Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing

The popular 4/2 stochastic volatility model reveals important features of volatility but a closed-form formula for derivative prices is still lacking. This paper proposes a modified form of the 4/2 model into which two scale double-mean-reverting stochastic volatility is incorporated in order to remedy its shortcomings. We obtain a closed-form formula for the prices of European derivatives. The formula can be explicitly calculated by taking derivatives of the Black–Scholes prices and thus faster calibration of the 4/2 model becomes available. We also show that the rescaled 4/2 model is flexible enough to capture essential features (skew or smile) of market implied volatilities.