turkmath.org

An equity option is a contract which allows to its owner the right, but not the obligation, to buy or sell shares of the underlying security at a specified price on or before the given date. Here, the underlying security is considered as a specific stock of a firm. In this study, while we price the equity option, we consider that the firm might default. In fact, the firm defaults when its asset value hits a stochastic barrier related to its outstanding obligations. We derive a partial integro-differential equation for pricing equity options when the underlying security is driven by a double-exponential jump-diffusion model. In order to find a numerical solution for the corresponding partial integro-differential equation, a localization of the infinite domain is used, and then, a finite difference scheme is applied. We also compare the approximate solutions obtained with the results of Monte Carlo simulation to validate our findings. This is joint work with Sinem Kozpınar, Ömür Uğur and Cansu Evcin.