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Asymptotic expansion of European options with mean-reverting stochastic volatility dynamics

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalFinance Research Letters
Publication statusPublished - Aug 2015
Publication typeA1 Journal article-refereed


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.


  • Option pricing, Series expansion, Partial Differential Equations, Stochastic volatility, Non-affine models

Publication forum classification

Field of science, Statistics Finland