A Second-order Finite Difference Method for Option Pricing Under Jump-diffusion Models
Yonghoon Kwon,Younhee Lee +1 more
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The stability of the proposed finite difference method and the second-order convergence rate with respect to a discrete $\ell^{2}$-norm are proved.Abstract:
We develop a finite difference method to solve partial integro-differential equations which describe the behavior of option prices under jump-diffusion models. With localization to a bounded domain of the spatial variable, these equations are discretized on uniform grid points over a finite domain of time and spatial variables. The proposed method is based on three time levels and leads to linear systems with tridiagonal matrices. In this paper the stability of the proposed method and the second-order convergence rate with respect to a discrete $\ell^{2}$-norm are proved. Numerical results obtained with European put options under the Merton and Kou models show the behaviors of the stability and the second-order convergence rate.read more
Citations
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps
TL;DR: This work adopts a two-step implicit-explicit (IMEX) time discretization scheme, the IMEX-CNAB scheme, where the jump term is treated explicitly using the second-order Adams--Bashforth (AB) method, while the rest is treated implicitly using the Crank--Nicolson (CN) method.
Journal ArticleDOI
IMEX schemes for pricing options under jump-diffusion models
Santtu Salmi,Jari Toivanen +1 more
TL;DR: In this paper, the authors proposed families of IMEX time discretization schemes for the pricing of options under a jump-diffusion process, which lead to tridiagonal systems.
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On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance
TL;DR: The implicit-explicit (IMEX) two-step backward differentiation formula (BDF2) method with variable step-size, due to the nonsmoothness of the initial data, is developed for solving backward differentiation problems.
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Second Order Accurate IMEX Methods for Option Pricing Under Merton and Kou Jump-Diffusion Models
TL;DR: Three implicit-explicit (IMEX) time semi-discretization methods are developed for solving parabolic partial integro-differential equations which arise in option pricing theory when the underlying asset follows a jump diffusion process, showing stability, convergence and computational complexity of the methods.
References
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Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
Option pricing when underlying stock returns are discontinuous
TL;DR: In this article, an option pricing formula was derived for the more general case when the underlying stock returns are generated by a mixture of both continuous and jump processes, and the derived formula has most of the attractive features of the original Black-Scholes formula.
BookDOI
Financial modelling with jump processes
Rama Cont,Peter Tankov +1 more
TL;DR: In this article, the authors provide a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists.
Journal ArticleDOI
Option valuation using the fast Fourier transform
Peter Carr,Dilip B. Madan +1 more
TL;DR: In this paper, the fast Fourier transform is used to value options when the characteristic function of the return is known analytically, and it is shown how to use it for value selection.
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