Financial Risk Management and Governance Credit Risk Portfolio Management. Prof. Hugues Pirotte
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1 Financial Risk Management and Governance Credit Risk Portfolio Management Prof. Hugues Pirotte
2 2 Beyond simple estimations Credit risk includes counterparty risk and therefore there is always a residual credit risk Identification of credit risk exposure» Not very easy since can be intimately linked to the market value» In particular, for derivatives» Contracts can be 1. Assets to the firm 2. Liabilities to the firm 3. Maybe both... Examples of vulnerable assets» (Defaultable) Options (insurances)» (Defaultable) Swaps
3 3 Some algebra about this... Assume that default probability is independent of the value of the derivative Define t 1, t 2, t n : times when default can occur q i : default probability at time t i. f i : The value of the contract at time t i R: Recovery rate The expected loss from defaults at time t i is q i (1-R) E[max(f i,0)] Defining u i =q i (1-R) and v i as the value of a derivative that provides a payoff of max(f i,0) at time t i, the PV of the cost of defaults is n i 1 u i v i
4 4 IRS vs. CS Expected exposure on pair of offsetting interest rate swaps and a pair of offsetting currency swaps (Hull, RMFI, Figure 12.2, page 281) Exposure Currency swaps Interest Rate Swaps Maturity
5 5 Two-sided default risk In a swap operation» There are two reciprocal credit exposures A B» The market value of the swap will evolve through time depending on the underlying market conditions» The creditworthiness of both counterparts may also evolve during the life of the swap If both exposures (market & credit) propose scenarios that are equally likely for both counterparts» Then the credit risk spread on the transaction should be 0. Otherwise, the value of the swap to a counterpart (let s take A) should be... f Exp Exp B A But swap credit risk remains a complex subject...
6 6 Netting f ij Other issues» We replace f i by in the definition of u i to calculate the expected cost of defaults by a counterparty j where j counts the contracts outstanding with the counterparty» The incremental effect of a new deal on the exposure to a counterparty can be negative! Collateralization» Contracts are marked to markets periodically (e.g. every day)» If total value of contracts Party A has with party B is above a specified threshold level it can ask Party B to post collateral equal to the excess of the value over the threshold level» After that collateral can be withdrawn or must be increased by Party B depending on whether value of contracts to Party A decreases or increases Downgrade triggers» A downgrade trigger is a clause stating that a contract can be closed out by Party A when the credit rating of the other side, Party B, falls below a certain level» In practice Party A will only close out contracts that have a negative value to Party B» When there are a large number of downgrade triggers they are counterproductive
7 Prof. H. Pirotte 7
8 8 CreditVaR: Methods Definition» Can be defined analogously to Market Risk VaR» A one year credit VaR with a 99.9% confidence is the loss level that we are 99.9% confident will not be exceeded over one year Vasicek s model» For a large portfolio of loans, each of which has a probability of Q(T) of defaulting by time T the default rate that will not be exceeded at the X% confidence level is 1 N Q( T) r N 1 ( X ) N 1 r where r is the Gaussian copula correlation Basle II» One-factor Gaussian copula model (Vasicek s model) with special formulations for the correlation parameter (that depends on PD in many cases) Portfolio models» How do we aggregate individual credit risks?
9 9 Portfolio Models: CreditRisk+ Simplified» A financial institution has N counterparts with a PD each (p).» Assuming independent defaults and that p is small, the probability of n defaults is given by a Poisson process of the form n e where Np n!» Combining this to a probability distribution of default losses on a single counterpart, this can produce a distribution of total losses for our current portfolio Also» Estimation per category of counterparts» Varying default rates Use a probability distribution based on historical data and link each category s PD to this distribution. CSFP provides an analytical form under some assumptions
10 10 Portfolio Models: CreditRisk+ (2) Otherwise, use a Monte Carlo simulation where the steps are: 1. Sample overall default rate 2. Calculate a PD for each category 3. Sample number of defaults for each category 4. Sample size of loss for each default 5. Calculate total loss 6. Repeat the simulation procedure many times Assuming categories linked to an overall PD distribution implied default correlations. The distribution of total losses will be thus positively skewed. Total losses
11 11 Portfolio Models: CreditMetrics Idea» Calculates credit VaR by considering possible rating transitions» A Gaussian copula model is used to define the correlation between the ratings transitions of different companies Framework
12 12 Portfolio Models: CreditMetrics
13 13 Portfolio Models: CreditMetrics
14 Prof. H. Pirotte 14 Results for the stand-alone case Source: CreditMetrics technical document
15 Prof. H. Pirotte 15 Add-in Incorporating the additional uncertainty around default: Source: CreditMetrics technical document
16 16 Portfolio Models: CreditMetrics
17 17 Portfolio Models: CreditMetrics
18 18 Portfolio Models: CreditMetrics
19 19 Portfolio Models: CreditMetrics (See the accompanying Excel file for a more precise matrix and calculations there is a property mismatch in this original application find it!)
20 20 Portfolio Models: CreditMetrics
21 Prof. H. Pirotte 21 Results from the portfolio case
22 22 Portfolio Models: CreditPortfolioView Uses a factor models that takes into account macro variables
23 23 References Some papers» Baz, Jamil (1995), Three Essays on Contingent Claims, Harvard PhD Thesis, August 1995.» Cossin & Pirotte (1999), Swap Credit Risk: An Empirical Investigation on Transaction Data, Journal of Banking and Finance, Vol. 21, No.10, October 1997, pp » Cossin & Pirotte (1998), How well do classical credit risk pricing models t swap transaction data?, European Financial Management, Vol. 4, No.1, March 1998, pp » Duffe, Darrel and Ming Huang (1996), Swap Rates and Credit Quality, Journal of Finance, 51(3), July 1996, » Duffee, G.R., (1995a), On Measuring Credit Risks of Derivative Instruments, Working paper, Federal Reserve Board, February Other documents» Documents by Credit Suisse Financial Products, RiskMetrics and McKinsey» Hull RMFI s slides
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