Probabilistic numerical approach for PDE and its application in the valuation of European options (Q2770163)
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scientific article; zbMATH DE number 1702889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Probabilistic numerical approach for PDE and its application in the valuation of European options |
scientific article; zbMATH DE number 1702889 |
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7 February 2002
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Black-Scholes equation
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parallel computation
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convergence
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convection-diffusion equations
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Brownian motion
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Monte Carlo method
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European options
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0.92416894
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0.89680064
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0.8964178
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0.89410955
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0.89115834
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0.88928354
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Probabilistic numerical approach for PDE and its application in the valuation of European options (English)
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The author describes a probabilistic numerical approach for a class of partial differential equations (PDEs; convection-diffusion equations) based on simulating Brownian motion and using the Monte Carlo method. The method is dimension-independent and allows for easy parallelization. Convergence properties of the solution are analyzed. The method is applied to the pricing of European options by simulating the price process instead of solving the Black-Scholes PDE for the case when the interest rate and the dividend rate are functions of the stock price, while the volatility is supposed to be constant.
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