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