Arai, Takuji

写真a

Affiliation

Faculty of Economics （Mita）

Position

Professor

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Research Areas 【 Display / hide 】

  • Natural Science / Mathematical analysis (Mathematical Finance)

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Research Keywords 【 Display / hide 】

  • Mathematical Finance

  • Probability Theory

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Papers 【 Display / hide 】

  • APPROXIMATE OPTION PRICING FORMULA for BARNDORFF-NIELSEN and SHEPHARD MODEL

    Arai T.

    International Journal of Theoretical and Applied Finance （International Journal of Theoretical and Applied Finance)  25 （ 2 ）  2022.03

    ISSN  02190249

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    For the Barndorf-Nielsen and Shephard model, we present approximate expressions of call option prices based on the decomposition formula developed by [T. Arai (2021) Alos type decomposition formula for Barndor-Nielsen and Shephard model, Journal of Stochastic Analysis 2 (2), 3]. Besides, some numerical experiments are also implemented to make sure how effective our approximations are.

  • PRICING and HEDGING of VIX OPTIONS for BARNDORFF-NIELSEN and SHEPHARD MODELS

    Arai T.

    International Journal of Theoretical and Applied Finance （International Journal of Theoretical and Applied Finance)  22 （ 8 ）  2019.12

    ISSN  02190249

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    The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein-Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

  • Optimal initial capital induced by the optimized certainty equivalent

    Arai T., Asano T., Nishide K.

    Insurance: Mathematics and Economics （Insurance: Mathematics and Economics)  85   115 - 125 2019.03

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  01676687

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    © 2019 Elsevier B.V. This paper proposes the notion of optimal initial capital (OIC) induced by the optimized certainty equivalent (OCE), as discussed in Ben-Tal and Teboulle (1986) and Ben-Tal and Teboulle (2007). It also investigates the properties of the OIC with various types of utility functions. It is shown that the OIC can be a monetary utility function (negative value of risk measure) for future payoffs with the decision maker's concrete criteria in the background.

  • A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus

    Arai T., Imai Y.

    Applied Mathematical Finance （Applied Mathematical Finance)  25 （ 3 ） 247 - 267 2018.05

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  1350486X

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    © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

  • Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models

    Takuji Arai, Yuto Imai and Ryo Nakashima

    Advances in Mathematical Economics 22   1 - 24 2018

    Research paper (scientific journal), Joint Work, Accepted

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • ジャンプ型確率ボラティリティモデルに対するボラティリティ・サーフェスの研究

    2022.04
    -
    2025.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(C), Principal investigator

  • 確率ボラティリティモデルに対する最適ヘッジ戦略の導出と数値計算法の研究

    2018.04
    -
    2021.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  • Malliavin解析による最適ヘッジ戦略の導出とその数値計算法の研究

    2015.04
    -
    2019.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

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Courses Taught 【 Display / hide 】

  • SEMINAR: ECONOMETRICS

    2023

  • RESEARCH SEMINAR B

    2023

  • RESEARCH SEMINAR A

    2023

  • MATHEMATICS FOR ECONOMICS

    2023

  • FINANCE THEORY

    2023

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