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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.

Suggested Citation

  • Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
  • Handle: RePEc:eee:jbfina:v:32:y:2008:i:2:p:283-298
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Ferstl, Robert & Weissensteiner, Alex, 2011. "Asset-liability management under time-varying investment opportunities," Journal of Banking & Finance, Elsevier, vol. 35(1), pages 182-192, January.
    5. Weissensteiner, Alex, 2010. "Using the Black-Derman-Toy interest rate model for portfolio optimization," European Journal of Operational Research, Elsevier, vol. 202(1), pages 175-181, April.
    6. 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.
    7. Sorwar, Ghulam & Dowd, Kevin, 2010. "Estimating financial risk measures for options," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1982-1992, August.
    8. Consiglio, Andrea & Carollo, Angelo & Zenios, Stavros A., 2014. "Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization," Working Papers 13-35, University of Pennsylvania, Wharton School, Weiss Center.
    9. Câmara, António, 2009. "Two counters of jumps," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 456-463, March.
    10. 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.

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