Approximate Analytical Pricing of European Options under the Non-affine Stochastic Volatility Model

Abstract

Abstract The non-affine stochastic volatility model has attracted increasing attention in recent years, due to its excellent performance in describing the nonlinear characteristics of asset price path. However, the fact that there is no close-form of option pricing formula under this model, restricts its use badly. To remove this restriction, two approximate analytical option pricing approaches are proposed in this paper, that is, the piecewise first-order Taylor expansion method and the perturbation-based asymptotic expansion method of implied volatility. The first method is used to derive an approximate characteristic function, then based on which the Fourier-Cosine expansion method calculates the European option price. In the second way, implied volatility of the European option price is asymptotically expanded around non-affine term of volatility. Compared with the existing methods in literature, numerical experiments show that the first method has higher accuracy, while the second method is of more practical significance. In addition, the accuracy of the first method is generally higher than that of the second method in most cases, while the second method performs better when the volatility is extremely small.