Warrants pricing: Stochastic volatility vs. Black-Scholes

Abstract This study investigates the stochastic volatility option pricing model of Hull and White [Journal of Finance 42 (1987) 281]. In particular, this study examines the out-of-sample performance of the pricing model applied to the valuation of covered warrants traded on the Taiwan Stock Exchange (TSE). Warrant values from Hull and White's stochastic volatility model and those from the Black–Scholes model are compared with observed option premiums. Pricing biases related to warrant strike price, time to maturity, volatility, and risk-free interest rate are also considered in this study. Empirical results indicate that the HW model with implied volatility outperforms others in predicting the warrant prices, indicating that the pricing model incorporated with stochastic volatility feature can improve the pricing of warrants. In addition, the pricing errors are systematically related to the degree to which the warrants are in-the-money, and the volatility of the underlying assets.

[1]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[2]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[3]  Daniel B. Nelson.  ARCH models as diffusion approximations , 1990 .

[4]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[5]  Christopher G. Lamoureux,et al.  Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities , 1993 .

[6]  V. Akgiray.  Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts , 1989 .

[7]  Donald P. Chiras,et al.  The information content of option prices and a test of market efficiency , 1978 .

[8]  Louis O. Scott.  Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application , 1987, Journal of Financial and Quantitative Analysis.

[9]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[10]  Richard J. Rendleman,et al.  STANDARD DEVIATIONS OF STOCK PRICE RATIOS IMPLIED IN OPTION PRICES , 1976 .

[11]  S. Beckers.  The Constant Elasticity of Variance Model and Its Implications For Option Pricing , 1980 .

[12]  E. Stein,et al.  Stock Price Distributions with Stochastic Volatility: An Analytic Approach , 1991 .

[13]  F. Black,et al.  The Valuation of Option Contracts and a Test of Market Efficiency , 1972 .

[14]  R. Officer.  The Variability of the Market Factor of the New York Stock Exchange. , 1973 .

[15]  James B. Wiggins.  Option values under stochastic volatility: Theory and empirical estimates , 1987 .

[16]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[17]  Lucille S. Mayne.  SUPERVISORY INFLUENCE ON BANK CAPITAL , 1972 .

[18]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .

[19]  Tie Su,et al.  An empirical test of the Hull‐White option pricing model , 1998 .

[20]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[21]  S. Chu,et al.  Volatility estimation for stock index options: A GARCH approach , 1996 .