Читать книгу Perturbation Methods in Credit Derivatives - Colin Turfus - Страница 17

Model risk management faces a problem that one of the Monte Carlo pricing models used for credit derivatives pricing is found to manifest anomalous‐looking behaviour when high volatility levels are used in conjunction with long times to maturity in the presence of significant rates‐credit correlation. Auditors have asked for the situation to be investigated and an assessment made of what the correct behaviour should be, with the possibility of a reserve being set aside to take account of the risk of model error in the event that such large volatilities are observed in practice.

It is noted that the calculations set out in Chapter 8 illustrate how to price credit‐contingent (default or survival) cash flows accurately under circumstances of relatively weak credit risk, with credit intensity represented by a Black–Karasinski short‐rate model; further, that the relevant formulae are not limited in terms of the size of the credit volatility. The formula (8.54) for the value of protection payments is coded up and compared with the results from the Monte Carlo engine as the volatility level is increased. While the analytic results are seen to increase linearly with the credit volatility, the Monte Carlo results are found to deviate from this behaviour. It is concluded that there is likely model error resulting in this circumstance. A proposal is made that, in the event that volatility levels exceed a given threshold, a reserve should be set aside based on the difference between the Monte Carlo results and analytic results derived using the formulae presented in Chapter 8. A suggestion is also made that the front office quantitative analysts consider integrating a pricer based on the analytic formulae into the pricing library and migrating trades over from the Monte Carlo model.

Buoyed by this success, the model validation team within the model risk management department consider implementing more of the analytic formulae in their benchmark library for use as “challenger models” in the model validation process. In addition they note from the suggestions in Chapter 16 that in addition to providing alternative benchmarks, these analytic formulae upon differentiation are able to provide explicit formulae for the sensitivity of prices to model and market parameters. In this way model uncertainty calculations can be conveniently carried out, potentially at a large number of points in the product‐model phase space. Thus the circumstances can be identified where the greatest model uncertainty is to be expected. In particular, model testing can be focussed on such “hot spots”.