Perturbation Methods in Credit Derivatives. Colin Turfus

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Perturbation Methods in Credit Derivatives - Colin Turfus


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so as to facilitate implementation, and fully general to allow real market data to be used without any modification or re‐working of results.

      1 1 Approximate solutions are sometimes presented as being valid for short times to maturity, but this limitation usually serves to limit the magnitude of the term variance which by construction tends to be a monotonically increasing function of time to maturity.

      Consider the following plausible scenarios where the methods set out in the remainder of this book are found to address the types of challenge faced by risk management groups, looking to capture risk more effectively and accurately under regulatory and other pressures without increasing computational overheads unduly or engaging in costly new model development.

      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

      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, 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.

      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.

      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


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