Counterparty Risk - wrong way risk and liquidity issues. Antonio Castagna -

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1 Counterparty Risk - wrong way risk and liquidity issues Antonio Castagna antonio.castagna@iasonltd.com

2 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

3 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

4 Definition Counterparty Wrong-Way Risk Counterparty risk is the risk that a party to an OTC derivative contract may fail to perform on its contractual obligations, causing losses to the other party. Losses are usually quantified in terms of the replacement cost of the defaulted derivatives. Counterparty risk can be: 1 One-Way: One party faces the exposures depending on the (ever positive) value of the position it holds against the other party; 2 Two-Way: Both parties may face exposures depending on the value of the positions they hold against each other. The feature distinguishing counterparty risk from lending risk is uncertainty of exposure at any future date: 1 Loan: exposure at any future date is the outstanding balance, which is certain (not taking into account prepayments); 2 Derivative: exposure at any future date is the replacement cost, which is determined by the market value at that date and is, therefore, uncertain.

5 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

6 Counterparty Risk Exposure of a Contract We start by assuming that no netting or margin agreement is in place. The market value of contract i with a counterparty is known only for the current date t = 0. For any future date t, the value V i (t) is random. If the counterparty defaults at time τ cpt before the contract s maturity, the economic loss is equal to the replacement cost of the contract: if V i (τ cpt) > 0, we do not receive anything from defaulting counterparty, but have to pay V i (tau cpt) to another counterparty to replace the contract; if V i (τ cpt) < 0, we receive V i (τ cpt) from another counterparty, but have to give this amount to the defaulting counterparty. Combining these two scenarios, we can specify contract-level exposure E i (t) at time t as: E i (t) = max[v i (t),0]

7 Counterparty Risk Exposure of a Contract At a future time T > t, the exposure is uncertain:

8 Theoretical Approaches to Default Modelling The second building block of the Counterparty Risk measurement is the prediction of the default of the counterparty. Jointly to the contract and portfolio level exposure, default determines the counterparty risk fully. In theoretical literature two approaches to model single defaults: Structural Models: Default occurs as soon as the firm value crosses a given barrier (from above) Reduced (Intensity-based) Models: The default time is modelled as the first jump time of a given jump process (typically a Poisson process), occurring with an intensity λ(t), also called hazard rate. This is the probability of a default occurring at an infinitesimal time after t given that it did not occur before, and can be a stochastic process itself.

9 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

10 Wrong/Right-Way Risk Wrong/right-way risk arises from dependence between credit quality of a counterparty and exposure to that counterparty. The risk is wrong (right) way when the exposure tends to increase (decrease) when counterparty credit quality worsens. Wrong/right-way risk can be general (dependence caused by systematic risk factors) or specific (dependence caused by counterparty-specific risk factors). Some examples: 1 We sell credit protection on X to Y: general right-way 2 We enter into oil receiver swap with oil producer: general wrong-way 3 We buy a put option on X stock from Y: general wrong-way 4 We buy a put option on X stock from X: specific wrong-way Specific wrong-way risk should be avoided. We analyse the impact of wrong-way risk for a swap portfolio on: The CVA adjustment for the risk-free value of a portfolio of swaps, to account for the expected losses given the default of the counterparty; The counterparty credit VaR.

11 Theoretical Framework to Include Wrong-Way Risk We assume that the default probability of the counterparty is stochastic over the reference period. Default is a jump whose probability of occurrence is determined by an intensity λ(t), which is a stochastic process. Roughly speaking, the intensity indicates the annual probability of default, so that if λ(t) = 2%, there is a 2% probability that our counterparty will go defaulted in next year. In our framework, the intensity varies over time, so that the defalt probability is not constant. The Expected positive exposure (EPE) of a swap is computed assuming that all Euribor/Libor rates have a terminal Lognormal distribution. It is possible to determine the distribution of the swap rates from the distributions of the single Euribor/Libor rates (an analytical approximation is used in our framework) We correlate the default intensity with the swap rates, and we derive analytical approximation for the expected losses (EPE PD). We tested this approximation against Montecarlo simulations and we found it very accurate.

