Small-time asymptotics for implied volatility under the multifactor volatility Heston model

Abstract

We obtain a small-maturity implied volatility asymptotic formula for a multifactor stochastic volatility model of Da Fonseca et al. (2008), which is based on Wishart processes. Unlike Da Fonseca and Grasselli (2011), a large deviations theory is utilized in our study. The advantage of this approach is that the expansion is free from rescaling since we do not require ancillary volatility scaler. In addition, we suggest a refinement for a small-maturity term structure of the implied volatility by deriving a first-order correction through saddlepoint expansion. We conduct numerical experiments to test the accuracy of the derived formulas. The asymptotic expansions are effective to describe the implied volatility when a maturity is small enough. If the application to market data is effective, such an approximation grants the user a convenient tool for calibrating option prices with a short-maturity.