A jump-diffusion approach to modelling vulnerable option pricing

Following the framework of Klein [1996. Journal of Banking and Finance 20, 1211–1229], this paper presents an improved method of pricing vulnerable options under jump diffusion assumptions about the underlying stock prices and firm values which are appropriate in many business situations. In contrast to Klein [1996. Journal of Banking and Finance 20, 1211–1229] model, jumps can be used to model sudden changes in stock prices and firm values. Further, with the jump risk, a firm can default instantaneously because of an unexpected drop in its value. Therefore, our model is able to provide sufficient conceptual insights about the economic mechanism of vulnerable option pricing. The numerical results show that a jump occurrence in firm values can increase the likelihood of default and reduce the vulnerable option prices.