Relevant bibliographies by topics / Double Exponential Jump-Diffusion

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  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Double Exponential Jump-Diffusion'

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Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Double Exponential Jump-Diffusion"

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Kou, S. G., and Hui Wang. "First passage times of a jump diffusion process." Advances in Applied Probability 35, no. 02 (June 2003): 504–31. http://dx.doi.org/10.1017/s0001867800012350.

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This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.
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Kou, S. G., and Hui Wang. "First passage times of a jump diffusion process." Advances in Applied Probability 35, no. 2 (June 2003): 504–31. http://dx.doi.org/10.1239/aap/1051201658.

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This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.
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3

Suzuki, Atsuo, and Katsushige Sawaki. "Game Russian Options for Double Exponential Jump Diffusion Processes." Journal of Mathematical Finance 04, no. 01 (2014): 47–54. http://dx.doi.org/10.4236/jmf.2014.41005.

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4

Zhou, Jiang, and Lan Wu. "Occupation times of refracted double exponential jump diffusion processes." Statistics & Probability Letters 106 (November 2015): 218–27. http://dx.doi.org/10.1016/j.spl.2015.07.023.

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Kou, S. G., and Hui Wang. "Option Pricing Under a Double Exponential Jump Diffusion Model." Management Science 50, no. 9 (September 2004): 1178–92. http://dx.doi.org/10.1287/mnsc.1030.0163.

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KUDRYAVTSEV, OLEG, and SERGEI LEVENDORSKIǏ. "PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 915–49. http://dx.doi.org/10.1142/s0219024906003834.

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We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.
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Wong, Hoi Ying, and Ka Yung Lau. "Analytical Valuation of Turbo Warrants under Double Exponential Jump Diffusion." Journal of Derivatives 15, no. 4 (May 31, 2008): 61–73. http://dx.doi.org/10.3905/jod.2008.707211.

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Liu, Yu-hong, I.-Ming Jiang, and Wei-tze Hsu. "Compound option pricing under a double exponential Jump-diffusion model." North American Journal of Economics and Finance 43 (January 2018): 30–53. http://dx.doi.org/10.1016/j.najef.2017.10.002.

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Ramezani, Cyrus A., and Yong Zeng. "Maximum likelihood estimation of the double exponential jump-diffusion process." Annals of Finance 3, no. 4 (November 3, 2006): 487–507. http://dx.doi.org/10.1007/s10436-006-0062-y.

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BOYARCHENKO, MITYA, and SVETLANA BOYARCHENKO. "DOUBLE BARRIER OPTIONS IN REGIME-SWITCHING HYPER-EXPONENTIAL JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1005–43. http://dx.doi.org/10.1142/s0219024911006620.

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We present a very fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential jump-diffusion (HEJD) models, which generalize the double-exponential jump-diffusion model pioneered by Kou and Lipton. Numerical tests demonstrate an excellent agreement of our results with those obtained using other methods, as well as a significant increase in computation speed (sometimes by a factor of 5). The first step of our approach is Carr's randomization, whose convergence we prove for barrier and double barrier options under strong Markov processes of a wide class. The resulting sequence of perpetual option pricing problems is solved using an efficient iteration algorithm and the Wiener-Hopf factorization.
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Dissertations / Theses on the topic "Double Exponential Jump-Diffusion"

1

Bu, Tianren. "Option pricing under exponential jump diffusion processes." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/option-pricing-under-exponential-jump-diffusion-processes(0dab0630-b8f8-4ee8-8bf0-8cd0b9b9afc0).html.

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The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models.
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2

Nadratowska, Natalia Beata, and Damian Prochna. "Option pricing under the double exponential jump-diffusion model by using the Laplace transform : Application to the Nordic market." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-5336.

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In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.

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Pszczola, Agnieszka, and Grzegorz Walachowski. "Testing for jumps in face of the financial crisis : Application of Barndorff-Nielsen - Shephard test and the Kou model." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-2872.

