Implied Volatility Model with Index Parameter

In the widely used Black-Scholes pricing model, the volatility is assumed to be a fixed constant. However, more and more empirical analyses have proved this assumption is incorrect in the real option market, the implied volatility has two key features: volatility smile and term structure. This paper modifies the deterministic implied volatility model proposed by Cassese and Guidolin, it deems implied volatility is not necessarily the quadratic function of moneyness and replaces the quadratic term of moneyness with an index parameter term. With the modified model some empirical analyses based on AAPL stock option are carried out. The experimental results show that the modified model is more flexible and has a better fitting and forecasting ability.