Pricing Vulnerable Options under Stochastic Asset and Liability

Abstract: In this paper pricing for vulnerable options is investigated. The discussed payoff function mainly derives from the Klein and the Ammann credit risk frameworks. Three stochastic processes, namely the underlying stock price, the asset value of the option writer, and the liability value of the option writer, are suitably modeled. Under the suggested payoff function, closed-form solutions for vulnerable European options are derived; moreover, adapting the Rubinstein’s approach, a general binomial pyramid algorithm for vulnerable options pricing is constructed