12 Credit Value Adjustment The Credit Valuation Adjustment (CVA) of an OTC derivatives portfolio with a given counterparty is the risk-neutral expectation of the discounted loss of value of the portfolio, due to default by the counterparty T n CVA = Sprd P(t,t k ) EPE(t k ) t k k=1 Sprd PD LGD is the CDS spread dealing in the market for the counterparty s debt. CVA can be computed analytically only at the contract level for several simple cases. Calculating discounted EPE at the counterparty level requires simulation. The market value of a portfolio of derivatives with a risky counterparty is given by the risk-free market value minus the relevant CVA, as defined above.

13 A Practical Example: Market Data We show an example, assuming the following market data for interest rates: Time Eonia Fwd Sread Fwd Libor % 0.65% 1.40% % 0.64% 1.39% % 0.64% 2.39% % 0.63% 2.63% % 0.63% 2.88% % 0.62% 2.99% % 0.61% 3.11% % 0.61% 3.26% % 0.60% 3.35% % 0.60% 3.47% % 0.59% 3.59% % 0.59% 3.69% % 0.58% 3.78% % 0.58% 3.88% % 0.57% 3.97% % 0.57% 4.07% % 0.56% 4.16% % 0.56% 4.23% % 0.55% 4.30% % 0.55% 4.37% % 0.54% 4.44% 5.00% 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% Euribor Fw d Eonia Fw d

14 A Practical Example: Market Data Market data for caps&floors and swaptions volatilities are: Caps&Floors Expiry Volatility % % % % % % % % % % % % % % % % % % % % Swaptions Expiry Tenor Volatility % % % % % % % % % % % % % % % % % % % 10 0

15 A Practical Example: Default Probabilities We assume that default is a jump occurring with an intensity λ following a CIR process: dλ t = κ(θ λ t)dt +ν λ tdz t Years PD % % % % % % % % % % Parameters are chosen to be: λ 0 3.0% κ 27.0% θ 3.0% ν 20.0% 25.00% 20.00% 15.00% 10.00% PD The resulting PD are shown beside. 5.00% 0.00%

16 A Practical Example: Constant Notional Portfolio We analyse how the CVA is affected by different levels of correlation between the (synthetic) swap rate of the portfolio and the intensity of default. The portfolio of swaps has a constant notional amount over next 10 years as shown below and it is a net receiver fixed rate. Years Notional We compute the CVA for different levels of correlation (nil=-0%, medium=-50%, high=-90%), and for different levels of the synthetic swap rate (at-the-money, in-the-money=atm+1%, out-of-the-money=atm-1%). Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % Adjustment over the risk-free swap rate to include the counterparty risk. Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % % -50% % % % -90% % % %

17 ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr Counterparty Wrong-Way Risk A Practical Example: Constant Notional Portfolio Expected Positive Exposure (OTM,ATM,ITM) Expected Loss Given Default (OTM,ATM,ITM) EPE EPE EPE

18 A Practical Example: Decreasing Notional Portfolio The same analysis on how the CVA is affected by different levels of correlation between the (synthetic) swap rate of the portfolio and the intensity of default, is performed for a declining notional swap portfolio over next 10 years, as shown below. It is a net receiver fixed rate. Years Notional We compute the CVA for different levels of correlation (nil=-0%, medium=-50%, high=-90%), and for different levels of the synthetic swap rate (at-the-money, in-the-money=atm+1%, out-of-the-money=atm-1%). Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % Adjustment over the risk-free swap rate to include the counterparty risk. Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % % -50% % % % -90% % % %

19 ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr Counterparty Wrong-Way Risk A Practical Example: Decreasing Notional Portfolio Expected Positive Exposure (OTM,ATM,ITM) Expected Loss Given Default (OTM,ATM,ITM) EPE EPE EPE

20 A Practical Example: Increasing Notional Portfolio Finally we operate the analysis on how the CVA is affected by different levels of correlation between the (synthetic) swap rate of the portfolio and the intensity of default, for an increasing notional swap portfolio over next 10 years, as shown below. It is still a net receiver fixed rate. Years Notional We compute the CVA for different levels of correlation (nil=-0%, medium=-50%, high=-90%), and for different levels of the synthetic swap rate (at-the-money, in-the-money=atm+1%, out-of-the-money=atm-1%). Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % Adjustment over the risk-free swap rate to include the counterparty risk. Corr Swap- OTM ATM ITM Def.Intens. 1.63% 2.63% 3.63% 0% % % % -50% % % % -90% % % %