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The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying

asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.

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4

"Quanto options under double exponential jump diffusion." 2007. http://library.cuhk.edu.hk/record=b5893201.

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Lau, Ka Yung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (leaves 78-79).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Background --- p.5
Chapter 2.1 --- Jump Diffusion Models --- p.6
Chapter 2.2 --- Double Exponential Jump Diffusion Model --- p.8
Chapter 3 --- Option Pricing with DEJD --- p.10
Chapter 3.1 --- Laplace Transform --- p.10
Chapter 3.2 --- European Option Pricing --- p.13
Chapter 3.3 --- Barrier Option Pricing --- p.14
Chapter 3.4 --- Lookback Options --- p.16
Chapter 3.5 --- Turbo Warrant --- p.17
Chapter 3.6 --- Numerical Examples --- p.26
Chapter 4 --- Quanto Options under DEJD --- p.30
Chapter 4.1 --- Domestic Risk-neutral Dynamics --- p.31
Chapter 4.2 --- The Exponential Copula --- p.33
Chapter 4.3 --- The moment generating function --- p.36
Chapter 4.4 --- European Quanto Options --- p.38
Chapter 4.4.1 --- Floating Exchange Rate Foreign Equity Call --- p.38
Chapter 4.4.2 --- Fixed Exchange Rate Foreign Equity Call --- p.40
Chapter 4.4.3 --- Domestic Foreign Equity Call --- p.42
Chapter 4.4.4 --- Joint Quanto Call --- p.43
Chapter 4.5 --- Numerical Examples --- p.45
Chapter 5 --- Path-Dependent Quanto Options --- p.48
Chapter 5.1 --- The Domestic Equivalent Asset --- p.48
Chapter 5.1.1 --- Mathematical Results on the First Passage Time of the Mixture Exponential Jump Diffusion Model --- p.50
Chapter 5.2 --- Quanto Lookback Option --- p.54
Chapter 5.3 --- Quanto Barrier Option --- p.57
Chapter 5.4 --- Numerical results --- p.61
Chapter 6 --- Conclusion --- p.64
Chapter A --- Numerical Laplace Inversion for Turbo Warrants --- p.66
Chapter B --- The Relation Among Barrier Options --- p.69
Chapter C --- Proof of Lemma 51 --- p.71
Chapter D --- Proof of Theorem 5.4 and 5.5 --- p.74
Bibliography --- p.78
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5

"Double barrier option pricing for double exponential jump diffusion model." 2008. http://library.cuhk.edu.hk/record=b5896844.

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Bao, Zhenhua.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Literature Review --- p.5
Chapter 2.1 --- Review of the Models --- p.6
Chapter 2.1.1 --- Black-Scholes-Merton Model --- p.6
Chapter 2.1.2 --- Merton's Jump Diffusion Model --- p.8
Chapter 2.1.3 --- Stochastic Volatility Jump Diffusion Model --- p.10
Chapter 2.1.4 --- Constant Elasticity of Variance (CEV) Model --- p.13
Chapter 2.2 --- Kou´ةs Double Exponential Jump Diffusion Model --- p.16
Chapter 2.2.1 --- The Model Formulation --- p.16
Chapter 2.2.2 --- The Merits of the Model --- p.17
Chapter 2.2.3 --- Preliminary Results --- p.20
Chapter 2.2.4 --- Extant Results on Option Pricing under the Model --- p.21
Chapter 2.3 --- The Laplace Transform and Its Inversion --- p.24
Chapter 2.3.1 --- The Laplace Transform --- p.24
Chapter 2.3.2 --- One-dimensional Euler Laplace Transform Inversion Algorithm --- p.25
Chapter 2.3.3 --- Two-dimensional Euler Laplace Transform Inversion Algorithm --- p.28
Chapter 2.4 --- Monte Carlo Simulation for Double Exponential Jump Diffusion --- p.32
Chapter 3 --- Pricing Double Barrier Option via Laplace Transform --- p.34
Chapter 3.1 --- Double Barrier Option and the First Passage Time --- p.35
Chapter 3.2 --- Preliminary Results --- p.35
Chapter 3.3 --- Laplace Transform of the First Passage Time --- p.38
Chapter 3.4 --- Pricing Double Barrier Option via Laplace Transform --- p.50
Chapter 4 --- Numerical Results --- p.54
Chapter 5 --- Conclusion --- p.57
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6

