Abstract
In this paper, we combine the reduced-form model with the structural model to discuss the European vulnerable option pricing. We define that the default occurs when the default process jumps or the corporate goes bankrupt. Assuming that the underlying asset follows the jump-diffusion process and the default follows the Vasicek model, we can have the expression of European vulnerable option. Then we use the measure transformation and martingale method to derive the explicit solution of it.
Highlights
We combine the reduced-form model with the structural model to discuss the European vulnerable option pricing
We define that the default occurs when the default process jumps or the corporate goes bankrupt
Su and Wang (2012) [19] assumed that the default intensity followed the stochastic model with jumps; the vulnerable option pricing was given based on the reduced-form model by the martingale method
Summary
Vulnerable option is a kind of option with credit risk. The pricing of credit risk has been concerned by scholars for a long time. Merton (1974) [1] firstly introduced option pricing into zero coupon bond with credit risk He assumed that the capital structure of corporate consisted of two parts which are assets and liabilities; the default occurred when the corporate was insolvent at maturity. Longstaff and Schwartz (1995) [4] assumed that the default boundary was a constant and the recovery rate was an exogenous ratio They derived the zero coupon bond pricing. Su and Wang (2012) [19] assumed that the default intensity followed the stochastic model with jumps; the vulnerable option pricing was given based on the reduced-form model by the martingale method. Wang (2016) [23] presented a pricing model which allows for the correlation between the intensity of default and the variance of the underlying asset and derived a closed-form solution for the vulnerable option. Jeon et al (2017) [25] studied the pricing of vulnerable path-dependent options using double Mellin transforms and obtained an explicit form pricing formula or semianalytic formula in each path-dependent option
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