Perturbation Methods in Credit Derivatives

CHAPTER 9Credit‐Equity Hybrid Modelling

9.1 BACKGROUND

We look to deal in this chapter with the problem of modelling equity derivatives in a context where credit risk is considered to impact on the pricing. We will, as in the previous chapter, make use of the reduced‐form approach pioneered in the classic paper of Merton [1976], wherein a diffusive process for equity price is supplemented by a jump process, driven by an intensity . Although it is not often recognised, Merton [1976] did not in this paper equate the jump process with default but (as its title suggests) with the arrival of a jump whose size (positive or negative) was governed by some assumed probability distribution. It was only in subsequent extensions that the jump was considered to be of size –1, taking the equity price to a terminal state of zero value; at the same time the default model was separated off from the equity model for the purpose of pricing credit derivatives whose payoff(s) do not depend on the equity price. In this chapter, as stated, we will be interested in the case where payoffs do depend on equity prices.

There is quite an extensive literature on different models of the joint credit‐equity process, although no clear consensus has arisen as to which approach is to be preferred. Based on the observation that, as the equity price decreases, the credit default intensity tends to increase, the ...