Constantinides, George M. and Jackwerth, Jens Carsten and Perrakis, Stylianos (2007): Option Pricing: Real and Risk-Neutral Distributions. Published in: Handbooks in Operations Research and Management Science: Financial Engineering , Vol. 15, : pp. 565-591.
Download (327kB) | Preview
The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.
|Item Type:||MPRA Paper|
|Original Title:||Option Pricing: Real and Risk-Neutral Distributions|
|English Title:||Option Pricing: Real and Risk-Neutral Distributions|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty|
|Depositing User:||Jens Jackwerth|
|Date Deposited:||24. Nov 2008 22:07|
|Last Modified:||19. May 2015 23:46|
Aït-Sahalia, Y., Lo, A. (1998). Nonparametric estimation of state price densities implicit in financial asset prices. Journal of Finance 53, 499–547.
Aït-Sahalia, Y., Lo, A. (2000). Nonparametric risk management and implied risk aversion. Journal of Econometrics 94, 9–51.
Amin, K.I. (1993). Jump diffusion option valuation in discrete time. Journal of Finance 48, 1833–1863.
Bates, D.S. (1991). The crash of ’87: Was it expected? The evidence from option markets. Journal of Finance 46, 1009–1044.
Bates, D.S. (2001). The market for crash risk. Working paper. University of Iowa, Iowa City.
Benzoni, L., Collin-Dufresne, P., Goldstein, R.S. (2005). Can standard preferences explain the prices of out-of-the-money S&P 500 options? Working paper.
University of Minnesota. Bergman, Y.Z., Grundy, B.D., Wiener, Z. (1996). General properties of option prices. The Journal of Finance 51, 1573–1610.
Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659.
Bliss, R.R., Panigirtzoglou, N. (2004). Option-implied risk aversion estimates. Journal of Finance 59, 407–446.
Bollen, N.,Whaley, R. (2004). Does net buying pressure affect the shape of implied volatility functions? Journal of Finance 59, 711–753.
Brown, D.P., Jackwerth, J. (2004). The kernel puzzle: Reconciling index option data and economic theory. Working paper. University of Wisconsin, Madison.
Constantinides, G.M. (1978).Market risk adjustment in portfolio valuation. Journal of Finance 33, 603– 616.
Constantinides, G.M. (1979). Multiperiod consumption and investment behavior with convex transactions costs. Management Science 25, 1127–1137.
Constantinides,G.M., Perrakis, S. (2002). Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs. Journal of Economic Dynamics and Control 26, 1323–1352.
Constantinides, G.M., Perrakis, S. (2007). Stochastic dominance bounds on American option prices in markets with frictions. Review of Finance 11, 71–115. Constantinides, G.M., Zariphopoulou, T. (1999). Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences. Finance and Stochastics 3, 345–369.
Constantinides, G.M., Zariphopoulou, T. (2001). Bounds on derivative prices in an intertemporal setting with proportional transaction costs and multiple securities. Mathematical Finance 11, 331–346.
Constantinides G.M., Czerwonko M., Jackwerth J., Perrakis S. (2007). Are options on index futures profitable for risk averse investors? Empirical Evidence. Working paper. University of Chicago, Chicago.
Constantinides, G.M., Jackwerth, J., Perrakis, S. (2007). Mispricing of S&P 500 index options. Review of Financial Studies, in press.
Cox, J., Ross, S.A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics 3, 145–166.
Cox, J., Ross, S.A., Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics 7, 229–263.
Delbaen, F., Schachermayer,W. (1994). A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463–520.
Engle, R.F., Gonzalez-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics 9/4, 345–359.
Garcia, R., Luger, R., Renault, E. (2003). Empirical assessment of an intertemporal option pricing model with latent variables. Journal of Econometrics 116, 49–83.
Han, B. (2004). Limits of arbitrage, sentiment and index option smile. Working paper. Ohio State University.
Harrison, J.M., Kreps, D.M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20, 381–408.
Harrison, J.M., Pliska, S.R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications 11, 215–260.
Huang, J. (2005). Option bounds and second order arbitrage opportunities. Working paper. Lancaster University.
Hull, J.C. (2006). Options, Futures, and Other Derivatives. Prentice Hall.
Jackwerth, J. (2000). Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433–451.
Jackwerth, J. (2004). Option-implied risk-neutral distributions and risk aversion. ISBN 0-943205-66-2, Research Foundation of AIMR, Charlotteville, USA.
Jackwerth, J., Rubinstein, M. (1996). Recovering probability distributions from option prices. Journal of Finance 51, 1611–1631.
Levy, H. (1985). Upper and lower bounds of put and call option value: Stochastic dominance approach. Journal of Finance 40, 1197–1217.
Liu, J., Pan, J., Wang, T. (2005). An equilibrium model of rare-event premia and its implications for option smirks. Review of Financial Studies 18, 131–164.
McDonald, R.L. (2005). Derivatives Markets. Addison–Wesley. Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184.
Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125–144.
Merton, R.C. (1982). On the mathematics and economics assumptions of continuous-time models. In: Essays in Honor of Paul Cootner. Prentice Hall, Englewood Cliffs, NJ.
Oancea, I., Perrakis, S. (2006). Stochastic dominance and option pricing: An alternative paradigm. Working paper. Concordia University.
Pan, J. (2002). The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics 63, 3–50.
Perrakis, S. (1986). Option bounds in discrete time: Extensions and the pricing of the American put. Journal of Business 59, 119–141. Perrakis, S., Ryan, P.J. (1984). Option pricing bounds in discrete time. Journal of Finance 39, 519–525.
Rendleman, R., Bartter, B. (1979). Two-state option pricing. Journal of Finance 34, 1092–1110.
Ritchken, P.H. (1985). On option pricing bounds. Journal of Finance 40, 1219–1233.
Ritchken, P.H., Kuo, S. (1988). Option bounds with finite revision opportunities. Journal of Finance 43, 301–308.
Rosenberg, J., Engle, R. (2002). Empirical pricing kernels. Journal of Financial Economics 64, 341–372. Ross, S.A. (1976). Options and efficiency. Quarterly Journal of Economics 90, 75–89.
Rubinstein, M. (1994). Implied binomial trees. Journal of Finance 3, 771–818.
Ryan, P.J. (2000). Tighter option bounds from multiple exercise prices. Review of Derivatives Research 4 (2), 155–188.
Ryan, P.J. (2003). Progressive option bounds from the sequence of concurrently expiring options. European Journal of Operational Research 151, 193–223.
Santa-Clara, P., Yan, S. (2004). Jump and volatility risk and risk premia: A new model and lessons from S&P 500 options. Working paper. UCLA.
Shefrin, H. (2005). A Behavioral Approach to Asset Pricing. Elsevier/North-Holland, Amsterdam.
Whaley, R.E. (2003). Derivatives. In: Constantinides, G.M., Harris, M., Stulz, R. (Eds.), Financial Markets and Asset Pricing: Handbook of the Economics of Finance, vol. 1B. In: Handbooks in Economics, vol. 21. Elsevier/North-Holland, Amsterdam.