A Gaussian semi-parametric implied volatility model

Abstract

Modeling the implied volatility has received extensive attention, as the implied volatility is an important parameter in option pricing. Usually the implied volatility can be approximated by fitting a polynomial about the strike and the maturity or by stochastic methods. In this article, a Gaussian semi-parametric model is proposed based on the quadratic polynomial semi-parametric model suggested by Borovkova. In the new model, the Gaussian function is used to construct a smooth term substituting the quadratic term in the polynomial model, and the arbitrage-free constraints are used to calibrate the model. The empirical tests show that the Gaussian semi-parametric model has a better performance in fitting and forecasting.