Perturbation Methods in Credit Derivatives

CHAPTER 10Credit‐FX Hybrid Modelling

10.1 BACKGROUND

In this chapter we shall look to deal with the problem of pricing multi‐currency derivative products depending on (stochastic) FX rates in a context where credit risk is considered to impact on the pricing. The model we shall choose for the FX process will be mathematically identical to that chosen for the equity process in the previous chapter. For that reason, the pricing kernel will have an identical structure and need not be re‐calculated for the new context.

We consider an economy with two currencies, foreign and domestic, and a credit default intensity process associated either with a corporation based in the foreign economy or with a foreign sovereign debt issuer, the CDS market for which operates in the domestic currency. We suppose, in the interests of tractability, that the foreign and domestic interest rates are deterministic, but that there is a stochastic exchange rate between the two currencies and further that upon default of the named issuer there is a decrease in the value of the foreign currency giving rise to a proportional downward jump in the exchange rate from foreign to domestic currency.

In particular we look in §10.3 to price quanto CDS, for which the debt against which default protection is bought is denominated in a different currency from that for which the default curve is inferred, in particular capturing the difference in the CDS spreads associated with the two currencies. The calculation presented ...