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Homotopy analysis method for option pricing under stochastic volatility. (English) Zbl 1216.91034

Summary: The homotopy analysis method, whose original concept comes from algebraic topology, is applied to connect the Black-Scholes option price (the good initial guess) to the option price under general stochastic volatility environment in a recursive manner. We obtain the homotopy solutions for the European vanilla and barrier options as well as the relevant convergence conditions.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
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References:

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