Conic finance theory, which has been developed over the past decade, replaces classical one-price theory with the bid-ask price economy in option pricing since the one-price principle ignores the bid-ask spread created by market liquidity. Within this framework, we investigate the European option pricing problem when stochastic interest rate, stochastic volatility, and double exponential jump are all taken into account. We show that the corresponding bid and ask prices can be formulated into a semi-analytical form with the Fourier-cosine method once the solution to the characteristic function is obtained. Some interesting properties regarding the new results are displayed via numerical implementation.

In this paper, the pricing of European options under a new two-factor non-affine stochastic volatility model is studied. In order to reduce the computational complexity, we use the Taylor expansion and Fourier-cosine method to derive an analytical approximation formula for European option prices. Numerical experiments prove that the proposed formula is fast and efficient for pricing European options compared with Monte Carlo simulations. The sensitivity of the parameters is analyzed to explain the rationality of the model. Finally, we present some preliminary empirical analysis revealing that the pricing performance of our proposed model is superior to that of the single-factor model.