Warrant Pricing: Jump-Diffusion vs. Black-Scholes

This paper investigates the warrant pricing abilities of dilution-adjusted versions of the Black-Scholes and Jump-Diffusion option pricing models. Because of the typically long lives of warrants, their pricing is hypothesized to benefit from use of the Jump-Diffusion model, which relaxes the Black-Scholes restriction against stock price jumps. Empirical results indicate that while the Black-Scholes model almost uniformly provides more efficient estimates, the Jump-Diffusion model generally provides less biased estimates of market value. Particularly for the valuation of out-of-the-money warrants and warrants on stocks with a history of large and/or frequent jumps, the Jump-Diffusion model may be preferred.

[1]  Using Jump-Diffusion Return Models to Measure Differential Information by Firm Size , 1986 .

[2]  Robert E. Whaley,et al.  On the valuation of American call options on stocks with known dividends , 1981 .

[3]  H. Glejser.  A New Test for Heteroskedasticity , 1969 .

[4]  Frederic P. Sterbenz,et al.  Warrant Exercise, Dividends, and Reinvestment Policy , 1988, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[5]  Michael G. Ferri,et al.  Investor expectations about callable warrants , 1988 .

[6]  S. Beckers.  A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns , 1981, Journal of Financial and Quantitative Analysis.

[7]  Eduardo S. Schwartz.  The valuation of warrants: Implementing a new approach , 1977 .

[8]  Dan Galai,et al.  PRICING OF WARRANTS AND THE VALUE OF THE FIRM , 1978 .

[9]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[10]  Variances and Option Prices in Theory and Practise* , 1978 .

[11]  D. C. Leonard,et al.  ON USING THE BLACK-SCHOLES MODEL TO VALUE WARRANTS , 1990 .

[12]  G. Constantinides.  Warrant Exercise and Bond Conversion in Competitive Markets , 1984, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[13]  R. Roll,et al.  An analytic valuation formula for unprotected American call options on stocks with known dividends , 1977 .

[14]  J. G. Hunt,et al.  WARRANT PRICING AND EXERCISE STRATEGIES: AN EMPIRICAL TEST USING COMMON STOCK UNITS , 1985 .

[15]  L. Ott,et al.  Statistics: A Tool for the Social Sciences , 1975 .

[16]  Ian A. Cooper,et al.  ESTIMATION AND USES OF THE TERM STRUCTURE OF INTEREST RATES , 1976 .

[17]  R. C. Merton,et al.  The impact on option pricing of specification error in the underlying stock price returns , 2011 .

[18]  J. A. Miles,et al.  The Use of Warrants in the Bail out of First Pennsylvania Bank: An Application of Option Pricing , 1982 .

[19]  W. Sterk.  Comparative Performance of the Black-Scholes and Roll-Geske-Whaley Option Pricing Models , 1983, Journal of Financial and Quantitative Analysis.

[20]  Maurice G. Kendall.  The advanced theory of statistics , 1958 .

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

[22]  J. V. Jordan,et al.  Tax Effects in Term Structure Estimation , 1984 .

[23]  S. James Press,et al.  A Compound Events Model for Security Prices , 1967 .

[24]  R. Geske,et al.  A note on an analytical valuation formula for unprotected American call options on stocks with known dividends , 1979 .

[25]  Beni Lauterbach,et al.  Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives , 1990 .

[26]  David C. Emanuel.  Warrant Valuation and Exercise Strategy , 1983, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[27]  Eric W. Noreen,et al.  Equilibrium Warrant Pricing-Models And Accounting For Executive Stock-Options , 1981 .

[28]  M. Rubinstein..  Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .