A Weighted Strike-Related Implied Volatility Model

The implied volatility in the Black-Scholes model is assumed as a constant. However, empirical analysis proves that the values of the implied volatility based on the same underlying asset vary with the underlying asset price, maturity date, time to maturity, and the strike price. Ronald Lagnado and Stanley Osher and Chiarella proposed the techniques for calibrating derivative pricing by solving an inverse problem. In this paper, an improved model is proposed. In which, the influence of the options with different strike prices is distinguished by weights and the choices of the weight functions are discussed. The approach we take is numerically solving an inverse problem which is more solid in theory than simple regression methods. Numerical results show that our model has better adaptivity and accuracy than traditional models.