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Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

Mingjia Li
2017 Open Journal of Statistics  
This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option; numerical calculation method is used to approximate the continuous  ...  Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming.  ...  In [10] , Ahmadian and Ballestra found it also performs well under a constant elasticity of variance model with jump diffusion.  ... 
doi:10.4236/ojs.2017.73032 fatcat:qby3qxxcqnhx3mdjiw3l5bzqda

Semi-discretization Algorithm for Option Pricing in CEV Jump-diffusion Model

2016 Revista Técnica de la Facultad de Ingeniería Universidad del Zulia  
This paper proposes an option pricing technique we developed to approximate hedge jump risk under a CEV jumpdiffusion model.  ...  Finally, we verified the model's stability, convergence and effectiveness through numerical experiments on a simulated pricing option scenario.  ...  option pricing problem under a discrete time jump-diffusion model.  ... 
doi:10.21311/001.39.3.7 fatcat:depkyglydff67fs2peyepclg4u

Empirical performance of models for barrier option valuation

Cathrine Jessen, Rolf Poulsen
2013 Quantitative finance (Print)  
For barrier options, the continuous-path models (Black-Scholes, constant elasticity of variance, and Heston) do almost equally well, while both models with jumps (Merton and Variance Gamma) perform markedly  ...  In this paper the empirical performance of five different models for barrier option valuation is investigated: the Black-Scholes model, the constant elasticity of variance model, the Heston stochastic  ...  We work with five popular, yet qualitatively different parametric models: the Black-Scholes model, the constant elasticity of variance model, the Heston stochastic volatility model, the Merton jump-diffusion  ... 
doi:10.1080/14697688.2012.723820 fatcat:ux3wen34hza3bbtxn5hxxdv5ei

Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options

Ning Cai, Nan Chen, Xiangwei Wan
2010 Mathematics of Operations Research  
Kou's double exponential jump diffusion model.  ...  In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under  ...  The authors are also grateful to Prof. Vadim Linetsky of Northwestern University, USA; Prof. S. G. Kou  ... 
doi:10.1287/moor.1100.0447 fatcat:nvjsr27tqvho7jljykm7nad5he

Option Pricing Under A Double Exponential Jump Diffusion Model

Steven G. Kou, Hui NMI1 Wang
2001 Social Science Research Network  
We demonstrate that a double exponential jump diffusion model can lead to an analytic approximation for finite-horizon American options (by extending the Barone-Adesi and Whaley method) and analytical  ...  The aim of this paper is to extend the analytical tractability of the Black-Scholes model to alternative models with jumps.  ...  that reduce the discretization bias in Monte Carlo pricing of barrier options under jump diffusion models.  ... 
doi:10.2139/ssrn.284202 fatcat:wnulsrisbzcx5ov4ncptwe4y2y

Option Pricing Under a Double Exponential Jump Diffusion Model

S. G. Kou, Hui Wang
2004 Management science  
We demonstrate that a double exponential jump diffusion model can lead to an analytic approximation for finite-horizon American options (by extending the Barone-Adesi and Whaley method) and analytical  ...  The aim of this paper is to extend the analytical tractability of the Black-Scholes model to alternative models with jumps.  ...  that reduce the discretization bias in Monte Carlo pricing of barrier options under jump diffusion models.  ... 
doi:10.1287/mnsc.1030.0163 fatcat:g5d6yawvxbh3zp6csramz2mvpm

Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering [chapter]

S.G. Kou
2007 Handbooks in Operations Research and Management Science  
with jump risk. (6) Multivariate jump-diffusion models.  ...  a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as barrier  ...  (e) Constant elasticity of variance (CEV) model; see, for example, Cox and Ross (1976) and Davydov and Linetsky (2001) .  ... 
doi:10.1016/s0927-0507(07)15002-7 fatcat:f63ntrs6pfhaxdyk7kda47trpy

A canonical optimal stopping problem for American options under a double exponential jump-diffusion model

Farid AitSahlia, Andreas Runnemo
2007 Journal of Risk  
This paper presents a simple numerical approach to compute accurately the values and optimal exercise boundaries for American options when the underlying process is a double exponential jump-diffusion  ...  Here, too, jump-diffusion pricing models can be reduced to a single optimal stopping problem, indexed by one more parameter, and linear spline approximations of the stopping boundary in the canonical scale  ...  In this paper, we develop a simple numerical method to price accurately finitelived American options using the aforementioned model.  ... 
doi:10.21314/jor.2007.154 fatcat:fiakcrdakfgojpnk65ok5eyyly

