Pricing vulnerable options with stochastic default barriers

In this paper, we investigate the pricing issue of vulnerable options by assuming that the dynamics of all assets are governed by jump-diffusion processes with common factors in both continuous process and jump process components. Moreover, assume credit default event occurs when the value of the counterparty's assets falls below the default barrier, which is stochastically affected by common factors as well. In the proposed framework, we derive a closed-form formula for vulnerable options and illustrate the impacts of stochastic barriers on option prices. Additionally, the U-shape curve appears when we investigate option prices against the volatility of default barriers.