target="_blank" rel="nofollow" href="#ulink_4331420a-dcf5-5ebe-a898-2477cae592d5">(2.1)
with
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
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
2.2 WRONG‐WAY INTEREST RATE RISK
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.
2.3 CONTINGENT CDS PRICING AND CVA
Encouraged by the successful migration of a large number of trades away from Monte Carlo models to more efficient analytic models, attention falls on a portfolio of contingent CDS trades offering counterparty default protection on interest rate (including cross‐currency) underlyings. Calculations for these are known to be very expensive on account of the need to integrate contributions from all possible default times in the exposure period, which requires in turn calculation of the value of the swap underlying at each such time for each Monte Carlo path. It is noted that analytic formulae for calculation of such protection are provided in §9.3.5 for single‐currency interest rate swaps and in §10.4 and §12.4 for cross‐currency swaps. The formulae are implemented and it is found that substantial speed‐up is achieve in pricing, and particularly in risk‐managing these trades.
The CVA desk hear about this and note that the CVA calculations they perform on interest rate portfolios are closely related to the contingent CDS protection pricing problem. They start looking into whether they could incorporate a similar analytic pricing approach into their workflow.
2.4 ANALYTIC INTEREST RATE OPTION PRICING
Another desk meanwhile trading hybrid products into emerging markets notices that the bank's pricing library now provides production‐quality analytic methods for option pricing under the Black–Karasinski model. They frequently use this model in preference to Hull–White as an interest rate model, as they find it performs better
