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In the present work, we propose a new multifactor stochastic volatility modelin which slow factor of volatility is approximated by a parabolic arc. Weretain ourselves to the perturbation technique to obtain approximate expressionfor European option prices. We introduce the notion of modified Black-Scholesprice. We obtain a simplified expression for European option price which isperturbed around the modified Black-Scholes price and have also obtained theexpression of modified price in terms of Black-Scholes price.

Quadratic approximation of slow factor of volatility in a Multi-factor Stochastic volatility Model