21 ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr ELgd Zero Corr ELgd Medium Corr ELgd High Corr Counterparty Wrong-Way Risk A Practical Example: Increasing Notional Portfolio Expected Positive Exposure (OTM,ATM,ITM) Expected Loss Given Default (OTM,ATM,ITM) EPE EPE EPE

22 Basel II Regulation: the IMM IMM approach is the most suited to properly take into account the market risks related to a given counterparty s portfolio The building blocks of the IMM approach: definition of a set of statistics for internal and regulatory purposes identification of market factors and generation of future scenarios pricing algorithms to price the contracts included in the books aggregation rules to evaluate the effects of the risk mitigation agreements a framework modelling the credit risk of the counterparties, the correlations amongst them and the correlation of counterparties with market risks to measure the full counterparty risk calculation of the counterparty exposure measures, i.e. its risk profile, credit value adjustment, economic and regulatory capital

23 Exposure Measures in the IMM Method Starting from exposure for each counterparty we can define other statistics and risk measures: Expected exposure (EE) [ ] EE i (t k ) = E max[v i (t k ),0] Expected positive exposure (EPE) EPE i (t k ) = 1 t k t 0 Effective Maturity M k EE i (t j )(t j t j 1 ) j=1 [ ] Σ T M = min k=1 Df(t k ) EPE i (t k ) Σ t k 1Y k=1 Df(t k ) EPE(t k ),5

24 Regulatory Capital Counterparty Wrong-Way Risk The Regulatory Capital (RC) is computed by means of the following quantities 1 EPE 2 The α factor (ratio of the EC calculated with full simulation, to the EC calculated with a constant exposure equal to EPE) 3 The Effective EPE (E EPE), which takes into account the roll-off risk EEPE(t k ) = max[eepe(t k 1 ),EPE(t k )] and it is actually the counterparty exposure measure which the RC is computed upon The α factor is calculated on a given time interval, but kept constant otherwise. The period between two calculations depends on the granularity and the time evolution of the portfolio

25 Regulatory Capital Counterparty Wrong-Way Risk For regulatory purposes, the capital can be determined as follows: MCR = α EEPE RW 8% dove RW = 12.5 K and ( ) N 1 (PD i )+r i N 1 (0.999) K = LGDN LGD PD 1 r 2 i i PD i = default probability for counterparty i LGD = loss given default r i = systemic risk load factor, also indicated by the Regulation equal to: 0.12 (1 e ( 50 PD) )/(1 e 50 )+0.24 [1 (1 e ( 50 PD) )/(1 e 50 )] α has to be estimated according to an internal model approved by the Surveillance Authority (with a 1.20 minimum), otherwise it has to be set equal to 1.40.

26 Regulatory Capital and Wrong-Way Risk We aim at introducing the wrong-way risk also in the counterparty credit VaR calculation. The idea is still to have a loan equivalent of the exposure, so that we can adjust the EPE or the EEPE measure to input into the regulatory formula. A possible approach to apply to the framework outlined above to compute the VaR is: Compute the stressed (99.9% c.l.) PD according to the supervisory formulae; Deduce which is the level of the default intensity consistent with the stressed PD; Compute the conditioned mean and variance of the risk factors determining the exposure of the derivative contracts; Compute the new EPE with the conditioned mean and variance; Calculate the wrong-way-adjusted Economic Capital with the new EPE or the corresponding E EPE.

27 Counterparty Credit VaR: an Example We analyze a swap portfolio expiring in 1 year, with monthly interest rate exchanges. The portfolio is net receiver fixed rate. The counterparty has a PD = 2.94% in next year, and this is produced by a jump process whose intensity is a stocahstic process with parameters seen above. We test 3 versions: constant (P1), moderately decreasing (P2) and incresing (P3) notional. According to the supervisory formula, the stressed PD at a 99.9% c.l. is 22.34%. Market rates and volatilities: Months Eonia 1M Libor Libor Vol % 0.99% 34.00% % 1.02% 34.50% % 1.05% 35.00% % 1.07% 35.50% % 1.10% 36.00% % 1.12% 36.50% % 1.15% 37.00% % 1.17% 37.50% % 1.20% 38.00% % 1.22% 38.50% % 1.25% 39.00% % 1.27% 39.50% Months P1 P2 P

