Pricing Vulnerable Options by Binomial Trees

Abstract

This paper proposes a simple algorithm extending the discrete CRR (1979) model to evaluate vulnerable derivatives, which include two stochastic processes, the underlying stock price and the assets value of the option writer. Introducing the concept of expected intrinsic value, univariate binomial tree model is applied to accomplish options pricing. It is both analytically verified and numerically illustrated that the proposed binomial tree model contains the Klein (1996) formula as a limiting case. Binomial pyramid algorithms are demonstrated for numerical comparisons. Numerical results of the two algorithms are rather close, but the proposed conditional binomial tree algorithm is computationally more efficient.