant improvements of the qualitative features of the EE profiles. Figure 7: EE profiles of an Interest Rate Futures (continuous red line), of a collateralized FRA (dashed green line) and of an uncollateralized FRA (continuous blue line). Figure A magnifies the behaviour of the three different profiles at maturity. All settings as in Figure 6. Following the considerations above, we conclude that Futures ensures a noticeable reduction of the credit exposure over the whole life of the contract with respect to corresponding uncollateralized FRAs. In particular, Futures ensures a large damping of the credit exposure at maturity date, where FRAs show an exposure spike due to their OTC bilateral margination mechanism Option on Stock-Index In this section we report the numerical results of MtF and EE simulation of an ETD and OTC Option on Stock-Index. For both contracts, the MtF at time step t s > t 0 on MC scenario j is given by the following expression Page 18 of 33

19 MtF j (t s ) = { Cs P j(t s ; T, K, S), t s T, j = {1,, N MC }, 0, t s > T, (21) where Cs is the homogenous contract size of the ETD and of the OTC contracts, P j (t s ; T, K, S) is the market premium of the option simulated at time step t s on MC scenario j, T is the maturity date of the option, K is the strike, and S is the option s underlying. Since for ETD Options on Stock-Index the margination applies only to short positions (see section 3.2), we focus on the seller side. Figure 8 shows the resulting MtF distributions of a short ETD and OTC options. We observe that the MtF distributions coincide over all the contracts lives. In particular, the margin mechanism of the ETD Option does not prescribe the daily settlement of the payoff and thus does not affect the MtM value of the contract, contrary to the Futures case in Figure 6. The clearing house, in order to hedge the counterparty risk related to the clearing member, requires to the option seller to maintain the Premium Margin equal to the MtM value. Figure 8: MtF distributions in terms of mean, 5% and 95% percentile of a short ETD Option on Stock-Index (continuous lines) and of a short OTC Option on Stock-Index (triangles) on DJ EuroStoxx 50, with strike price 2700 (in the money), contract size 10 and maturity date in 2 years. Valuation date: 31/12/2013. Figure 9 shows the EE profiles for a short ETD Option, for a short-collateralized OTC Option, and for a short uncollateralized OTC Option. As in the case of Futures and FRA of section 5.1, the collateral mechanism of the collateralized OTC Option replicates the margination of the ETD Option. We observe that the EEs of the ETD Option and of the collateralized OTC Option coincide and differ from zero over the whole life of the two contracts. This is due to scenarios in which the option seller, with a negative MtF, has over-collateralized the position, that is, E j (t s ) = MtF j (t s ) C j (t s ) > 0, with C j (t s ) < MtF j (t s ) < 0. This is due to adverse scenarios with negative and increasing MtF, in which we must receive collateral amount back from the counterparty, but the counterparty stops to margin collateral, defaults, and we must close out the position with too much posted collateral. In these scenarios, Page 19 of 33

20 the loss suffered by the surviving counterparty amounts to the difference between the netting set value at the close out date and the collateral value 10 days before. In formulas MtF j (t s ) > MtF j (t s 1 ), C j (t s ) = MtF j (t s 1 ), E j (t s ) = MtF j (t s ) MtF j (t s 1 ) > 0, (22) In particular, both EEs show a large final peak, given by the time lag between the payoff settlement at maturity and the collateral return at the following margination date (see the discussion at the end of previous section 5.1). On the other hand, the short uncollateralized OTC Option in Figure 9 displays a zero EE over the whole life of the contract, since the MtF of a short option is always negative and generate a null EE (MtF j (t s ) < 0, C j (t s ) = 0 j EE(t s ) = 0). Figure 9: EE profiles of a short ETD Option on Stock-Index (continuous red line), of a shortcollateralized OTC Option on Stock-Index (green dotted line) and of a short uncollateralized OTC Option on Stock-Index (continuous blue line). Figure B magnifies the behaviour of the three different profiles at maturity. All settings as in Figure 8. Following the considerations above, we conclude that short ETD Options on Stock-Index do not generate any exposure reduction with respect to corresponding OTC Options. In the case of a portfolio of short and long Options on Stock-Index, with a net value that can be both positive and negative, the EE for ETD Options will be higher than or equal to the EE generated by uncollateralized OTC Options, since ETD Options generate exposure even if the net value of the portfolio is negative Option on Interest Rate Futures In this section we report the numerical results of MtF and EE simulation for ETD and OTC American Options on Interest Rate Futures. For the ETD option, the MtF at time step t s > t 0 on MC scenario j is given by the following expression Page 20 of 33

