Accurate Evaluation of European and American Options Under the CGMY Process
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چکیده
منابع مشابه
Accurate Evaluation of European and American Options Under the CGMY Process
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 ...
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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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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...
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We consider American options in a market where the underlying asset follows a Variance Gamma process. We prove results on the continuity of the exercise boundary, on the smooth fit principle and on the behavior of the exercise boundary near maturity. We also propose a numerical method to find the American option price and the exercise boundary. It is known that the American option price satisfi...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2007
ISSN: 1064-8275,1095-7197
DOI: 10.1137/050637613