28 Counterparty Credit VaR: an Example EPE and EEPE (OTM,ATM,ITM) Portfolio P1 (Constant Notional). Tables below show the effective EPE for different levels of correlation and average fixed rate of the portfolio, and the ratio (α) with the 0-correlation case. Beside the figures show the EPE and the effective EPE for a correlation of 10%, for the three fixed rate values indicated in the tables EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.85% 1.10% 1.35% 0% % % EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.85% 1.10% 1.35% 0% % % EPE EPE WV EEPE WV EEPE

29 Counterparty Credit VaR: an Example EPE and EEPE (OTM,ATM,ITM) Portfolio P2 (Decreasing Notional). Tables below show the effective EPE for different levels of correlation and average fixed rate of the portfolio, and the ratio (α) with the 0-correlation case. Beside the figures show the EPE and the effective EPE for a correlation of 10%, for the three fixed rate values indicated in the tables EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.84% 1.09% 1.34% 0% % % EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.84% 1.09% 1.34% 0% % % EPE EPE WV EEPE WV EEPE

30 Counterparty Credit VaR: an Example EPE and EEPE (OTM,ATM,ITM) Portfolio P3 (Increasing Notional). Tables below show the effective EPE for different levels of correlation and average fixed rate of the portfolio, and the ratio (α) with the 0-correlation case. Beside the figures show the EPE and the effective EPE for a correlation of 10%, for the three fixed rate values indicated in the tables EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.88% 1.13% 1.38% 0% % % EPE EPE WV EEPE WV EEPE OTM ATM ITM Corr Swap-Def.Intens. 0.88% 1.13% 1.38% 0% % % EPE EPE WV EEPE WV EEPE

31 Counterparty Credit VaR: Some Conclusions The experiments we have presented above seem to show that, at least as far as the wrong-way risk is concerned, the regulatory coefficient α is in many cases too low. This is even more evident if consider the fact that we chose very small value for the correlation. Actually, the stressed PD s in a Merton (Gaussian copula) approach, such as the regulatory one, are determined by the stressed level of a common factor affecting all the debtors and producing a correlation amongst defaults. The correlation with respect to this factor does not need to be the same as the correlation between the single total PD and market risk factors (in our examples, the swap rates) and it is likely lower than the correlation with the specific factors, although not always this is the case. We have not explored in the analysis this extension, but it would be straightforward to set the default intensity of each conuterparty as: λ D = λ i +p i λ C where λ C is an intensity process common to all counterparties and λ i is specific to each counterparty.

32 Counterparty Credit VaR: Some Conclusions The α (for the part due to the wrong-way) is also a function of the features of the portfolio of contracts with a counterparty, in terms of average fixed rate received (or paid) and evolution of the aggregated notional over time. The main finding is that one α good for all occasions is not a wise choice. When considering also the correlation amongst the defaults of all the counterparties, some diversification effects may be expected, so that the α can actually be lower than 1.40 which is the standard level set by regulation if the bank is not able to compute a full deployed VaR. To introduce a rich structure of correlation amongst counterparties defaults, the regulatory formula has to be enhanced so as to include more factors. Extensions of the Merton s (Gaussian copula) approach are available and some of them can be effectively solved in very good analytic approximations. It is important to check which is the real contribution of the correlations to the Economic Capital for management purposes. For regulatory purposes, the proposed α = 1.40 seems to be very favorable to banks to save allocated capital.

33 Index Counterparty Wrong-Way Risk Liquidity Risk Pricing in OTC Derivatives 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

34 Collateral and Margin Agreements Liquidity Risk Pricing in OTC Derivatives Collateral agreement is a contract between two counterparties that requires one or both counterparties to post collateral (typically cash or high quality bonds) under certain conditions. Margin agreement is a legally binding collateral agreement with specific rules for posting collateral, which include: 1 Minimum transfer amount: defines the minimum amount of collateral that can be exchanged. If the exposure entails a collateral posting below the minimum, amount, no collateral is provided; 2 A threshold, defined for one (unilateral agreement) or both (bilateral agreement) counterparties. If the difference between the net portfolio value and already posted collateral exceeds the threshold, the counterparty must provide collateral sufficient to cover this excess (subject to minimum transfer amount); 3 Frequency: defines the periodicity of the exposure calculation and of the determination of the collateral to post. The terms of the rules depend mainly on the credit qualities of the counterparties involved.

