Generalized Option Betas
Affiliation(s)
Department of Business Administration, European University Viadrina, Frankfurt, Germany. Griffith Business School, Griffith University, Nathan, Australia.
Department of Business Administration, European University Viadrina, Frankfurt, Germany. Griffith Business School, Griffith University, Nathan, Australia.
ABSTRACT
This paper extends the option betas presented by Cox and Rubinstein (1985) and Branger and Schlag (2007). In particular, we show how the beta of the underlying asset affects both an option’s covariance beta and its asset pricing beta. In contrast to Branger and Schlag (2007), the generalized option betas coincide if the options are evaluated according to the CAPM option pricing model of Husmann and Todorova (2011). The option betas are presented in terms of Black-Scholes option prices and are therefore easy to use in practice.
Cite this paper
S. Husmann and N. Todorova, "Generalized Option Betas," Journal of Mathematical Finance, Vol. 3 No. 3, 2013, pp. 347-356. doi: 10.4236/jmf.2013.33035.
S. Husmann and N. Todorova, "Generalized Option Betas," Journal of Mathematical Finance, Vol. 3 No. 3, 2013, pp. 347-356. doi: 10.4236/jmf.2013.33035.
References
[1] J. C. Cox and M. E. Rubinstein, “Options Markets,” Prentice-Hall, Englewood Cliffs, 1985. [2] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654. doi:10.1086/260062 [3] J. D. Coval and T. Shumway, “Expected Options Returns,” Journal of Finance, Vol. 56, No. 3, 2007, pp. 983-1009. doi:10.1111/0022-1082.00352 [4] A. Goyal and A. Saretto, “Cross-Section of Option Returns and Volatility,” Journal of Financial Economics, Vol. 94, No. 2, 2009, pp. 310-326. doi:10.1016/j.jfineco.2009.01.001 [5] S. X. Ni, “Stock Option Returns: A Puzzle,” Working Paper, Hong Kong University of Science and Technology, 2009. [6] N. Branger and C. Schlag, “Option Betas: Risk Measures for Options,” International Journal of Theoretical and Applied Finance, Vol. 10, No. 7, 2007, pp. 1137-1157. doi:10.1142/S0219024907004585 [7] S. Husmann and N. Todorova, “CAPM Option Pricing,” Finance Research Letters, Vol. 8, No. 4, 2011, pp. 213-219. doi:10.1016/j.frl.2011.03.001 [8] R. C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica, Vol. 41, No. 5, 1973, pp. 867-887. doi:10.2307/1913811 [9] R. C. Merton, “Theory of Finance from the Perspective of Continuous Time,” Journal of Financial and Quantitative Analysis, Vol. 10, No. 4, 1975, pp. 659-674. doi:10.2307/2330617 [10] R. A. Jarrow and D. B. Madan, “Is Mean-Variance Analysis Vacuous: Or Was Beta Still Born?” European Finance Review, Vol. 1, No. 1, 1997, pp. 15-30. doi:10.1023/A:1009779113922 [11] S. Husmann and A. Stephan, “On Estimating an Asset’s Implicit Beta,” Journal of Futures Markets, Vol. 27, No. 10, 2007, pp. 961-979. doi:10.1002/fut.20285 [12] D. B. Owen, “A Table of Normal Integrals,” Communications in Statistics—Simulation and Computation, Vol. 9, No. 4, 1980, pp. 389-419. doi:10.1080/03610918008812164 [13] M. E. Rubinstein, “A Simple Formula for the Expected Rate of Return of an Option over a Finite Holding Period,” Journal of Finance, Vol. 39, No. 5, 1984, pp. 1503-1509. doi:10.1111/j.1540-6261.1984.tb04920.x
[1] J. C. Cox and M. E. Rubinstein, “Options Markets,” Prentice-Hall, Englewood Cliffs, 1985. [2] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654. doi:10.1086/260062 [3] J. D. Coval and T. Shumway, “Expected Options Returns,” Journal of Finance, Vol. 56, No. 3, 2007, pp. 983-1009. doi:10.1111/0022-1082.00352 [4] A. Goyal and A. Saretto, “Cross-Section of Option Returns and Volatility,” Journal of Financial Economics, Vol. 94, No. 2, 2009, pp. 310-326. doi:10.1016/j.jfineco.2009.01.001 [5] S. X. Ni, “Stock Option Returns: A Puzzle,” Working Paper, Hong Kong University of Science and Technology, 2009. [6] N. Branger and C. Schlag, “Option Betas: Risk Measures for Options,” International Journal of Theoretical and Applied Finance, Vol. 10, No. 7, 2007, pp. 1137-1157. doi:10.1142/S0219024907004585 [7] S. Husmann and N. Todorova, “CAPM Option Pricing,” Finance Research Letters, Vol. 8, No. 4, 2011, pp. 213-219. doi:10.1016/j.frl.2011.03.001 [8] R. C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica, Vol. 41, No. 5, 1973, pp. 867-887. doi:10.2307/1913811 [9] R. C. Merton, “Theory of Finance from the Perspective of Continuous Time,” Journal of Financial and Quantitative Analysis, Vol. 10, No. 4, 1975, pp. 659-674. doi:10.2307/2330617 [10] R. A. Jarrow and D. B. Madan, “Is Mean-Variance Analysis Vacuous: Or Was Beta Still Born?” European Finance Review, Vol. 1, No. 1, 1997, pp. 15-30. doi:10.1023/A:1009779113922 [11] S. Husmann and A. Stephan, “On Estimating an Asset’s Implicit Beta,” Journal of Futures Markets, Vol. 27, No. 10, 2007, pp. 961-979. doi:10.1002/fut.20285 [12] D. B. Owen, “A Table of Normal Integrals,” Communications in Statistics—Simulation and Computation, Vol. 9, No. 4, 1980, pp. 389-419. doi:10.1080/03610918008812164 [13] M. E. Rubinstein, “A Simple Formula for the Expected Rate of Return of an Option over a Finite Holding Period,” Journal of Finance, Vol. 39, No. 5, 1984, pp. 1503-1509. doi:10.1111/j.1540-6261.1984.tb04920.x