Pricing Vulnerable Options Subject to Stochastic Evolution of Writer's Assets and Liabilities
| Autor: | Yu-Chung Liu, 劉育忠 |
|---|---|
| Rok vydání: | 2006 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 94 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. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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