6.3.1 European Calls and Puts under Cash Dividends -- 6.4 POISSON PROCESSES -- 6.4.1 Closed Form Solution for European Call Option -- 6.5 OPTIONS ON FUTURES -- 6.5.1 Solution for European Call and Put Options -- 6.6 JUMP DIFFUSION MODEL -- 6.6.1 Bankruptcy! -- 6.6.2 Lognormal Jumps -- 6.7 EXCHANGE ONE ASSET FOR ANOTHER -- 6.7.1 Closed Form Solution -- 6.7.2 Using a Different Currency (Change of Numeraire) -- 6.7.3 Recovering the Closed Form Solution -- 6.8 STOCHASTIC VOLATILITY -- 6.9 SUMMARY -- CHAPTER 7: Interest Rate and Credit Derivatives -- 7.1 INTEREST RATE MODELING AND DERIVATIVES -- 7.2 MODELING THE TERM STRUCTURE OF INTEREST RATES -- 7.2.1 Spot Rates -- 7.2.2 Zero-Coupon Bonds -- 7.2.3 Forward Rates -- 7.2.4 Discount Factors -- 7.2.5 Instantaneous Rates -- 7.2.6 Two Choices for Underlying Variables -- 7.3 MODELS BASED ON THE SHORT RATE -- 7.3.1 The Short Rate of Interest and a Money Market Account -- 7.3.2 Single Factor Short Rate Models -- 7.3.2.1 Vasicek Model -- 7.3.2.2 Cox-Ingersoll-Ross Model -- 7.3.2.3 Additional Single Factor Short Rate Models -- 7.3.3 Multifactor Short Rate Models -- 7.4 MODELS BASED ON FORWARD RATES -- 7.4.1 An Important Detour on Forwards -- 7.4.1.1 Market Price of Risk for Forwards -- 7.4.1.2 Pricing Options on Forwards -- 7.4.1.3 Simplified Pricing in Units of the Bond -- 7.5 LIBOR MARKET MODEL -- 7.5.1 Discount Factors are Forward Prices -- 7.5.2 LMM with Discount Factors as Underlying Variables -- 7.5.2.1 Calibration of the Market Prices of Risk -- 7.5.2.2 Using the Forward Analogy -- 7.5.2.3 Formal Three Step Approach -- 7.5.3 Forward Rates as Underlying Variables -- 7.5.4 Pricing a Caplet in the Right Units -- 7.5.4.1 LMM Caplet Formula -- 7.5.4.2 From Caplets to Floorlets and Beyond -- 7.6 HEATH-JARROW-MORTON MODEL -- 7.7 CREDIT DERIVATIVES -- 7.7.1 Defaultable Bonds -- 7.7.1.1 Different Types of Recovery