In this paper, 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.
Bibliographical noteFunding Information:
This work was supported by the Ministry of Knowledge Economy and Korea Institute for Advancement in Technology through the Workforce Development Program in Strategic Technology.
All Science Journal Classification (ASJC) codes
- Applied Mathematics