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Monte Carlo methods for portfolio cr...

Chen, Zhiyong.

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Monte Carlo methods for portfolio credit derivatives.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Monte Carlo methods for portfolio credit derivatives./
作者:	Chen, Zhiyong.
面頁冊數:	141 p.
附註:	Adviser: Paul Glasserman.
Contained By:	Dissertation Abstracts International67-10B.
標題:	Economics, Finance. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3237211
ISBN:	9780542915451

Monte Carlo methods for portfolio credit derivatives.
Chen, Zhiyong.

Monte Carlo methods for portfolio credit derivatives. - 141 p.

Adviser: Paul Glasserman.

Thesis (Ph.D.)--Columbia University, 2006.

Portfolio credit derivatives are contracts tied to an underlying portfolio of defautable reference assets, and have payoffs that depend on the default times of the underlying assets. Valuing these contracts often entails Monte Carlo simulation of these default times, and is usually a rare-event simulation problem. The hedging of credit derivatives involves the calculation of the sensitivities of the contract value with respect to parameters of the default-time distributions.

ISBN: 9780542915451Subjects--Topical Terms:

626650
Economics, Finance.

Monte Carlo methods for portfolio credit derivatives.
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502 $a Thesis (Ph.D.)--Columbia University, 2006.
520 $a Portfolio credit derivatives are contracts tied to an underlying portfolio of defautable reference assets, and have payoffs that depend on the default times of the underlying assets. Valuing these contracts often entails Monte Carlo simulation of these default times, and is usually a rare-event simulation problem. The hedging of credit derivatives involves the calculation of the sensitivities of the contract value with respect to parameters of the default-time distributions.
520 $a In the first part of this thesis, we develop an importance sampling technique, an extension of the algorithm introduced by Joshi and Kainth (2004), for pricing basket default swaps and CDO tranches. We analyze, extend and improve the Joshi-Kainth algorithm. It could be shown that their algorithm can actually increase variance. Our alternative is guaranteed to reduce variance, even when defaults are not rare. Along the way, we provide a rigorous underpinning in a setting sufficiently general to include both the original method and the version proposed in this thesis.
520 $a The second part considers sensitivities of the contract value with respect to changes in the credit spreads of the underlying assets. We derive and analyze Monte Carlo estimators of the sensitivities. The payoff of a credit derivative is often discontinuous in the underlying default times, and this complicates the accurate estimation of sensitivities. Discontinuities introduced by changes in one default time can be smoothed by taking conditional expectations given all other default times. We use this to derive estimators and to give conditions under which they are unbiased. We also give conditions under which an alternative likelihood ratio method estimator is unbiased. We illustrate the application and verification of these conditions and estimators in the particular case of the multifactor Gaussian copula model, but the methods are more generally applicable.
520 $a In the last part, we investigate a control variate method for pricing a CDO tranche, or more precisely, for estimating cumulative loss on this tranche. The expected cumulative loss given the number of defaults in the reference portfolio can be computed semi-analytically. We use this to construct our control variate, which is also a good approximation of the true value.
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