Download or read book Affine POD Galerkin Schemes for Option Pricing in Jump diffusion Models written by Jianjie Lu and published by . This book was released on 2014 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Option Pricing for an Affine Jump Diffusion Model written by Zhiqiu Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of this thesis, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion (AJD) model. Let log stock price under risk-neutral measure follow an AJD model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work. In the second part of this thesis, we study the European option pricing problem when the underlying stock follows an AJD model whose jump interarrival time has a Cox-Ingersoll-Ross type intensity dynamics. An analytic formula of a European option pricing is derived using the Fourier inversion transform technique. We develop a Monte Carlo algorithm to simulate the dynamics of an AJD model. We observe AJD At-The-Money (ATM) European option prices using the Monte Carlo simulation converge to the Fourier analytic ones as the number of simulation paths increases.
Download or read book A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Levy Models written by Rama Cont and published by . This book was released on 2004 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Levy process or, more generally, a time-inhomogeneous jump-diffusion process. We discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the Levy measure. We propose an explicit-implicit time-stepping scheme to solve the equation and study stability and convergence of the schemes proposed, using the notion of viscosity solution. Numerical tests are performed for the Merton jump-diffusion model and for the Variance Gamma model with smooth and non-smooth payoff functions. Our scheme can be used for European and barrier options, applies in the case of pure-jump models or degenerate diffusion coefficients, and extends to time-dependent coefficients.
Download or read book Essays on Empirical Performance of Affine Jump diffusion Option Pricing Models written by Xiang Zhang and published by . This book was released on 2012 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Jump diffusion Models written by Alexander Pitkin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust and Efficient IMEX Schemes for Option Pricing Under Jump Diffusion Models written by Santtu Salmi and published by . This book was released on 2013 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint family is absolutely stable only for c = 0, while the IMEX-CNAB and the IMEX-BDF2 families are absolutely stable for all c ∈ [0, 1]. The IMEX-CNAB c = 0 scheme produced the smallest error in our numerical experiments.
Download or read book Pricing Options in Jump Diffusion Models written by Liming Feng and published by . This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integro-differential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) term is treated explicitly. In particular, the popular IMEX Euler scheme is first order accurate in time. Second order accuracy in time can be achieved by using the IMEX midpoint scheme. In contrast to the above approaches, we propose a new high-order time discretization scheme for the PIDE based on the extrapolation approach to the solution of ODEs, that also treats the diffusion term implicitly and the jump term explicitly. The scheme is simple to implement, can be added to any PIDE solver based on the IMEX Euler scheme, and is remarkably fast and accurate. We demonstrate our approach on the examples of Merton's and Kou's jump-diffusion models, diffusion-extended Variance Gamma model, as well as the two-dimensional Duffie-Pan-Singleton model with correlated and contemporaneous jumps in the stock price and its volatility. By way of example, pricing a one-year double-barrier option in Kou's jump-diffusion model, our scheme attains accuracy of $10^{-5}$ in 72 time steps (in 0.05 seconds). In contrast, it takes the first-order IMEX Euler scheme more than 1.3 million time steps (in 873 seconds) and the second-order IMEX midpoint scheme 768 time steps (in 0.49 seconds) to attain the same accuracy. Our scheme is also well suited for Bermudan options. Combining simplicity of implementation and remarkable gains in computational efficiency, we expect this method to be very attractive to financial engineering modelers.
Download or read book Pricing European Style Options Under Jump Diffusion Processes with Stochastic Volatility written by Artur Sepp and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jump-diffusions. We provide a broad description of the issues and a detailed summary of the main points and features of the models proposed. First, we consider a wide class of affine jump-diffusions proposed for the asset price dynamics: jump-diffusions, diffusions with stochastic volatility, jump-diffusions with stochastic volatility, and jump-diffusions with stochastic volatility and jump intensity. Next we apply the Fourier transform for solving the problem of European option pricing under these price processes. We present two solution methods: the characteristic formula and the Black-Scholes-style formula. Finally, we discuss numerical implementation of pricing formulas and apply the considered processes for modeling the DAX options volatility surface.
Download or read book Option Pricing on Jump diffusion Models written by and published by . This book was released on 2009 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Activity Jump Models for Option Pricing written by Mercy Muthoni Koimburi and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is thesis aims to look at option pricing under affine jump diffusion processes, with particular emphasis on using Fourier transforms. The focus of the thesis is on using Fourier transform to price European options and Barrier options under the Heston stochastic volatility model and the Bates model. Bates model combines Merton's jump diffusion model and Heston's stochastic volatility model. We look at the calibration problem and use Matlab functions to model the DAX options volatility surface. Finally, using the parameters generated, we use the two stated models to price barrier options.
Download or read book Consistency Conditions for Affine Term Structure Models Ii Option Pricing Under Diffusions with Embedded Jumps written by Sergei Levendorskii and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient conditions for the application of the Feynman-Kac formula for option pricing for wide classes of affine term structure models in the jump-diffusion case are derived generalizing earlier results for bond pricing in the pure diffusion case.
Download or read book Option Pricing in Affine Generalized Merton Models written by Christian Bayer and published by . This book was released on 2015 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we consider affine generalizations of the Merton jump diffusion model [7] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in [1]. We conclude with some numerical examples.
Download or read book Option Pricing and Jump diffusion Models written by Zongwu Zhu and published by . This book was released on 2005 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Option Pricing Under Jump diffusion Models written by Tao Wu and published by . This book was released on 2010 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Using POD Methods for Option Pricing with Diffusion Models written by Elena Schnell and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavelet Galerkin Schemes for Option Pricing in Multidimensional L vy Models written by Christoph Winter and published by . This book was released on 2008 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Option Pricing for a Stochastic volatility Jump diffusion Model written by Guoqing Yan and published by . This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the accurate and fast European option pricing formulas, we calibrate the models to S&P 500 Index option quotes by least squares method. Spot variance and structural parameters for different models including Black-Scholes, Stochastic-Volatility. SVJD-Uniform, SVJD-Normal, SVJD-DbExp are estimated. Fitting performance of different models are compared and our proposed SVJD-Uniform model is found to fit the market data the best.
