We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the t-copula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and a scaled chi-square random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chi-square random variable. Then, conditional on the chi-square random variable, we apply the importance sampling procedure developed for the Gaussian copula model in Glasserman, Kang, Shahabuddin (2005b). We support our importance sampling procedure by numerical examples.

This paper is based on a talk with the above title given at the SemStat meeting on Extreme Value Theory and Applications in Gothenburg on December 13, 2001

We consider the extreme tail behavior of the CreditMetrics model for portfolio credit losses. We generalize the model to allow for alternative distributions of the risk factors. We consider two special cases and provide alternative tail approximations. The results reveal that one has to be careful in applying extreme value theory for computing extreme quantiles efficiently. The applicability of extreme value theory in characterizing the tail shape very much depends on the exact distributional assumptions for the systematic and idiosyncratic credit risk factors. Key words: portfolio credit risk; extreme value theory; tail events; tail index; CreditMetrics; second and higher order expansions. JEL Codes: G21; G33; G29; C19. ∗We thank seminar participants at EURANDOM (Eindhoven), and risk conferences in Basle and Montreal for useful comments. Correspondence to: alucasecon.vu.nl, s.straetmansberfin.unimaas.nl, pieter.klaassennl.abnamro.com, or spreijwins.uva.nl.

This paper proposes a pricing model for the FDIC's reinsurance risk. We derive a closed-form Weibull call option pricing model to price a call-spread a reinsurer might sell to the FDIC. To obtain the risk-neutral loss-density necessary to price this call spread we risk-neutralize a Weibull distributed FDIC annual losses by a tilting coecient estimated from the traded call options on the BKX index. An application of the proposed approach yield reasonable reinsurance prices and also shows that tilting is embedded in the FDIC's risk-based insurance premiums.

In their formula, Black & Scholes evaluate a European call on an underlying asset without distinguishing between the di¤erent risks borne by the asset. Applying the Black & Scholes ’ pricing methodology and distinguishing between the market risk and idiosyncratic risk, as Sharpe (1964) did, we obtain a new pricing formula for a European call. The parameters of this formula include the volatilities of the two risk factors, or alternatively, the volatility of the market factor and that of the stock. We then build a market factor replicating portfolio (MFR) which is a naively divesi…ed portfolio. Under some regularity conditions, the diversi…cation e¤ect known to o¤set the speci…c risks applies. The price of a European call on a stock may then be expressed in terms of the volatilities of the MFR portfolio and of the underlying stock (and of its beta). Finally,we compare our formula to that of Black & Scholes and to the valuation proposed by Corrado & Su. We focus on the existence of a volatility smile and we give an explanation competing with the one proposed by stochastic volatility models (e. g. Heston [1993]) or models assuming a non normal distribution for the assets’ returns (e. g. Corrado & Su [1996], [1997]).