A new weak approximation scheme of diffusion and its application to Finance
| Project/Area Number |
15540110
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
NINOMIYA Syoiti Tokyo Institute of Technology, Graduate School of Innovation Management, Professor, 大学院・イノベーションマネジメント研究科, 教授 (70313377)
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| Co-Investigator(Kenkyū-buntansha) |
KUSUOKA Shigeo Univ.of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (00114463)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Stochastic Differential Equation / Numerical Method / Simulation / quasi-Monte Carlo / 確立微分方程式 / 微分方程式の数値解法 / 数理ファイナンス / ファイナンス / Runge-Kutta法 / 高速化 / 金融派生商品 / 拡散過程 / 確率微分方程式の数値解法 |
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| Research Abstract |
The object of this project is to establish the Kusuoka approximation. Kusuoka approximation is a new scheme that approximate E[f(X(T)] where X(t) denotes a diffusion process and f a function with some regularity. This problem is called weak approximation. By using the Kusuoka approximation, it is expected that we can reduce the number of the dimension of the domain of integration which arises in the last step of the approximation. This integral dimension is a very critical factor if we use quasi-Monte Carlo techniques. In this project, we have achieved the following successes :
1. The discovery of a versatile algorithm that enables us to apply the Kusuoka approximation easily to any diffusion processes described by SDEs.
2. The algorithm above also is compatible with quasi-Monte Carlo method.
3. We have applied the algorithm to financial derivative pricing problem and showed that our new algorithm makes at least 800 times faster calculation than existing methods.
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Report
(4 results)
Research Products
(6 results)
