Abstract
The volatility is a crucial variable in option pricing and hedging strategies. The aim of this paper is to provide some initial evidence of the empirical relevance of genetic programming to volatility's forecasting. By using real data from S&P500 index options, the genetic programming's ability to forecast Black and Scholes-implied volatility is compared between time series samples and moneyness-time to maturity classes. Total and out-of-sample mean squared errors are used as forecasting's performance measures. Comparisons reveal that the time series model seems to be more accurate in forecasting-implied volatility than moneyness time to maturity models. Overall, results are strongly encouraging and suggest that the genetic programming approach works well in solving financial problems.
Highlights
The Black-Scholes BS formula 1 is commonly used to price derivative securities, it has some well-known deficiencies
Nine generated GP volatility models are selected for time series M1S1· · · M9S9 and nine generated GP volatility models are selected for moneyness-time to maturity classification M1C1· · · M9C9
To assess the internal and external accuracy of these generated GP volatility models, we use the MSE total computed for the enlarged sample and the MSE out-of-sample computed for external samples to the training one, as performance’s measures
Summary
The Black-Scholes BS formula 1 is commonly used to price derivative securities, it has some well-known deficiencies. Prior to the October 1987 stock market crash, there appeared to be symmetry around the zero moneyness, where in-the-money ITM or out-of-the-money OTM options have higher implied volatilities than at-the-money ATM options This dependency of implied volatility on the strike, for a given maturity, became known as the smile effect, the exact structure of volatility varied across markets and even within a particular market from day to day. Journal of Applied Mathematics and Decision Sciences such as S&P500 index options , where the symmetric smile pattern U-shape has changed to more of a sneer This is often referred to in the markets as the “volatility smirk,” where call option-implied volatilities are observed to decrease monotonically with strike price. This can arise when the market places a relatively greater probability on a downward price movement than an upward movement, resulting in a negatively skewed implied terminal asset distribution
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