| Project/Area Number |
16K03731
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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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| Research Field |
Money/ Finance
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 局所ボラティリティモデル / 高速フーリエ変換 / バミューダ型オプション / 数理ファイナンス / 数値計算 / 社債 / オプション / 金融工学 |
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| Outline of Final Research Achievements |
The aim of this research proposal was to construct a new asymptotic expansion method for pricing options using the binomial tree methods on the local volatility model, such as CEV model. Unfortunately, we could not derive the price accurately as long as we use a lower order asymptotic expansion to construct a binomial tree. In order to confirm this, we proposed a new computation method of option price; an asymptotic expansion formula for the option price in a CEV model using the asymptotic expansion technique and Fourier analysis. This approach enables us to derive the higher order terms using only algebraic computation. Furthermore, this method enables us to derive not only the price of European options, but also the price of options with an early exercise feature, such as Bermudan options and American options. I regret that the first proposal was not fully successful. On the other hand, we proposed an alternative method for pricing options in the local volatility model.
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| Academic Significance and Societal Importance of the Research Achievements |
オプション価格の計算で用いられるブラック・ショールズ・モデルではオプションのスマイル・カーブを説明できずより一般的なモデルが数多く提案されてきた。その中でも局所ボラティリティ・モデルのような非線形なモデルにおいてオプションの価格計算を行う方法を考察をした。二項分岐モデルによる計算は断念したものの、数値フーリエ解析を用いることでジャンプの項が入ったCEVモデルにも適用できるオプション価格計算法を提案することができた。また、FFTを有効に使うことでバミューダ型やアメリカ型オプションといったより広いクラスの金融商品の計算にも適用可能な手法を提案できた。
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