Pricing options on scenario trees
We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.
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- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- de Lange, Petter E. & Fleten, Stein-Erik & Gaivoronski, Alexei A., 2004. "Modeling financial reinsurance in the casualty insurance business via stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 991-1012, February.
- Jens Carsten Jackwerth., 1996.
"Recovering Risk Aversion from Option Prices and Realized Returns,"
Research Program in Finance Working Papers
RPF-265, University of California at Berkeley.
- Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
- Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
- M. A. H. Dempster & J. P. Hutton, 1999. "Pricing American Stock Options by Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 229-254.
- Rubinstein, Mark, 1985. " Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-80, June.
- Ait-Sahalia, Yacine & Lo, Andrew W., 2000.
"Nonparametric risk management and implied risk aversion,"
Journal of Econometrics,
Elsevier, vol. 94(1-2), pages 9-51.
- Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- M. A. H. Dempster & D. G. Richards, 2000. "Pricing American Options Fitting the Smile," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 157-177.
- Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
- J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
- Pieter Klaassen, 1998. "Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/Liability Management: A Synthesis," Management Science, INFORMS, vol. 44(1), pages 31-48, January.
- Christine A. Brown & David M. Robinson, 2002. "Skewness and Kurtosis Implied by Option Prices: A Correction," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 25(2), pages 279-282.
- Rosenberg, Joshua V. & Engle, Robert F., 2002.
"Empirical pricing kernels,"
Journal of Financial Economics,
Elsevier, vol. 64(3), pages 341-372, June.
- Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
- Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
- Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
- Hercules Vladimirou & Nikolas Topaloglou & Stavros A. Zenios, 2006. "A Stochastic Programming Framework for International PortfolioManagement," Computing in Economics and Finance 2006 404, Society for Computational Economics.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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