Pricing derivative credit risk (Q1294780)

This book is concerned with the valuation of credit risk in a derivative context. It addresses the following three aspects of derivative credit risk: counterparty default risk, options on risky bonds, and credit derivatives. Its focus is on derivatives with counterparty credit risk, but pricing models are proposed for all the above three issues. After a short recapitulation of some basics of contingent claim valuation in chapter 2, the book starts in chapter 3 with an extensive review of credit risk models. The long subsection 3.1 about models for pricing credit-risky bonds covers the literature up to 1997 in a rather comprehensive way. Subsections 3.2 and 3.3 about pricing derivatives with counterparty risk and about pricing credit derivatives (like debt insurance or spread derivatives) are much shorter. Chapter 4 derives explicit formulae for the prices of vulnerable call and put options when the payoff at maturity \(T\) is given by \[ X_T I_{\{V_T\geq D_T\}} + \delta_T X_T I_{\{V_T < D_T\}} \] with \(\delta_T = V_T/D_T\) and (for a call) \(X_T = (S_T-K)^+\). The basic assumption is that the underlying asset \(S\), the value \(V\) of the firm's assets and the value \(D\) of the firm's liabilities all follow correlated geometric Brownian motions with constant parameters, and interest rates are either constant or given by a Gaussian model. By exploiting the particular payoff structure, explicit pricing formulae can be given in terms of a bivariate normal distribution. Several special cases recover previously derived formulae (Black-Scholes, Margrabe, Jamshidian), and numerical examples illustrate the effects of parameter constellations. Chapter 5 proposes a hybrid model where the recovery rate in case of default and also the intensity of default can depend on the firm value. Of course, such a model admits no closed-form pricing formulae, and so the major part of the chapter is devoted to implementation issues in binomial lattice structures. The final chapter 6 briefly considers credit derivatives by means of a compound option pricing approach. Again, both chapters give a number of numerical results. Although the mathematics in the book must be read and used with a lot of care, the book is overall quite useful in that it gives a practically oriented presentation of ideas in pricing credit risk. The survey in chapter 3 is well done; it would be even more useful if the book had an author index. Being explicit, the formulae in chapter 4 are of course very handy, even if one has to question the appropriateness of all the Gaussian assumptions, and the thorough discussion of implementation issues in chapter 5 is also informative.