Pricing Exotic Options under Levy Process with Numerical Methods

Pricing options is an important activity in quantitative finance for financial engineering purpose. Exotic options are class of options with nonstandard features serving market segments: specific hedging need, tax, accounting, legal, regulatory requirements or offer unique payoffs in particular market circumstances. The introduction of Levy process into pricing procedure is a realistic reflection to the heavy tail property of returns of financial assets which the Wiener process is unable to capture. Exotic options can be priced with Black-Scholes-like formula, solving SDE, solving Black-Scholes-like PDE, tree-based approach, Fourier transform based methods or simulation. As there may not exist a close-form formula for pricing, finding a fast and accurate numerical method for pricing options is more than desirable.


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