An Analytical Approximation for European Options Under a Regime‐Switching Heston‐ α Model

ABSTRACT In this paper, we propose a regime‐switching (R‐S) Heston‐ α model and consider the analytical pricing of European options. With a constant elasticity of variance specification to reflect the level dependence between the high volatility and the volatile volatility and an R‐S mechanism to capture the impact of changing economic conditions, this model is proved, through an empirical study, to have much better pricing performance than the original Heston model. The non‐affine nature of the newly‐proposed model has however, precluded the use of most existing analytical approaches developed for affine models, and the R‐S mechanism has undoubtedly brought in additional difficulties in deriving analytical option pricing formula. Albeit the inherent mathematical difficulties, we have managed to derive an analytical approximation for the price of European options under such a complicated model, which allows the calibration of the model to be completed at an appropriate speed. Numerical experiments suggest that the newly derived formula has an acceptable degree of accuracy for general parameter settings. Empirical results also confirm the practicability of the newly‐proposed model to real financial markets.