Researches on Asymptotic Expansion Approaches around Non-Gaussian Distributions
Project/Area Number |
15K17087
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Money/ Finance
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Research Institution | Tokyo Metropolitan University (2016-2017) University of Tsukuba (2015) |
Principal Investigator |
Takehara Kohta 首都大学東京, 社会科学研究科, 准教授 (70611747)
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Project Period (FY) |
2015-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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Keywords | 漸近展開法 / 解析近似解 / オプション価格解 / SABRモデル / デリバティブ価格評価 / 金融数値解法 / オプション価格評価 |
Outline of Final Research Achievements |
In this research, we analyse "an asymptotic expansion approach," known as a useful tool for practitioners in pricing derivatives or risk managements. Especially, we extend the "original" approach which expands the target process around Normal distribution, to the ours expanding the target around more general stochastic processes whose distributions are available. We also try to analyse the mathematical structures in our expansion. As a result, the underlying problem for solving the stochastic differential equation is transformed into the problem for solving infinite numbers of ordinary differential equations with hierarchical dependence, via projecting correction terms onto the "central" terms in our expansion. To confirm usefulness and accuracy of our proposing technique, it is applied to practically important examples, such as an expansion of lamuda-SABR model with mean-reversion around original SABR model, and satisfactory results are observed.
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Report
(4 results)
Research Products
(9 results)