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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:
91G20Derivative securities
91G80Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
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