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The Arithmetic Average case of Asian Options. Reducing the PDE to the BS equation

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We consider the path-dependent contingent claims where the underlying asset follows an arithmetic average process. Considering the no-arbitrage PDE of these claims, we first determine the underlying Lie Point Symmetries. After determination of the invariants, we transform the PDE to the Black-Scholes (BS) equation. We then transform the BS equation into the heat equation and we provide some general solutions to that equation. This procedure appears for the first time in the finance literature.

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