Exact Simulation of Occupation Times [chapter]

Roman N. Makarov, Karl Wouterloot
2012 Monte Carlo and Quasi-Monte Carlo Methods 2010  
The simulation methods are applied to pricing occupation time derivatives and quantile options under the double-exponential jump-diffusion process and the constant elasticity of variance (CEV) diffusion  ...  A novel algorithm for the exact simulation of occupation times for Brownian processes and jump-diffusion processes with finite jump intensity is constructed.  ...  Acknowledgements The first author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) for a Discovery Research Grant.  ... 
doi:10.1007/978-3-642-27440-4_33 fatcat:w4od3fgwsnaqrhaqgtq7hrmgnm

A General Framework for Pricing Asian Options Under Markov Processes

Ning Cai, Yingda Song, Steven Kou
2015 Operations Research  
Numerical experiments indicate that our pricing method is accurate and fast under popular Markov process models, including the CIR model, the CEV model, Merton's jump diffusion model, the double-exponential  ...  jump diffusion model, the variance gamma model, and the CGMY model.  ...  Lévy models, stochastic volatility models, and the constant elasticity of variance (CEV) model.  ... 
doi:10.1287/opre.2015.1385 fatcat:jz7jr4wd4rfzzawmwykgaob5pi

A Jump-Diffusion Model for Option Pricing

S. G. Kou
2002 Management science  
To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model.  ...  In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and pathdependent options.  ...  Acknowledgments This paper was previously titled "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability."  ... 
doi:10.1287/mnsc.48.8.1086.166 fatcat:xx6mnjvjifeztgal7wcocpfyom

A Jump Diffusion Model For Option Pricing

Steven G. Kou
2000 Social Science Research Network  
To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model.  ...  In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and pathdependent options.  ...  Acknowledgments This paper was previously titled "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability."  ... 
doi:10.2139/ssrn.242367 fatcat:jue6fsavvvfopfq5az6mwhh4ce

Pricing Exotic Discrete Variance Swaps under the 3/2-Stochastic Volatility Models

Chi Hung Yuen, Wendong Zheng, Yue Kuen Kwok
2015 Applied Mathematical Finance  
We consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor variance swaps, under the 3/2-stochastic volatility models with jumps in asset price.  ...  Pricing properties of these exotic discrete variance swaps with respect to various model parameters are explored.  ...  We also thank the funding support of the Hong Kong Grants Council under Project 642110 of the General Research Funds.  ... 
doi:10.1080/1350486x.2015.1050525 fatcat:h2kk52ihzfh3jdkj6rng77rmpu

Laplace Transform Method for Pricing American CEV Strangles Option with Two Free Boundaries

Zhiqiang Zhou, Hongying Wu
2018 Discrete Dynamics in Nature and Society  
The aim of this paper is to develop a Laplace transform method for pricing American Strangles options with the underlying asset price following the constant elasticity volatility (CEV) models.  ...  Laplace transform method (LTM) has a lot of applications in the evaluation of European-style options and exotic options without early exercise features.  ...  Authors' Contributions Hongying Wu carried out the experiments in Section 4 and Zhiqiang Zhou made the main contributions to the Acknowledgments The work was supported by Natural Science Foundation of  ... 
doi:10.1155/2018/5908646 fatcat:skpcfkkx6zcxho42niyckcduku

Closed-Form Approximate Solutions of Window Barrier Options with Term-Structure Volatility and Interest Rates Using the Boundary Integral Method

Yi-Long Hsiao
2012 Journal of Mathematical Finance  
Figlewski and Gao [14] used the adaptive mesh model to discuss option pricing. Albert, Fink, Fink [15] priced barrier options using an adaptive mesh model under a jump-diffusion process.  ...  Boyle and Tian [18] proposed a modified explicit finite difference approach to the valuation of barrier options, but their method is not particularly efficient in dealing with discrete barrier option pricing  ...  Since Merton [2] first derived the analytical closed-barrier option pricing under the constant elasticity of variance (CEV) process.  ... 
doi:10.4236/jmf.2012.24032 fatcat:3so54omcrvadnevtfo3m5mluvy
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