Barrier options were first priced by Merton in 1973 using partial differential equation. In this ... more Barrier options were first priced by Merton in 1973 using partial differential equation. In this work, we present a closed form formula for pricing European barrier option with a moving barrier that increases with time to expiration. We adopted a three-step approach which include; justifying that barrier options satisfy the Black-Scholes partial differential equation under certain conditions, partial differential equation transformation, and solution using Fourier Transform and method of images. We concluded that all barrier options satisfy the Black-Scholes partial differential equation under different domains, expiry conditions, and boundary conditions. And also that closed form solution for several versions of barrier option exists within the Black-Scholes framework and can be found using this approach.
Barrier options were first priced by Merton in 1973 using partial differential equation. In this ... more Barrier options were first priced by Merton in 1973 using partial differential equation. In this work, we present a closed form formula for pricing European barrier option with a moving barrier that increases with time to expiration. We adopted a three-step approach which include; justifying that barrier options satisfy the Black-Scholes partial differential equation under certain conditions, partial differential equation transformation, and solution using Fourier Transform and method of images. We concluded that all barrier options satisfy the Black-Scholes partial differential equation under different domains, expiry conditions, and boundary conditions. And also that closed form solution for several versions of barrier option exists within the Black-Scholes framework and can be found using this approach.
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Papers by Akinyemi David