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Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options

Author

Listed:
  • Wajih Abbasi

    (College of Business and Economics, Qassim University, Saudi Arabia,)

  • Petr H jek

    (Unicorn College and Central Bohemia University, Prague, The Czech Republic,)

  • Diana Ismailova

    (Kokshetau University Named after Abai Myrzakhmetov, Kazakhstan,)

  • Saira Yessimzhanova

    (Narxoz University, Kazakhstan,)

  • Zouhaier Ben Khelifa

    (ECSTRA Center of Research on Economics and Finance, HEC Carthage, Tunisia)

  • Kholnazar Amonov

    (Central Bohemia University, Prague, The Czech Republic.)

Abstract

This research focuses on the empirical comparative analysis of three models of option pricing: (a) The implied volatility daily calibrated Black Scholes model, (b) the Cox and Ross univariate model with the volatility which is a deterministic and inverse function of the underlying asset price and (c) the Kou jump diffusion model. To conduct the empirical analysis, we use a diversified sample with options written on three US indexes during 2007: Large cap (Standard and Poor 500 [SP 500]), Hi-Tech cap (Nasdaq 100) and small cap (Russell 2000). For the estimation of models parameters, we opted for the data-fitting technique using the trust region reflective algorithm on option prices, rather than the more common maximum likelihood or generalized method of moments on the history of the underlying asset. The analysis that we conducted clearly shows the supremacy of Kou model. We also notice that it provided better results for the Nasdaq 100 and Russell 2000 index options than for the SP 500 ones. Actually, this supremacy comes from the ability of this model to be as close as possible of market participant's behavior thanks to its double exponential distribution characterized by three main properties: (a) Leptokurtic feature, (b) psychological specificity of investors and (c) memory-less feature.

Suggested Citation

  • Wajih Abbasi & Petr H jek & Diana Ismailova & Saira Yessimzhanova & Zouhaier Ben Khelifa & Kholnazar Amonov, 2016. "Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1918-1929.
    • Handle: RePEc:eco:journ1:2016-04-83
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    References listed on IDEAS

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    More about this item

    Keywords

    Jump-diffusion; Kou Model; Leptokurtic Feature; Trust-Region-Reflective Algorithm; US Index Options;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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