We develop methods for pricing European options under general mean-reverting stochastic volatility dynamics, which can be used with both affine and non-affine volatility models. In our methods, the option price under stochastic volatility is expanded as a power series of parameters or variables by transferring the original partial differential equation to a set of solvable inhomogeneous Black–Scholes equations. The analytic approximation is more generally applicable than the fast Fourier transform, because it does not rely on the existence of a characteristic function. Finally, we numerically demonstrate our approach with the Heston, 3/2, and continuous-time GARCH models.
- Jufo-taso 1
!!ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)
- Applied Mathematics