Robust numerical valuation of European and American options under the CGMY process
نویسندگان
چکیده
منابع مشابه
Robust Numerical Valuation of European and American Options under the CGMY Process
We develop an implicit discretization method for pricing European and American options when the underlying asset is driven by an infinite activity Lévy process. For processes of finite variation, quadratic convergence is obtained as the mesh and time step are refined. For infinite variation processes, better than first order accuracy is achieved. The jump component in the neighborhood of log ju...
متن کاملNumerical Valuation of American Options Under the CGMY Process
American put options written on an underlying stock following a Carr-Madan-Geman-Yor (CGMY) process are considered. It is known that American option prices satisfy a Partial Integro-Differential Equation (PIDE) on a moving domain. These equations are reformulated as a Linear Complementarity Problem, and solved iteratively by an implicit-explicit type of iteration based on a convenient splitting...
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A finite-difference method for integro-differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second-order accurate independently of the degree of the singularity in the Lévy measure. The singularity is ...
متن کاملNumerical Valuation of European and American Options under Kou's Jump-Diffusion Model
Numerical methods are developed for pricing European and American options under Kou’s jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a...
متن کاملNumerical valuation of options under Kou’s model
Numerical methods are developed for pricing European and American options under Kou’s jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a...
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ژورنال
عنوان ژورنال: The Journal of Computational Finance
سال: 2007
ISSN: 1460-1559
DOI: 10.21314/jcf.2007.169