Analysis of Quantization Error in Financial Pricing via Finite Difference Methods
| Autor: | Nat Chun-Ho Leung, Christina C. Christara |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Computer science
010103 numerical & computational mathematics 01 natural sciences symbols.namesake 0502 economics and business Order (group theory) Applied mathematics Point (geometry) 050207 economics 0101 mathematics Mathematics Finance Numerical Analysis 050208 finance Partial differential equation business.industry Quantization (signal processing) Applied Mathematics 05 social sciences Finite difference method Expression (computer science) Grid 010101 applied mathematics Computational Mathematics Valuation of options Fourier analysis symbols Finite difference scheme business Greeks Smoothing |
| Zdroj: | SIAM Journal on Numerical Analysis. 56:1731-1757 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/17m1139655 |
| Popis: | In this paper, we study the error of a second order finite difference scheme for the one-dimensional convection-diffusion equation. We consider non-smooth initial conditions commonly encountered in financial pricing applications. For these initial conditions, we establish the explicit expression of the quantization error, which is loosely defined as the error of the numerical solution due to the placement of the point of non-smoothness on the numerical grid. Based on our analysis, we study the issue of optimal placement of such non-smoothness points on the grid, and the effect of smoothing operators on quantization errors. |
| Databáze: | OpenAIRE |
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