PRICES OF WARRANTS IN THE SINGAPORE STOCK MARKET : AN EMPIRICAL STUDY OF THE CONSTANT ELASTICITY OF VARIANCE MODEL

Abstract

Many studies on the valuation of derivative securities and liabilities are inspired by the seminal contribution of Black and Scholes (1973). In the area of warrant valuation, Galai and Schneller (1978) rigorously provides a modification to the Black-Scholes (BS) Call Option valuation to price warrants.

However, as warrants have longer life than calls, the constant variance assumption of equity returns may not hold well for warrant pricing. This study relaxes the constant variance assumption and introduces a richer model to capture a non-constant variance of equity returns.

In this study, we utilize the Constant Elasticity of Variance (CEV) model of Cox and Ross (1976) that incorporates an inverse relationship between the variance of equity returns and the value of the firm. The "inverse relationship" has been observed and documented by many studies. (Black, 1975; Beckers, 1981) Preliminary investigation on selected stocks traded on the Singapore stock market in this study verifies the existence of such an "inverse relationship”.

We use two different estimates of the variance of equity returns for our CEV model - historical variance and implied standard deviation (ISD). Our results show that using historical variance, the CEV model improves only marginally over the BS model with respect to how close the theoretical prices are to the observed prices. However, using the implied standard deviation, we show that there is a significant improvement. Thus our study confirms to other studies that show that the ISDs are the best predictor of expected volatility of stock's price. (Latane and Rendleman, 1976; Schmalensee and Trippi, 1978)