35 Index Counterparty Wrong-Way Risk Liquidity Risk Pricing in OTC Derivatives 1 Counterparty Wrong-Way Risk 2 Liquidity Risk Pricing in OTC Derivatives

36 Pricing OTC Derivatives with CSA Liquidity Risk Pricing in OTC Derivatives In a very general fashion, the price at time 0 of a derivatives contract which is not subject to counterparty risk is: V 0 = E Q [ e T 0 r sds V T ] where V T is the terminal pay-off of the contract; r t is the (possibly time dependent) risk-free interest rate. When counterpaty risk is considered, then we have to include the so called CVA (the expected losses we suffer when on default of the counterparty) the and DVA (the expected losses the counterparty suffers on our default): V CCP 0 = E Q [ e T 0 r sds V T ] CVA+DVA The terminal value of the contract is still discounted ad the risk-free rate r t, but then the price is adjusted with the net effect due to the losses upon default of the two counterparties involved in the trade.

37 Pricing OTC Derivatives with CSA Liquidity Risk Pricing in OTC Derivatives Assume now we have a CSA agreement operating between the two counterparties. The CSA provides for a daily margining mechanism of the full variation of the NPV (nowadays a very common form of the CSA). The party that owns a positive balance on the collateral account (corresponding to a positive NPV of the contract) pays the rate c t to the other party. The pricing of the contract can be now be operated by excluding the default risk (there is still a very small residual risk between two daily margining). It can be shown that the pricing formula is very similar to the standard case we have seen above, but with the collateral rate c t replacing the risk-free rate r t.: V CSA 0 = E Q [ e T 0 c sds V T ] (1)

38 Pricing OTC Derivatives with CSA Liquidity Risk Pricing in OTC Derivatives This result is very convenient, since we have a well defined rate that has to be paid on the collateral balance (set within the contract), whereas the risk-free rate is very difficult to determine in the current market environment (it used to be the Libor in the interbank market). Usually the daily margined CSA agreements set the remuneration of the collateral at the EONIA for contracts in euro (or some equivalent OIS rate for other currencies). EONIA (OIS) rates can be considered the best approximation of a risk-free rate. Nevertheless there is still one assumption that is made when deriving the pricing formula with the CSA: The rate at which the bank can lend money is the same of the one it can borrow money. This assumption can be easily relaxed when we price contracts whose NPV can be always either positive or negative (e.g.: a long or a short position on an option contract). When the NPV of the contract can switch from positive to negative and/or from negative to positive (e.g.: forward and swap contracts) then relaxing the assumption is trickier.

39 Pricing OTC Derivatives with CSA Liquidity Risk Pricing in OTC Derivatives Assume we have a contract whose value during the life of the contract at any time 0 < t < T, V t can be positive or negative. We also assume that the bank can invest cash at a risk-free rate equal to the collateral rate r t = c t, but it has a funding spread f t when borrowing money over a short period, so that the total funding cost is r t +f t. When considering the funding spread in the pricing of a collateralized derivatives contract, it can be shown that the valuation equation can be written as: V CSA 0 = E Q [ e T 0 c u f u1 {Vu<0} du V T ] = E Q [ e T 0 c udu V T ]+LVA (2) where LVA = E Q [ T 0 ] e s 0 c udu min(v s(0),0)f sds (3)

40 Pricing OTC Derivatives with CSA Liquidity Risk Pricing in OTC Derivatives Equation (3) can be computed numerically with a good degree of approximation: it accounts for the funding cost that the bank has to pay when financing the cash injection in the collateral account, expressed has a spread f t over the risk-free rate r t = c t, which on the contrary is the rate the bank can invest at. We name this quantity Liquidity Value Adjustment (LVA) As an example, when we price a (K-fix rate receiver) swap contract starting in t i and ending in T = t N, the minimum value of the contract is min(v t,0) = min( V t,0) = max(s i,n K,0). Assume we divide the period between the evaluation time t 0 = 0 and the expiry in N intervals. The LVA can be written as: LVA Swp = N Pay(t i ;t i,t,k)f ti t i (4) i=1 where Pay is the value of a payer swaption struck at K, expiring in t i and written on a swap starting in t i and maturing in T.