21 MtF j ETD (t s ) = { N[P j(t s ) P j (t s 1 )], t s T, j = {1,, N MC }, 0, t s > T, (23) while for the OTC option the MtF is given by MtF j OTC (t s ) = { NP j(t s ), t s T, j = {1,, N MC } 0, t s > T, (24) where P j (t s ) is the option premium at time step t s on scenario j. Equation (23) reflects the margin mechanism of the ETD instruments, and the MtF of the ETD Option corresponds to the Variation Margin maturated between two consecutive time steps (t s 1 and t s ) of the simulation scenario. At inception the MtF of the ETD option is equal to zero since the option premium is paid forward, while the OTC option premium is different from zero and depends on the moneyness of the option. Figure 10 shows the resulting MtF distributions for the two options. We observe that during the life of the contracts the two instruments display very different distributions. The MtF of the ETD option is characterized by a lower variance, with an average close to zero. This effect is a consequence of the margination mechanism described in section 3.3. The lower tail of the ETD MtF distribution displays negative values with a 5% percentile always under the zero threshold, corresponding to scenarios in which the option holder has to deliver Variation Margin in correspondence of a decrease of the option MTF. On the other hand, the OTC MTF distribution displays the typical option premium evolution floored to zero on the lower tail and with extreme values on the upper tail. The MtF spikes observed near maturity are due to the appearance of extreme scenarios in the simulated underlying interest rate yield curves. Figure 10: MtF distributions in terms of mean, 5% percentile and 95% percentile of an ETD American Option (continuous lines) and of an OTC American Option (dashed lines) on Futures on Euribor 3M, with Futures notional 1 Mln, strike price (out the money) and maturity date in June Valuation date: 31/12/2013. Page 21 of 33

22 Figure 11 shows the EE profiles for three American Options on Interest Rate Futures: ETD, collateralized OTC, and uncollateralized OTC. As we can expect from the analysis of the MtF profiles, the ETD EE is smaller than the corresponding uncollateralised OTC EE, reflecting the lower volatility of its MtF distribution, while it is equal to the collateralised OTC EE. Furthermore, all the EEs show a decreasing trend as the instruments approach to maturity. This derives from the fact that the options are out the money and their MtF reflects the time value of the options. As long as we reach the maturity, the options time value approaches zero and the MtF of the option approaches the intrinsic value, which is zero for out the money options. Figure 11: EE profiles of a long ETD option (continuous red line), a long-collateralised OTC option (dashed green line), and a long uncollateralized OTC option (continuous blue line) on Interest Rate Futures. All settings as in Figure 10. We conclude that the margination mechanism embedded in the ETD Option on Interest Rate Futures produce a significant reduction of the EE with respect to corresponding OTC option. Page 22 of 33

23 5.4. OTC vs ETD in a real framework In the previous sections we compared ETDs and OTCs counterparty risk measures computed in both cases with the special 10 days time simulation grid discussed in section 4.4. Actually, counterparty risk measures for large, complex and long lasting OTC netting sets cannot be computed in practice using the time grid above, because of prohibitive computational cost. Hence, in this section we compare ETDs and OTCs counterparty risk measures within a more realistic setting, in which the ETD grid is 10-days regular as above, while the OTC grid is characterised by a decreasing time step density (daily up to 1 week, weekly up to 1 month, monthly up to 1 year, bimonthly up to 3 years, then proceeding with longer and longer time steps). In particular, we still adopt a 10 days margin period of risk, but we must resort to the Brownian Bridge technique (see section 4.4) to compute the collateral, C(t s ) = MtF(t s Δt MPR ), since, given a time step t s included in the time simulation grid, the time step t s Δt MPR is not, in general, included in the grid. Figure 12 and Figure 13 show the resulting MtF distributions and EE profiles for long ETD and OTC Call options on equity index, respectively (we remind that long positions on ETD options on equity index are not collateralised, see section 3.2). We observe that the two simulations on different time grids lead to very similar results. Just small differences appear at extreme percentiles of the MtF and in the EE just before maturity. Larger differences are observed just after the instruments maturity at 1Y, when the profiles of the OTC option drops to zero more slowly than the ETD s MtF distribution. This effect is explained with the different time steps in the two time simulation grids: the OTC grid is bi-monthly after 1Y, the ETD grid is 10 days regularly spaced. Figure 12: MtF distributions in terms of mean, 5% percentile and 95% percentile of a long ETD Call option (computed on the 10 days time grid) and a long OTC call option (computed on the real time grid) on EuroStoxx50 index, both ATM, with maturity 1Y. Despite the very good approximation in describing the MtF distributions, relevant differences in the EE can emerge when we consider collateralised positions for which, in the OTC case, we compute the collateral amount with the Brownian Bridge technique. Figure 14 shows the EE and PFE95 profiles of a short ETD Call option on equity index (collateralised), and the corresponding unilateral CSA OTC Call option. Page 23 of 33

