Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

Abstract

In this paper we investigate, since both, the theoretical and the empirical point of view, the pricing of European call options under a hybrid CEV-Heston model. CEV-Heston model captures two typical behaviors of financial assets: (i) the leverage effect and (ii) the stochastic volatility. We prove theoretically that the CEV-Heston model covers the leverage-effect and show empirically the volatility clustering property. Then, we utilize a decomposition of the option price to get an approximate formula for European call options. The accuracy of this estimate is compared with the Monte Carlo method. The results show the efficiency of our approximate formula.