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Option pricing under a normal mixture distribution derived from the Markov tree model

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  • Bhat, Harish S.
  • Kumar, Nitesh

Abstract

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form expression for European call option prices. We also suggest a regression tree-based method for estimating three volatility parameters σ, σ+, and σ− required to apply the MT model. We apply the MT model to price call options on 89 non-dividend paying stocks from the S&P 500 index. For each stock symbol on a given day, we use the same parameters to price options across all strikes and expires. Comparing against the Black–Scholes model, we find that the MT model’s prices are closer to market prices.

Suggested Citation

  • Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:762-774
    DOI: 10.1016/j.ejor.2012.07.003
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Harish S. Bhat & Nitesh Kumar, 2015. "Large-Scale Empirical Tests of the Markov Tree Model," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 3(3), pages 1-39, July.
    2. Gradojevic Nikola, 2016. "Multi-criteria classification for pricing European options," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 123-139, April.
    3. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    4. Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.
    5. repec:eee:ejores:v:262:y:2017:i:1:p:381-400 is not listed on IDEAS

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