新井 拓児 (アライ タクジ)

Arai, Takuji

写真a

所属(所属キャンパス)

経済学部 (三田)

職名

教授

HP

外部リンク

 

研究分野 【 表示 / 非表示

  • 自然科学一般 / 数理解析学 (数理ファイナンス)

研究キーワード 【 表示 / 非表示

  • 数理ファイナンス

  • 確率論

 

論文 【 表示 / 非表示

  • 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年03月

    ISSN  02190249

     概要を見る

    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年12月

    ISSN  02190249

     概要を見る

    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年03月

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  01676687

     概要を見る

    © 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年05月

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  1350486X

     概要を見る

    © 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年

    研究論文(学術雑誌), 共著, 査読有り

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KOARA(リポジトリ)収録論文等 【 表示 / 非表示

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競争的研究費の研究課題 【 表示 / 非表示

  • 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年04月
    -
    2025年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 新井 拓児, 基盤研究(C), 補助金,  研究代表者

  • 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年04月
    -
    2021年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 新井 拓児, 基盤研究(C), 補助金,  研究代表者

  • 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年04月
    -
    2019年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 新井 拓児, 基盤研究(C), 補助金,  研究代表者

 

担当授業科目 【 表示 / 非表示

  • 計量経済学演習

    2022年度

  • 計量経済学演習

    2021年度

  • 研究会d

    2021年度

  • 研究会c

    2021年度

  • 研究会(卒業論文)

    2021年度

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