Forecasting Performance of Constant Elasticity of Variance Model: Empirical Evidence from India

This study tested the forecasting performance of Constant Elasticity of Variance (CEV) and benchmark Black-Scholes (BS) option pricing model for pricing S&P CNX Nifty 50 Index options of India. This study adopts a common method of evaluating the performance of an option pricing model that involves calculating the error metrics, Percentage Mean Error (PME) and Mean Absolute Percentage Error (MAPE). For the purpose of this research we used the Non-Linear Least Square (NLLS) loss function to imply option-related parameters while estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset option data and placed options in one of 15 moneyness-maturity groups. The optimal set of parameters is then used to compute the models price. The prices are compared analytically by updating the parameters of two models continuatiously by using cross-sectional option data almost every day. Aim of this study is to first find out parameters of two models analytically then to show that the parameters of the models estimated from option prices can be used to produce reliable predictions of the day-ahead relationship between option prices and index volatility. Constant Elasticity of Variance model, introducing only one more parameter compared with Black-Scholes formula, improves the performance notably in 9 out of 15 PME and 12 out of 15 MAPE moneyness-maturity groups and also increases the stability of implied volatility. Therefore, with much less implementational cost and faster computational speed, the CEV option pricing model can be a better candidate than Black-Scholes model. JEL Classification: C01, C13, C52, C53, G17.