Index Option Pricing via Nonparametric Regression

Abstract

Investors typically use the Black-Scholes (B-S) parametric model to value financial options. However, there is extensive empirical evidence that the B-S model, assuming constant volatility of stock returns, is far from adequate to price options. This paper, using nonparametric regression, incorporates a volatility-adjusting mechanism into the B-S model and prices options on the S&P 500 Index. Specifically, the upgraded B-S model, referred to as the B-S nonparametric model, is equipped with such a mechanism whose function is to assign larger volatilities for larger log returns and smaller volatilities for smaller log returns to characterize volatility clustering, a phenomenon such that large/small log returns tend to be followed by large/small log returns. Using the B-S nonparametric models as a yardstick, our simulation results show that, across the board, the B-S parametric model considerably overprices both call and put options.

Keywords

• Black-Scholes Parametric Model
• Black-Scholes Nonparametric Models
• Index Options
• Volatility
• Kernels