41 A Practical Example Counterparty Wrong-Way Risk Liquidity Risk Pricing in OTC Derivatives We show an example, assuming the following market data for interest rates: Time Eonia Fwd Spread Fwd Libor % 0.65% 1.40% % 0.64% 1.39% % 0.64% 2.39% % 0.63% 2.63% % 0.63% 2.88% % 0.62% 2.99% % 0.61% 3.11% % 0.61% 3.26% % 0.60% 3.35% % 0.60% 3.47% % 0.59% 3.59% % 0.59% 3.69% % 0.58% 3.78% % 0.58% 3.88% % 0.57% 3.97% % 0.57% 4.07% % 0.56% 4.16% % 0.56% 4.23% % 0.55% 4.30% % 0.55% 4.37% % 0.54% 4.44% 5.00% 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% Euribor Fw d Eonia Fw d

42 A Practical Example Counterparty Wrong-Way Risk Liquidity Risk Pricing in OTC Derivatives Market data for caps&floors and swaptions volatilities are: Caps&Floors Expiry Volatility % % % % % % % % % % % % % % % % % % % % Swaptions Expiry Tenor Volatility % % % % % % % % % % % % % % % % % % % 10 0

43 Liquidity Risk Pricing in OTC Derivatives A Practical Example: Collateralized Swap We price under a CSA agreement a receiver swap whereby we we pay the Libor fixing semi-annually (set at the previous payment date) and we receive the fixed rate annually. With market data shown above, the fair rate can be easily calculated (we are using the new market standard approach to employ the EONIA/OIS curve for discounting and the 6M Libor curve to project forward rates). We assume also that we have to pay a funding spread of 15bps over the EONIA/OIS curve. This is applied to the ENE plotted beside. LVA % Fair Swap rate % Swap Rate + Coll. Fund % Difference % - (1.0000) (2.0000) (3.0000) (4.0000) (5.0000) (6.0000) (7.0000) ENE

44 Liquidity Risk Pricing in OTC Derivatives A Practical Example: Collateralized Swap We may be interested in calculating the impact of the liquidity of a collateralized swap with respect to a more conservative measure than the ENE, similarly to what happens in the counterparty risk management. We choose the Potential Future Exposure, which is the expected negative NPV of the swap at a given level of confidence, set in this example at the 99% and computed with market volatilities. The funding spread is still 15bps over the EONIA/OIS curve. The Potential Future Exposure (blue line), and the ENE (purple line, same as before) for comparison, are plotted beside. LVA % Fair Swap rate % Swap Rate + Coll. Fund % Difference % - (5.0000) ( ) ( ) ( ) ( ) ( ) PFE ENE

45 About Iason Counterparty Wrong-Way Risk Liquidity Risk Pricing in OTC Derivatives Iason is a company created by market practitioners, financial quants and programmers with valuable experience achieved in dealing rooms of financial institutions. Iason offers a unique blend of skills and expertise in the understanding of financial markets, in the pricing of complex financial instruments and in the measuring and the management of banking risks. The company s structure is very flexible and grants a fully bespoke service to our Clients. Iason believes that the ability to develop new quantitative finance approaches through research as well as to apply those approaches in practice, is critical to innovation in risk management and derivatives pricing. It brings into all the areas of the risk management a new and fresh approach based on the balance between rigour and efficiency Iason s people aimed at when working in the dealing rooms. Besides tailor made services, Iason offers software applications to calculate and monitor credit VaR and conterparty VaR, fund transfer pricing and loan pricing, liquidity-at-risk. c Iason This is a Iason s creation. The ideas and the model frameworks described in this presentation are the fruit of the intellectual efforts and of the skills of the people working in Iason. You may not reproduce or transmit any part of this document in any form or by any means, electronic or mechanical, including photocopying and recording, for any purpose without the express written permission of Iason ltd.