Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options
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)...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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EconJournals
2016-10-01
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| Series: | International Journal of Economics and Financial Issues |
| Online Access: | https://www.econjournals.com/index.php/ijefi/article/view/2094 |
| _version_ | 1828026964348239872 |
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| author | Wajih Abbasi Petr Hájek Diana Ismailova Saira Yessimzhanova Zouhaier Ben Khelifa Kholnazar Amonov |
| author_facet | Wajih Abbasi Petr Hájek Diana Ismailova Saira Yessimzhanova Zouhaier Ben Khelifa Kholnazar Amonov |
| author_sort | Wajih Abbasi |
| collection | DOAJ |
| description |
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.
Keywords: Jump-diffusion; Kou model; Leptokurtic feature; Trust-region-reflective algorithm; US index options
JEL Classifications: C3; C8; G12; G13
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| first_indexed | 2024-04-10T13:27:41Z |
| format | Article |
| id | doaj.art-39af03d6e5b749909bc800a12c0091dc |
| institution | Directory Open Access Journal |
| issn | 2146-4138 |
| language | English |
| last_indexed | 2024-04-10T13:27:41Z |
| publishDate | 2016-10-01 |
| publisher | EconJournals |
| record_format | Article |
| series | International Journal of Economics and Financial Issues |
| spelling | doaj.art-39af03d6e5b749909bc800a12c0091dc2023-02-15T16:11:47ZengEconJournalsInternational Journal of Economics and Financial Issues2146-41382016-10-0164Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index OptionsWajih Abbasi0Petr Hájek1Diana Ismailova2Saira Yessimzhanova3Zouhaier Ben Khelifa4Kholnazar Amonov5College of Business and Economics, Qassim UniversityUnicorn College and Central Bohemia University, PragueAl-Farabi Kazakh National UniversityTurar Ryskulov New Economic UniversityECSTRA Center of Research on Economics and Finance, HEC CarthageCentral Bohemia University, Prague 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. Keywords: Jump-diffusion; Kou model; Leptokurtic feature; Trust-region-reflective algorithm; US index options JEL Classifications: C3; C8; G12; G13 https://www.econjournals.com/index.php/ijefi/article/view/2094 |
| spellingShingle | Wajih Abbasi Petr Hájek Diana Ismailova Saira Yessimzhanova Zouhaier Ben Khelifa Kholnazar Amonov Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options International Journal of Economics and Financial Issues |
| title | Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options |
| title_full | Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options |
| title_fullStr | Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options |
| title_full_unstemmed | Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options |
| title_short | Kou Jump Diffusion Model: An Application to the S&P 500; Nasdaq 100 and Russell 2000 Index Options |
| title_sort | kou jump diffusion model an application to the s p 500 nasdaq 100 and russell 2000 index options |
| url | https://www.econjournals.com/index.php/ijefi/article/view/2094 |
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