Introduction to Credit Derivatives Uwe Fabich

Outline Market Overview § Mechanics of Credit Default Swap § Standard Credit Models § Credit Derivatives 2

Credit Derivatives Market Overview Total Market Size > $5, 000 billion § Growth rate of more than 30% over the last years § New Basel Capital Accord § Credit Derivatives 3

Credit Derivatives Market Overview § Product overview Credit Derivatives 4

Credit Default Swap (CDS) Most Basic Credit Derivatives Product § A CDS is used to transfer credit risk § Starting Point for pricing of Exotic Credit Derivatives § Investor can buy protection vs default of a reference entity- this is economically equivalent to shorting a credit § Credit Derivatives 5

Mechanics of a CDS Premium leg: Protection buyer pays a spread at each date § Protection leg: Protection seller pays Face Value in exchange for bond if default occurs § Credit Derivatives 6

7 Credit Models Structural Model - based on Merton (1974) § Reduced Form Model - based on Jarrow/Turnbull (1995) § Credit Derivatives

Merton Model Lognormal stochastic process represents the firm‘s total Asset Value value § Default only occurs at maturity § Standard Black Scholes assumption § Shareholders are long a European Call on the firm‘s asset, Strike= Face Value of Debt § From Put-Call Parity: Debt= Risk Free Bond – European Put § Credit Derivatives 8

9 Merton Model asset value and volatility are not observable § However, equity value and volatilty are. Black Scholes gives us: § where § With these results we can price risky debt: where Credit Derivatives

Merton Model § Once we have the value of the risky bond it is easy to calculate the credit spread: . . . and build a spread curve Example: (K=100; AV=140, 115, 98) Credit Derivatives 10

Problems with the Merton Model § Black Scholes assumptions do not hold § Only one zero coupon bond outstanding § Diffusion Model is continous § Pricing of Credit Derivatives with more exotic payoffs is beyond the limit of the model Credit Derivatives 11

Reduced Form Model Purpose: Arbitrage free valuation of default linked payoffs § Default is treated as exogenous event § Default event is the first event of a Poisson counting process. § Conditional probability of default is defined as hazard rate: § . . . integration leads to the survival probality: Credit Derivatives 12

Reduced Form Model § Pricing of contingent claims if payment is made at time T: where if payment is made when default occurs: Probability of defaulting in time interval from t to t+dt is . . . and by integrating over the density of default time Credit Derivatives 13

Reduced Form Model § Pricing CDS Spreads Present Value Protection leg Present Value Premium leg Credit Derivatives 14

Reduced Form Model § Pricing CDS Spreads Protection Leg=Premium Leg Credit Derivatives 15

16 Recovery Rates Credit Derivatives

17 Conclusion There is a lot to learn for me But the rewards are high Credit Derivatives