Pricing Vulnerable Options Subject to Stochastic Evolution of Writer's Assets and Liabilities
Date Issued
2006
Date
2006
Author(s)
Liu, Yu-Chung
DOI
en-US
Abstract
This paper presents both closed-form formulas and binomial tree algorithms to evaluate vulnerable derivatives. The payoff function extends mainly from the Klein (1996) and the Ammann (2001) credit risk frameworks. Three stochastic processes -- the underlying stock price, the assets value of the option writer, and the liabilities value of the option writer -- are suitably modeled. Closed-form solutions are derived for vulnerable European options under the suggested payoff function. Adopting the innovation of expected intrinsic value with a trick of dimension reduction by Liu and Liu (2006), a conditional binomial tree (CBT) algorithm for two correlated stochastic processes, the underlying stock price and the asset-to-debt ratio process, are properly established. Moreover, following Rubinstein (1994), a general binomial pyramid (BP) algorithm is set up. Both algorithms serve as discrete approximations for vulnerable European and vulnerable American options evaluation. It is analytically verified and numerically illustrated that the proposed binomial tree model contains the closed-form formula as a limiting case. Some sensitivity analyses for the discussed vulnerable options are also included.
Subjects
信用風險
脆弱選擇權評價
期望內含價值
條件二項樹演算法
二項金字塔演算法
Credit Risk
Vulnerable Option Pricing
Expected Intrinsic Value
Conditional Binomial Tree Algorithm
Binomial Pyramid Algorithm
Type
thesis
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