Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach

A barrier option is an exotic path-dependent option contract where the right to buy or sell

is activated or extinguished when the underlying asset reaches a certain barrier price during the

lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing

formulas for barrier options with general payoffs and exponential barriers on underlying assets that

have jump-diffusion dynamics. With the same approach we also price barrier options on underlying

futures contracts.