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Year 2016, Volume: 6 Issue: 4, 1918 - 1929, 01.09.2016

Abstract

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

Year 2016, Volume: 6 Issue: 4, 1918 - 1929, 01.09.2016

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 (SP500), Hi-Tech cap (Nasdaq100) and small cap (Russell2000). 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 Nasdaq100 and Russell2000 index options than for the SP500 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.

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Details

Other ID JA33BG27EN
Journal Section Research Article
Authors

Wajih Abbasi This is me

Petr Hájek This is me

Diana Ismailova This is me

Saira Yessimzhanova This is me

Zouhaier Ben Khelifa This is me

Kholnazar Amonov This is me

Publication Date September 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 4

Cite

APA Abbasi, W., Hájek, P., Ismailova, D., Yessimzhanova, S., et al. (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, 6(4), 1918-1929.
AMA Abbasi W, Hájek P, Ismailova D, Yessimzhanova S, Khelifa ZB, Amonov K. Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options. IJEFI. September 2016;6(4):1918-1929.
Chicago Abbasi, Wajih, Petr Hájek, Diana Ismailova, Saira Yessimzhanova, Zouhaier Ben Khelifa, and Kholnazar Amonov. “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 6, no. 4 (September 2016): 1918-29.
EndNote Abbasi W, Hájek P, Ismailova D, Yessimzhanova S, Khelifa ZB, Amonov K (September 1, 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 6 4 1918–1929.
IEEE W. Abbasi, P. Hájek, D. Ismailova, S. Yessimzhanova, Z. B. Khelifa, and K. Amonov, “Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options”, IJEFI, vol. 6, no. 4, pp. 1918–1929, 2016.
ISNAD Abbasi, Wajih et al. “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 6/4 (September 2016), 1918-1929.
JAMA Abbasi W, Hájek P, Ismailova D, Yessimzhanova S, Khelifa ZB, Amonov K. Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options. IJEFI. 2016;6:1918–1929.
MLA Abbasi, Wajih et al. “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, vol. 6, no. 4, 2016, pp. 1918-29.
Vancouver Abbasi W, Hájek P, Ismailova D, Yessimzhanova S, Khelifa ZB, Amonov K. Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options. IJEFI. 2016;6(4):1918-29.