An analytical approximation of European option prices under a hybrid GARCH-Vasicek model with double exponential jump in the bid-ask price economy

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.