Forecasting Volatility Using Interpolation and Numerical Methods

Forecasting volatility is important to financial asset pricing because a more accurate forecast will allow for a more accurate model to price financial assets. Currently the VIX is used as a measure of volatility in the market as a whole, but a major issue with this is that it is calculated based on manually traded options on the S\u26P 500. Another method of forecasting volatility is that of solving for volatility from the Black-Scholes model in option pricing, but this method is not consistent across prices; for different strike prices, a different volatility will be found, creating what is known as a volatility smile. I will develop a method which calculates a similar measure of volatility to the Black-Scholes method and the VIX, but using electronically traded options on the SPY ETF which tracks the S\u26P 500. I will also be incorporating the mathematical model developed by Britten-Jones and Neuberger in their 2000 paper, which is another variation from the method in which the VIX is calculated. The method developed will provide a smoother and more accurate forecast of volatility over any given time frame, with a 30 day forecast being the industry norm. The method will also have the ability to forecast volatilities for individual assets, not simply the whole market