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Asset Prices and Investment Theories Based on Statistical Learning

Research Project

Project/Area Number 20K01587
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 07030:Economic statistics-related
Research InstitutionHitotsubashi University

Principal Investigator

NAKAMURA Nobuhiro  一橋大学, 大学院経営管理研究科, 特任教授 (90323899)

Project Period (FY) 2020-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2022: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords低ベータ・アノマリー / 信用デフォルト・スワップ / ハミルトンニアン・モンテ・カルロ / 分散リスクプレミアム / 歪度リスクプレミアム / 確率的分散 / 自己励起的ジャンプ / ベイズ推定 / クレジット・デフォルト・スワップ / 確率分散・確率相関 / 自己・相互励起ジャンプ / Hamiltonian Monte Carlo / 自己励起・相互励起過程 / ハザードレートモデル / 確率分散ジャンプモデル / VIX指数 / SKEW指数 / FBSDE / 2次拡散確率ボラティリティ / VIX、VVIX / 信用デリバティブ / ジャンプモデル / 金利期間構造推定 / ベータ変動リスクプレミアム / 統計的学習理論 / オプション評価
Outline of Research at the Start

資産価格理論におけるアノマリーの一つであるベータリスクアノマリー、「何故、ベータリスクの低い資産のリターンが高くなるのか?」を主要な課題とし、ベータの変動リスクプレミアムからのアプローチを試みる。そのためには、オプション価格の分析を組み合わせる必要があり、解析解を持たない場合でもその統計的推定が可能な方法論の確立を目指す。近年、盛んに研究されている機械学習、統計的学習理論を用いた金融時系列の動的構造推定とリスク管理・投資モデルの構築の可能性を探求する。

Outline of Final Research Achievements

Based on a paper pointing out that the cause of the low beta anomaly is the credit risk of individual firms, we conducted a study to extract credit information from corporate CDS (Credit Default Swap). Assuming several models of hazard rates, we analyzed CDS of Japanese individual firms and found a model with a high degree of fit. We were able to show that the statistical estimation method, that is, Bayes estimation combined with the numerical solver of ordinary differential equations works when volatility indices and options, for which no analytical solution is available, are used as observables. In the estimation of the dynamic structure of financial time series using statistical learning theory, we estimated Eurozone sovereign bonds with a cointegration structure and solved the Bellman equation to obtain the optimal investment.

Academic Significance and Societal Importance of the Research Achievements

金融時系列の動的構造として動的ベータ、信用リスク、確率分散、自己・相互励起ジャンプ、共和分構造をもつ確率金利などを研究し、統計的学習の一例としてHamiltonian Monte Carlo法を用いたBayes推定と金融時系列を特徴付ける常微分方程式の数値解法を組み合わせることで統計的推論が可能であることを明らかにした点で学術的意義があると考えられる。金融資産のリスク管理や最適投資問題に対しても応用の可能性を示すことができた点で社会的意義があるものといえよう。

Report

(4 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (16 results)

All 2023 2022 2021 2020

All Journal Article (6 results) (of which Peer Reviewed: 2 results,  Open Access: 2 results) Presentation (10 results)

  • [Journal Article] Cointegration analysis of hazard rates and CDSs: Applications to pairs trading strategy2023

    • Author(s)
      Kensuke Kato, and Nobuhiro Nakamura
    • Journal Title

      Physica A: Statistical Mechanics and its Applications

      Volume: 612 Pages: 128489-128489

    • DOI

      10.1016/j.physa.2023.128489

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Dynamic Relationship between Volatility Risk Premia of Stock and Oil Returns2023

    • Author(s)
      Nobuhiro Nakamura, Kazuhiko Ohashi, and Daisuke Yokouchi
    • Journal Title

      Journal of Risk and Financial Management

      Volume: 16 Issue: 3 Pages: 173-173

    • DOI

      10.3390/jrfm16030173

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Modeling Self And Mutual Excitations in Credit Default Swaps:Bayesian Statistical Inference2022

