On CAPM and Black-Scholes, differing risk-return strategies

McCauley, Joseph L. and Gunaratne, Gemunu H. (2003): On CAPM and Black-Scholes, differing risk-return strategies. Published in: Physica A , Vol. 329, (0203): pp. 170-177.

Abstract

In their path-finding 1973 paper Black and Scholes presented two separate derivations of their famous option pricing partial differential equation (pde). The second derivation was from the standpoint that was Black’s original motivation, namely, the capital asset pricing model (CAPM). We show here, in contrast, that the option valuation is not uniquely determined; in particular, strategies based on the delta-hedge and CAPM provide different valuations of an option although both hedges are instantaneouly riskfree. Second, we show explicitly that CAPM is not, as economists claim, an equilibrium theory.

• Item Type: MPRA Paper
• Additional Information: We correct an error in the original black-Scholes paper, and emphasize that CAPM (i) is not an 'equilibrium' model, and (ii) no particular distribution is required for CAPM, the only requirement is that the variance is finite.
• Institution: University of Houston
• Language: English
• Keywords: Capital asset pricing model (CAPM); nonequilibrium; financial markets; Black-Scholes; option pricing strategies
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C65 - Miscellaneous Mathematical Tools

References

1. W.F. Sharpe, J. Finance XIX (1964) 425. 2. F. Black, J. Portfolio Management 4 (1989)1. 3. Z. Bodie, Z., R.C. Merton, Finance, Prentice-Hall, Saddle River, N.J., 1998. 4. J. L. McCauley, Physica A285 (2000) 506. 5. H.R. Varian, Microeconomics, Norton, N.Y., 1992. 6. P. Gopikrishnan, B. Rosenow, V. Plerou, H.E. Stanley, Phys. Rev. E64 (2001); B. Rosenow, V. Plerou, P. Gopikrishnan, P., H.E. Stanley, Portfolio Optimization and the Random Magnet Problem, (preprint, 2001) 7. F. Black, M. Scholes, J. Political Economy 81 (1973) 637. 8. M.F.M. Osborne, in P. Cootner, (Ed.), The Random Character of Stock Market Prices, MIT, Cambridge, 1964. 9. N. Wax (ed.), Selected Papers on Noise and Stochastic Processes, Dover, N.Y., 1954. 10. M. Baxter, A. Rennie, Financial Calculus, Cambridge, Cambridge, 1996. 11. J. Hull, Options, Futures, and Other Derivatives, Prentice-Hall, Saddle river, N.J., 1997. 12. H. Föllmer in S. Howison, P.R. Kelly, P. Wilmott, (editors) Mathematical Models in Finance, Chapman & Hall, London, 1995. 13. J. L. McCauley, Physica A237 (1997) 387; Discrete Dynamical Systems in Nature and Society 1 (1997) 17.