Numerical solution of variational inequalities for pricing Asian options by higher order Lagrange–Galerkin methods |
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| Institution: | 1. Departamento de Matemática Aplicada, Universidade de Santiago, Campus Sur s/n, 15706-Santiago, Spain;2. Departamento de Matemáticas, Universidade da Coruña, Campus Elviña s/n, 15071-A Coruña, Spain;1. School of Management, Qufu Normal University, Rizhao, 276826, PR China;2. L.R.I, UMR 8623, CNRS and Université Paris-Sud 11, F-91405 Orsay, France;3. Institute for Interdisciplinary Research, Jianghan University, Wuhan, PR China;1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China;2. College of Mathematics, Putian University, Putian 351100, PR China;1. Royal Military Academy, Renaissancelaan 30, B-1000 Brussels, Belgium;2. Ghent University, Department of Flow, Heat and Combustion Mechanics, St.-Pietersnieuwstraat 41, B-9000 Gent, Belgium;1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. Department of Financial Affairs Office, Sichuan University of Arts and Science of China, Dazhou, Sichuan 635000, PR China;3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modelling and High-Performance Scientific Computating, Xiamen University, Xiamen 361005, China |
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| Abstract: | Asian options prices can be modelled in the Black–Scholes framework leading to two-factor models depending on the asset price, the average of the asset price and the time. They can also involve inequality constraints, as in the case of Amerasian options, leading to variational inequalities (VI). In the first section, we completely describe the pricing model for fixed-strike Eurasian and Amerasian options and list some properties satisfied by the option value function. Then, since no solutions in closed form are known, we deal with the numerical solution of the above problems proposing a general methodology: an iterative algorithm for the VI, combined with higher order Lagrange–Galerkin methods for partial differential equations. Finally, numerical results are shown. |
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