    • Author(s)
      中村信弘
    • Journal Title

      Proceedings of the 56-th JAFEE meeting, (2021:Winter)

      Volume: 56 Pages: 57-68

    • Related Report
      2021 Research-status Report
  • [Journal Article] Variance and Skewness Risk Premia: The Impact of State Dependent Self-Exciting Jumps2021

    • Author(s)
      中村信弘
    • Journal Title

      Proceedings of the 55-th JAFEE meeting, (2021:Summer)

      Volume: 55 Pages: 53-64

    • Related Report
      2021 Research-status Report
  • [Journal Article] IPDE-Based Bayesian Statistical Inference for CIR Interest Rate Model with Poisson Jump2021

    • Author(s)
      Takuya Kitabayashi and Nobuhiro Nakamura
    • Journal Title

      Proceedings of the 54-th JAFEE meeting

      Volume: 54 Pages: 24-35

    • Related Report
      2020 Research-status Report
  • [Journal Article] PDE-Based Bayesian Inference: Some Applications to FBSDEs in Finance2020

    • Author(s)
      Nobuhiro Nakamura
    • Journal Title

      Proceedings of the 53-th JAFEE meeting

      Volume: 53 Pages: 120-131

    • Related Report
      2020 Research-status Report
  • [Presentation] 確率的レバレッジ効果がオプション市場のインプライド・スキューに与える影響:自己励起型ジャンプモデルとの比較2023

    • Author(s)
      渡邉裕也, 中村信弘
    • Organizer
      日本金融・証券計量・工学学会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Exploring Cointegrated Asset Dynamics:The Impact of Stochastic Variances and Mutually Exciting Jumps2023

    • Author(s)
      Nobuhiro Nakamura
    • Organizer
      日本金融・証券計量・工学学会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Modeling Self And Mutual Excitations in Credit Default Swaps:Bayesian Statistical Inference2022

    • Author(s)
      Nobuhiro Nakamura
    • Organizer
      日本ファイナンス学会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Arbitrage-Free Co-Integrated Term Structure Model of Interest Rates towards Yield Curve Arbitrage2022

    • Author(s)
      Nobuhiro Nakamura
    • Organizer
      日本金融・証券計量・工学学会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Modeling Self And Mutual Excitations in Credit Default Swaps:Bayesian Statistical Inference2022

    • Author(s)
      中村信弘
    • Organizer
      第56回日本金融・証券計量・工学学会
    • Related Report
      2021 Research-status Report
  • [Presentation] Variance and Skewness Risk Premia: The Impact of State Dependent Self Exciting Jumps2021

    • Author(s)
      中村 信弘
    • Organizer
      第29回日本ファイナンス学会
    • Related Report
      2021 Research-status Report
  • [Presentation] Variance and Skewness Risk Premia: The Impact of State Dependent Self-Exciting Jumps2021

    • Author(s)
      中村信弘
    • Organizer
      第55回日本金融・証券計量・工学学会
    • Related Report
      2021 Research-status Report
  • [Presentation] IPDE-Based Bayesian Statistical Inference for CIR Interest Rate Model with Poisson Jump2021

    • Author(s)
      Takuya Kitabayashi and Nobuhiro Nakamura
    • Organizer
      日本金融・証券計量・工学学会
    • Related Report
      2020 Research-status Report
  • [Presentation] PDE-Based Bayesian Inference: Some Applications to FBSDEs in Finance2020

    • Author(s)
      Nobuhiro Nakamura
    • Organizer
      日本金融・証券計量・工学学会
    • Related Report
      2020 Research-status Report
  • [Presentation] Variance Risk Premium and Predictability of Returns: Quadratic Variance, Self-Exciting Jump Models2020

    • Author(s)
      Nobuhiro Nakamura and Kazuhiko Ohashi
    • Organizer
      日本ファイナンス学会
    • Related Report
      2020 Research-status Report

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Published: 2020-04-28   Modified: 2024-01-30  

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