Читать книгу Perturbation Methods in Credit Derivatives - Colin Turfus - Страница 13

Another issue arises shortly after at the same bank, this time raised by the market risk department. While the credit trading desk for developed markets uses analytic pricing for most vanilla credit products, the emerging markets desk, in recognition of the possibility of significant “wrong‐way” risk associated with correlation between credit default risk and the local interest rate on foreign‐denominated floating rate notes, uses a Monte Carlo approach with short‐rate models representing both the credit intensity and the local rates processes. Market risk currently use the same (analytic pricing‐based) risk engine for the trades of both desks. However, auditors have suggested, and market risk are now concerned, that there may be problems with back‐testing of the Internal Model for market risk as a result of the discrepancy between the risk model and the emerging markets model, with only the latter capturing the wrong‐way risk. They would prefer not to incur the significant cost of migrating part of the bank's credit portfolio to be priced by a Monte Carlo engine instead of an analytic approach.

However, it turns out that there is no need for the risk model to be changed to perform Monte Carlo pricing of floating rate notes. From results presented in Chapter 8, rather than (2.1), the protection leg can be priced using (8.54) which incorporates the wrong‐way risk to a high degree of accuracy. Likewise the value of floating rate payments denominated in the local (foreign) currency can be priced using (8.58) to the same high level of accuracy. Here again, recourse to Monte Carlo simulation is avoided and computational resources are spared.

In the wake of this discussion, a question arises as to whether the quanto CDS trades currently priced with an analytic model taking account of FX‐credit risk might likewise face the possibility of wrong‐way rates‐credit correlation risk, potentially in relation to both domestic and foreign currencies. It turns out from the extended calculations set out in Chapter 12 that the impact of wrong‐way risk, from correlation of credit with the FX rate and with both interest rates on the value of a protection leg, can be taken into consideration by use of an effective credit intensity given by (12.46). Similarly the value of foreign currency coupon payments priced with a domestic currency credit curve can be obtained by making use of an effective credit intensity given by (12.38). Furthermore, it is seen that the value of a foreign currency float leg can be obtained to good accuracy by use of (12.39). In this case too, no recourse is needed to Monte Carlo methods.