2013 Fiscal Year Final Research Report
Higher Order weak approximation of Stochastic Differential Equations with application to finance
| Project/Area Number |
22540115
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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 東京工業大学, 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(Renkei-kenkyūsha) |
KUSUOKA Shigeo 東京大学, 大学院数理科学研究科, 教授 (00114463)
NAKANO Yumiharu 東京工業大学, 大学院イノベーションマネジメント研究科, 准教授 (00452409)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 確率微分方程式 / 弱近似 / シミュレーション / 数理ファイナンス / 金融派生商品 / 高頻度取引 / 数値計算 |
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| Research Abstract |
The following 5 results are achieved: [1] A new higher order algorithm for pricing barrier-type derivatives is found. [2] A computer program library of Kusuoka approximation for general SDEs are constructed and made public. [3] A new family of stochastic variables that enables 7th order weak approximation is constructed. [4] A new variable transformation method for Heston stochastic volatility models found. The transformed Heston model can be calculated faster by the NN algorithm. [5] A new index process from which we can detect lead/lag relations between two stochastic processes is constructed.
Results [1][2] and [3] are expected from the beginning of this research project. [4] and [5] are the spin-offs of the main project.
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