Hsu, Wei-Tze, and 徐維澤. "Compound Option Pricing under a Double Exponential Jump-Diffusion Model." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/01758835014765166549.

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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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7

Lin, Yen-Chen, and 林彥誠. "The pricing of double barrier options under a mixed-exponential jump diffusion model." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/40797048587471285710.

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碩士
國立臺北大學
統計學系
101
This paper studies the prices of double barrier options under a mixed-exponential jump diffusion model, which consists of a continuous part driven by Borownian motion and a jump part with jump sizes having a mixed-exponential distribution.The mixed-exponential distribution can approximate any distribution in the sense of weak convergence, including various heavy-tailed distributions. Because of the capability of handling overshoot and undershoot under mixed-exponential jump diffusion process, an explicit form of the Laplace transform of the joint distribution of the first passage time and overshoot is derived.Base on this result, we obtain the double Laplace transform of the joint distribution of the first passage time and the asset price at the expiration date. Finally, we apply the two-side, two-dimensional Euler inversion algorithm to the Laplace transforms and hence the prices of the double barrier options are obtained.
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8

Chang, Wen-Chieh, and 張汶傑. "A Parisian option framework for corporate security valuation under the double exponential jump diffusion process." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/53484115834461724666.

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碩士
國立交通大學
財務金融研究所
98
After the worldwide financial crisis in 2007, credit risk of the company is getting vast attention not only from academic but also from people in practice. Specifically, many firms had good rating but suddenly default during the financial crisis. Hence, how to accurately model the default risk of the firm is a much more important issue nowadays. In this paper, we develop a more efficient numerical simulation method to value the corporate risky bond. Our model employs the structural approach for valuing corporate bonds under the double exponential jump diffusion process (Kou 2002). This approach has more flexibility in matching the empirical data than previous models. In addition, to make our model more realistic, we adopt the caution time setting, which is parallel to the Parisian option in option pricing, to model the bond safety covenant.
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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement." Thesis, 2010. http://hdl.handle.net/10012/5741.

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While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.
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Book chapters on the topic "Double Exponential Jump-Diffusion"

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Karimov, Azar. "Stock Prices Follow a Double Exponential Jump-Diffusion Model." In Contributions to Management Science, 37–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65009-8_5.

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Grudsky, S. M., and O. A. Mendez-Lara. "Double-Barrier Option Pricing Under the Hyper-Exponential Jump Diffusion Model." In Operator Theory and Harmonic Analysis, 197–217. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76829-4_10.

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Conference papers on the topic "Double Exponential Jump-Diffusion"

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Cerna, Dana. "Wavelet-Galerkin Method for Option Pricing under a Double Exponential Jump-Diffusion Model." In 2018 5th International Conference on Mathematics and Computers in Sciences and Industry (MCSI). IEEE, 2018. http://dx.doi.org/10.1109/mcsi.2018.00037.

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Chunfa Wang, Huang Haoran, Song Jing, and Zheng Huan. "Option pricing for a double exponential jump diffusion model with regime-switching using FFT." In 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC). IEEE, 2011. http://dx.doi.org/10.1109/aimsec.2011.6010387.

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Jin Hua, Liu Shancun, and Song Dianyu. "Pricing options in a mixed fractional double exponential jump-diffusion model with stochastic volatility and interest rates." In 2012 International Conference on Information Management, Innovation Management and Industrial Engineering (ICIII). IEEE, 2012. http://dx.doi.org/10.1109/iciii.2012.6339904.

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