Research on mathematical expressions and numerical methods of optimal hedging strategies for stochastic volatility models
| Project/Area Number |
18K03422
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Keio University |
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Principal Investigator |
Arai Takuji 慶應義塾大学, 経済学部(三田), 教授 (20349830)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 数理ファイナンス / 確率論 / 数値計算 |
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| Outline of Final Research Achievements |
This project aimed to derive an expression of the mean-variance hedging for the Barndorff-Nielsen and Shephard(BNS) model and develop its numerical scheme. The results obtained are (1) derivation of local risk-minimizing for digital options, (2) derivation of decomposition and approximation formulas for option prices for the BNS model, and (3) computation of option prices for the BNS model using unsupervised deep learning.
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| Academic Significance and Societal Importance of the Research Achievements |
ジャンプ型モデルに対するmean-variance hedgingの導出は難しく、本研究ではその準備段階しかできなかった。しかし、伊藤解析を用いた分解公式の研究や深層学習を用いたアプローチなど新たな試みに挑戦したことで、研究手法の幅を拡げることに成功した。様々な手法を組み合わせることにより、ファイナンスにおける数学的知見を金融実務へ還元する礎を築けたものと確信している。
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Report
(6 results)
Research Products
(13 results)
