Quadratic approximation of the slow factor of volatility in a multifactor stochastic volatility model

A new multifactor stochastic volatility model is proposed in which the slow volatility factor is approximated by a quadratic arc. The perturbation technique is used to obtain the approximate expression for the European option price. The notion of a modified Black-Scholes price is introduced. A simplified expression for the European option price, perturbed around the modified Black-Scholes price, is obtained. An expression of modified price is also obtained in terms of the Black-Scholes price. The effect of this modification on pricing is explained, the accuracy of the approximate option pricing formula established, and its computational cost discussed.