Pricing vulnerable options with variable default boundary under jump-diffusion processes

For the pricing of vulnerable options, we improve the results of Klein and Inglis [Journal of Banking and Finance] and Tian et al. [The Journal of Futures and Markets], considering the circumstances in which the writers of options face financial crisis. Our pricing model faces the risks of default and the occasional impact experienced by the underlying assets and counterparty's assets. The correlation between the option's underlying assets and the option writer's assets is clearly modeled. Asset prices are driven by the jump-diffusion processes of two related assets. Furthermore, we consider a variable default boundary (VDB) based on the option's potential debt and the option writer's other liabilities. In case financial distress happens, the payout rate is connected to the option writer's assets. Through the Taylor expansion, we derive an approximate explicit valuation for vulnerable options.