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&P 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&P 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.