Compound Option Pricing under a Double Exponential Jump-Diffusion Model
碩士 === 國立成功大學 === 財務金融研究所 === 97 === This paper introduces the jump-diffusion process into pricing compound options and derives the related valuation formulas. We assume that the dynamic of the underlying asset return process consists of a drift component, a continuous Wiener process and discontinuo...
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ndltd-TW-097NCKU53040092016-05-04T04:17:32Z http://ndltd.ncl.edu.tw/handle/01758835014765166549 Compound Option Pricing under a Double Exponential Jump-Diffusion Model 雙指數跳躍擴散模型下之複合選擇權評價 Wei-Tze Hsu 徐維澤 碩士 國立成功大學 財務金融研究所 97 This paper introduces the jump-diffusion process into pricing compound options and derives the related valuation formulas. We assume that the dynamic of the underlying asset return process consists of a drift component, a continuous Wiener process and discontinuous jump-diffusion processes which have jump times that follow the compound Poisson process and the logarithm of jump size follows the double exponential distribution proposed by Kou (2002). Numerical results indicate that the advantage of combining the double exponential distribution and normal distribution is that it can capture the phenomena of both the asymmetric leptokurtic features and the volatility smile. In addition, in order to examine the effect of the jumps, we compare three European option call models and three compound option models with and without jumps, and we observe that the higher the jump frequency we set, the greater the option values we obtain. The numerical results also show that the European call option and compound option models with jumps can reduce to those models without jumps when the jump frequency is set to zero. Furthermore, the compound call option under the double exponential jump diffusion model which we derived is more generalized than Gukhal (2004) and Geske (1979), and thus has wider application. Yu-hong Liu 劉裕宏 2009 學位論文 ; thesis 80 en_US |
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碩士 === 國立成功大學 === 財務金融研究所 === 97 === This paper introduces the jump-diffusion process into pricing compound options and derives the related valuation formulas. We assume that the dynamic of the underlying asset return process consists of a drift component, a continuous Wiener process and discontinuous jump-diffusion processes which have jump times that follow the compound Poisson process and the logarithm of jump size follows the double exponential distribution proposed by Kou (2002). Numerical results indicate that the advantage of combining the double exponential distribution and normal distribution is that it can capture the phenomena of both the asymmetric leptokurtic features and the volatility smile. In addition, in order to examine the effect of the jumps, we compare three European option call models and three compound option models with and without jumps, and we observe that the higher the jump frequency we set, the greater the option values we obtain. The numerical results also show that the European call option and compound option models with jumps can reduce to those models without jumps when the jump frequency is set to zero. Furthermore, the compound call option under the double exponential jump diffusion model which we derived is more generalized than Gukhal (2004) and Geske (1979), and thus has wider application.
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Yu-hong Liu |
author_facet |
Yu-hong Liu Wei-Tze Hsu 徐維澤 |
author |
Wei-Tze Hsu 徐維澤 |
spellingShingle |
Wei-Tze Hsu 徐維澤 Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
author_sort |
Wei-Tze Hsu |
title |
Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
title_short |
Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
title_full |
Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
title_fullStr |
Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
title_full_unstemmed |
Compound Option Pricing under a Double Exponential Jump-Diffusion Model |
title_sort |
compound option pricing under a double exponential jump-diffusion model |
publishDate |
2009 |
url |
http://ndltd.ncl.edu.tw/handle/01758835014765166549 |
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