• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Optimal hedging strategies and its numerical methods under the incomplete markets

Research Project

Project/Area Number 17K13764
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Money/ Finance
Research InstitutionNishogakusha University (2019)
Tokyo Metropolitan University (2018)
Waseda University (2017)

Principal Investigator

Imai Yuto  二松學舍大學, 国際政治経済学部, 講師 (60732229)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
KeywordsLocal risk minimization / Mean-variance hedging / Fast Fourier transform / Malliavin calculus / Lévy processes / Le'vy processes / FPGA / GPU / 最適ヘッジ戦略 / Local Risk Minimization / Fast Fourier Transform / Computational Finance / 幾何Lévyモデル / FFT / 数理ファイナンス / 数値計算
Outline of Final Research Achievements

We study both the mathematical and numerical aspects of optimal hedging strategies and numerical calculations for financial derivative securities under the incomplete markets.
In particular, the following two points were focused on the application of the study to financial practice: (i) mathematically derive a representation of the hedging strategy and express it in a numerically computable form, (ii) actually perform numerical calculations by applying the representations to various models and compare the results with those obtained from mathematically rigorous representations and with those obtained by different methods. The Car-Madan method, which uses a fast Fourier transform, was adopted as a numerical calculation method that is widely applicable not only in research but also in practice.

Academic Significance and Societal Importance of the Research Achievements

本研究により、Local Risk Minimization戦略を採用した場合のEuropean Call optionの数値計算可能な式をいくつかのモデルに対して数学的に導出することができた。従来はMonte Carlo法を用いてのみ計算可能であったが、本研究成果を用いることで高速Fourier変換を用いて計算することが可能となった。これにより、従来に比して極めて高速に計算結果が得られることがわかった。これにより、option価格を高速に計算可能になるのみならず、現実的な時間でパラメータ推定を行うことが可能となった。

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (11 results)

All 2019 2018 2017

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Int'l Joint Research: 4 results,  Invited: 7 results)

  • [Journal Article] A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus2018

    • Author(s)
      Arai Takuji、Imai Yuto
    • Journal Title

      Applied Mathematical Finance

      Volume: 25 Issue: 3 Pages: 247-267

    • DOI

      10.1080/1350486x.2018.1506259

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models2018

    • Author(s)
      T. Arai, Y. Imai and R. Nakashima
    • Journal Title

      Advances in Mathematical Economics

      Volume: 22

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the difference between locally risk-minimizing and delta hedging strategies for exponential Levy models2017

    • Author(s)
      Takuji Arai and Yuto Imai
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 34 Issue: 3 Pages: 845-858

    • DOI

      10.1007/s13160-017-0268-6

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Local risk-minimization for Barndorff-Nielsen and Shephard models2017

    • Author(s)
      Takuji Arai, Yuto Imai and Ryoichi Suzuki
    • Journal Title

      Finance & Stochastics

      Volume: 21 Issue: 2 Pages: 551-592

    • DOI

      10.1007/s00780-017-0324-8

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] A Numerically Efficient Closed Form Representation of Mean-Variance Hedging for Exponential Additive Processes and Hardware Acceleration for Financial Analysis2019

    • Author(s)
      Imai, Yuto
    • Organizer
      Soedirman’s International Conference on Mathematics and Applied Sciences
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Monte Carlo simulations for finance and its hardware accelerations2019

    • Author(s)
      Imai, Yuto
    • Organizer
      School on Mathematical Modeling and Simulation, State Islamic University of Syarif Hidayatullah Jakarta
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Monte Carlo simulations for finance and its hardware accelerations2019

    • Author(s)
      今井悠人
    • Organizer
      第1回八戸数学応用数理研究集会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Transform methods and numerical analysis for exponential Le'vy models2019

    • Author(s)
      Yuto Imai
    • Organizer
      The First SMU-TMU Joint Workshop on Mathematical Finance and Financial Engineering
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Local Risk Minimization Strategies and Transform Techniques2018

    • Author(s)
      今井悠人
    • Organizer
      丸の内QFセミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] How to model option prices under incomplete markets - with short history of mathematical finance2018

    • Author(s)
      Yuto Imai
    • Organizer
      Seminar nasional matematika dan terapannya ‘Mathematics in Theory and Application to Nature’, Universitas Jenderal Soedirman(Indonesia)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the difference between locally risk-minimizing and delta hedging strategies for exponential Lèvy models2017

    • Author(s)
      今井悠人
    • Organizer
      2017年度中之島ワークショップ「金融工学・数理計量ファイナンスの諸問題 2017」
    • Related Report
      2017 Research-status Report
    • Invited

URL: 

Published: 2017-04-28   Modified: 2021-02-19  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi