Pricing vulnerable options with jump risk and liquidity risk

In this paper, we consider vulnerable options with jump risk and liquidity risk. In the proposed framework, we allow discontinuous changes in the information processes and the liquidity discount factors as well, and default risk is taken into consideration. Specially, we investigate the effect of jumps in the liquidity discount factors and find that the effects of jumps in the liquidity discount factors are stable for different maturities and alternative moneynesses. Further, option prices behave differently with respect to alternative intensities of common jumps, depending on whether there are jumps in the liquidity discount factors or not.