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Pricing options on scenario trees

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  • Topaloglou, Nikolas
  • Vladimirou, Hercules
  • Zenios, Stavros A.

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 32 (2008)
Issue (Month): 2 (February)
Pages: 283-298

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Handle: RePEc:eee:jbfina:v:32:y:2008:i:2:p:283-298

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References

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  12. 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.
  13. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  14. 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.
  15. 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.
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Citations

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Cited by:
  1. Sorwar, Ghulam & Dowd, Kevin, 2010. "Estimating financial risk measures for options," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1982-1992, August.
  2. Ferstl, Robert & Weissensteiner, Alex, 2009. "Asset-Liability Management under time-varying Investment Opportunities," MPRA Paper 15068, University Library of Munich, Germany.
  3. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
  4. Cremers, Martijn & Driessen, Joost & Maenhout, Pascal & Weinbaum, David, 2008. "Individual stock-option prices and credit spreads," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2706-2715, December.
  5. Câmara, António & Krehbiel, Tim & Li, Weiping, 2011. "Expected returns, risk premia, and volatility surfaces implicit in option market prices," Journal of Banking & Finance, Elsevier, vol. 35(1), pages 215-230, January.
  6. Câmara, António, 2009. "Two counters of jumps," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 456-463, March.
  7. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Accounting for the impact of higher order moments in foreign equity option pricing model," Economic Modelling, Elsevier, vol. 28(4), pages 1726-1729, July.
  8. Sun, Qi & Dong, Yucheng & Xu, Weidong, 2013. "Effects of higher order moments on the newsvendor problem," International Journal of Production Economics, Elsevier, vol. 146(1), pages 167-177.

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