24 Figure 13: EE profiles for a long ETD Call option (continuous red line) and a long OTC call option (dashed blue line). All settings as in Figure 12. Eff EPE 1Y (OTC) / Eff EPE 1Y (ETD) Mean Eff PFE 95 (OTC) / Mean Eff PFE 95 (ETD) Short Call option unilateral CSA Short Call option bilateral CSA Figure 14: EE (left) and PFE 95 (right) profiles of a short ETD Call option (continuous red line) and a short OTC Call option (blue dashed line). All other settings as in Figure 13. The table below the figure show the ratios between mean effective measures. We also added the bilateral CSA case for sake of completeness. Page 24 of 33

25 The sharp peaks in the exposures has been explained in section 5.2: in this case the OTC peak is smoothed with respect to the ETD peak because of the longer time simulation steps around 1 year. As a consequence, the effective risk measures can be appreciably different, as shown in the table of Figure 14. Furthermore, non-negligible differences appear also in the OTC option EE before maturity (Figure 14, left hand side, rectangle), because of the approximation introduced by the Brownian Bridge (see the discussion below). We now consider linear instruments, such as Futures on equity index. The EE and PFE95 profiles are shown in Figure 15. Also in this case we observe the EE differences at maturity already encountered in the previous case (Figure 14). On the contrary, we do not observe the same EE profiles differences before maturity. The different behaviour of linear and non-linear instruments has to with the Brownian Bridge approximation, as explained below. Eff EPE 1Y (OTC) / Eff EPE 1Y (ETD) Mean Eff PFE 95 (OTC) / Mean Eff PFE 95 (ETD) Short Forward bilateral CSA Figure 15: EE and PFE 95 profiles for a short ETD Futures (red continuous line) and a short OTC collateralized Forward (blue dashed line) on equity index. The table below the figure show the ratios between the time-weighted effective measures. All settings as in Figure 12. In order to further investigate the nature of the difference in the EE profiles, highlighted in the rectangle of Figure 14 (left side), we analyse the distribution of MtF differences between two subsequent time steps near 300 days (=0.82 Y) future time. The basic assumption underlying the Brownian Bridge, used in the simulation of OTCs, is that such distribution is normal. Figure 16 shows that the distribution is approximately normal in case of linear payoffs (top left graph), but deviates significantly from the normal in case of optional payoffs (the other three graphs). Page 25 of 33

26 Figure 16: MtF differences distribution between time steps at 290 and 300 days for a Forward (top left) a Call option ATM (top right), ITM (bottom right), OTM (bottom left). Gaussian fits are plotted in red. We further observe that the large peak in the Call option MtF distribution near zero is related to the option delta: the smaller the delta the larger the peak. In fact, when the option is deep OTM (delta << 1) and its MtF is small on most scenarios, we expect a large probability of small MtF differences, while when the option is deep ITM (delta 1) and its MtF approaches the linear Forward case, we expect a large probability of symmetric positive and negative differences, with approximately normal distribution. We conclude that the (strong) violation of the normality condition at the bottom of the Brownian Bridge technique accounts for the difference found in Figure 14 (rectanglee, left side) between the ETD and OTC simulation frameworks. Thus, significant differences in counterparty risk measures may appear even for very similar and simple instruments, depending on the simulation framework used. 6. Capital Simulation In this section we analyse the different capital requirements emerging for ETDs and OTCs between Internal Model Method (IMM) and standard method (CEM, Current Exposure Method) as depicted in CRR IV regulation. The IMM method is expected to be more risk sensitive but, on average, less severe in terms of capital requirement, in particular regarding collateralized exposures. However, this may not be the case for ETDs as we will see in the following. The capital requirement for the counterparty (substitution) risk can be expressed as K = 8% RWA = 8% RW EAD, (25) where EAD is the Exposure at Default and RW is a Risk Weight, both specific for the counterparty. The IMM and CEM EADs are given respectively by EAD IMM = α (Eff EPE + IM), (26) EAD CEM = CE + Add On Notional, (27) Page 26 of 33