Читать книгу Perturbation Methods in Credit Derivatives - Colin Turfus - Страница 12

A Korean client of a US bank wishes to sell protection on KRW‐denominated sovereign Korean debt and/or that of some systemically important Korean corporation. Providing a KRW‐based CDS rate is available, this can be used to price the protection (in KRW) according to the well-known formula

(2.1)

with the KRW short rate, the instantaneous KRW‐denominated credit spread and the expected recovery level on the debt post‐default. This can, if wished, be converted to a USD‐based price at today's spot exchange rate.

However, it may be that the KRW‐based spread is less liquid than the USD‐based alternative and the desk (or risk management department) prefer to use the latter. There is likely to be a so‐called quanto spread betweeen the USD CDS rate and the local KRW equivalent (reflecting the expected reduced value of a KRW protection payment after the default of a systemically important credit). This can be addressed by assuming a downwards jump‐at‐default in the value of KRW/USD exchange rate. Such remains amenable to analytic calculation. However, if the trader wants to take into account the additional possibility that the KRW/USD rate is negatively correlated with the credit spread, she appears to have no choice but to resort to Monte Carlo simulation of both the FX rate and the instantaneous credit spread (or credit default intensity).

However, referring to Chapter 10, she sees that a highly accurate modification to the above analytic formula is available for exactly this situation. This consists in simply replacing in the above with the effective credit intensity defined in (10.17).

If it happens that the coupons paid by the US bank are USD‐denominated (as will often be the case), there is a quanto effect here also which prevents the coupon leg being priced straightforwardly by analytic means. However, recourse to Monte Carlo simulation can again be avoided if, in the discount factor used to price the coupon payment at time , is replaced by an effective credit intensity given this time by (10.9). In this way the trade can be priced and risk‐managed entirely using analytic formulae.