Barrier option pricing for exchange rates under the Levy–HJM processes

In this paper, we present closed-forms for the valuation of the barrier option whose underlying is exchange rate under the multi-dimensional Levy process, including stochastic interest rates and stochastic assets. Instantaneous forward interest rates are assumed under the Heath et al. [1992. Econometrica 60, 77–105] framework, and the analytic formulas of the exchange rate barrier option are obtained when the Levy process is restricted in a double exponential process.