Pricing vulnerable European options with stochastic default barriers

This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull–White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.