在因子關聯模式下利用條件重點抽樣法評價一籃子違約交換

林柏均(Po-Chun Lin)

指導教授 ： 韓傳祥 ； 謝文萍

國立清華大學/理學院/統計學研究所/碩士(2008年)

摘要

Valuation of Basket Default Swaps (BDS), equivalent to calculation of the fair premium, is a challenging task in practice. The closed form solution of such contract is usually hard to find, thus we must resort to Monte Carlo (MC) method. Under ordinary scenarios, the MC method works well and yields an acceptable estimator. However, when high-rating assets are in one basket, naïve Monte Carlo is no more efficient (slow in convergence), or not effective
at all (providing uninformative zero estimators.)

To improve the quality of valuation, we propose two algorithms to refine the crude Monte Carlo. Both algorithms rely on conditional expectation and importance sampling (IS) techniques. The first algorithm is conditional on all
marginal factors, and then choose an appropriate IS
distribution carefully for the common factor. The second algorithm, however, does things reversely. We condition on the common factor in the first step, and shift every factor mean to “important” regions, by the conditional independence property. We find that conditioning on all trivial factors and changing the measures of principal
factors is the best strategy. Both algorithms greatly outperform basic MC, measured in variances, when the default events are very rare.

Besides, sensitivity analysis and comparisons of both algorithms’ performances are also presented. We also show that precise estimations from our algorithms are beneficial to both valuation (pricing) and Greek calculation (hedging.)

關鍵字

Gaussian Copula ； Conditional Importance Sampling ； Factor Model ； Basket Default Swaps

參考文獻

[3] Burtschell, X., J. Gregory, and J.-P. Laurent. (2007). Beyond the Gaussian

[1] Black, F. and J. Cox (1976). Valuing Corporate Securities: Some Effects

[2] Brigo, D. and F. Mercurio (2006). Interest Rate Models - Theory and Practice:

With Smile, Inflation and Credit, Springer-Verlag.

Copula: Stochastic and local correlation. Journal of Credit Risk,