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2006 Fiscal Year Final Research Report Summary

Option Pricing Models Based on Levy Process and Entropy, and Applications

Research Project

Project/Area Number 16540113
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya City University

Principal Investigator

MIYAHARA Yoshio  Nagoya City University, Graduate School of Economics, Professor, 大学院経済学研究科, 教授 (20106256)

Co-Investigator(Kenkyū-buntansha) MISAWA Tetsuya  Nagoya City University, Graduate School of Economics, Professor, 大学院経済学研究科, 教授 (10190620)
IBARAKI Satoru  Nagoya City University, Graduate School of Economics, Associate Professor, 大学院経済学研究科, 助教授 (10252488)
FUJIWARA Tsukasa  Hyogo University of Teacher Education, Department of Mathematics, Associate Professor, 学校教育学部, 助教授 (30199385)
Project Period (FY) 2004 – 2006
Keywordsmathematical finance / option pricing / incomplete market / geometric Levy process / equivalent martingale measure / relative entropy / calibration / geometric stable process
Research Abstract

We have studied the option pricing problems in the incomplete asset market. In the previous research we have constructed the basic frameworks of the [GLP & MEMM] pricing models, in which the geometric Levy processes are adopted as the underlying asset price processes and the MEMM (=minimal entropy martingale measure) is adopted as the equivalent martingale measure. So in this research we have investigated the fundamental properties of this model and have established the method how to apply this model to the practical option pricing problems.
After that we have investigated the properties of this model by the computer simulation methods, and we have obtained a good result that this model has the possibility to realize the volatility smile/skew properties of the option prices in the markets.
Next we have made empirical analysis on the market prices of the options, and we have obtained such a result that this model fits very well to the option prices in the market in the case that the underlying asset process moves very rapidly. Especially we could have seen that the [Geometric Stable Process & MEMM] model is very desirable in the sense that this model has the possibility to fit to very wide class of the option price data in the market.

  • Research Products

    (22 results)

All 2007 2006 2005 2004

All Journal Article (22 results)

  • [Journal Article] サポートベクトル学習アルゴリズムの開発と株価データヘの応用2007

    • Author(s)
      杉浦 洋祐, 茨木 智
    • Journal Title

      Discussion Papers in Economics, Nagoya City University 459

      Pages: 1-66

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Support vector algorithm and its applications to stock price data (in Japanese)2007

    • Author(s)
      Y.Sugiura, S.Ibaraki
    • Journal Title

      Discussion Papers in Economics, Nagoya City University No. 459

      Pages: 1-66

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Volatility Smile/Smirk Properties of [GLP & MEMM]Models2006

    • Author(s)
      Y.Miyahara, N.Moriwaki
    • Journal Title

      数理解析研究所考究録1462「確率数値解析における諸問題、VII」 1462

      Pages: 156-170

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Martingale measures for the geometric Levy process models2006

    • Author(s)
      Y.Miyahara
    • Journal Title

      統計数理研究所共同研究リポート184『無限分解可能過程に関連する諸問題(10)』 184

      Pages: 24-37

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The[GLP & MEMM]Pricing Model and Related Problems2006

    • Author(s)
      Y.Miyahara
    • Journal Title

      Proceedings of the 5th Ritsumeikan International Symposium "SP and Appl. to Math-Finance"

      Pages: 125-156

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Variance minimal martingale measures for geometric Levy processes2006

    • Author(s)
      M.Jeanblanc, Y.Miyahara
    • Journal Title

      Discussion Papers in Economics, Nagoya City University 444

      Pages: 1-22

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] MEMM に基づいた幾何安定過程オプション価格モデルの実証分析2006

    • Author(s)
      森脇 成彦, 宮原 孝夫
    • Journal Title

      Discussion Papers in Economics, Nagoya City University 454

      Pages: 1-18

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Marginal value approach to pricing Temperature options and its empirical example on daily temperatures in Nagoya2006

    • Author(s)
      Y.Emoto, T.Misawa
    • Journal Title

      Discussion Papers in Economics, Nagoya City University 450

      Pages: 1-13

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Similarity Analysis of Time Series Data by Wavelet Approximation2006

    • Author(s)
      T.Mori, T.Misawa
    • Journal Title

      Journal of the Japanese Society of Computational Statistics 19

      Pages: 15-26

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] From the minimal entropy martingale measures to the optimal strategies for the exponential utility maximization2006

    • Author(s)
      T.Fujiwara
    • Journal Title

      Asia-Pacific Financial Markets 11

      Pages: 367-391

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Volatility smile/smirk properties of [GLP & MEMM] models,2006

    • Author(s)
      Y.Miyahara, N.Moriwaki
    • Journal Title

      RIMS Kokyuroku 1462

      Pages: 156-170

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Martingale measures for the geometric Levy process models2006

    • Author(s)
      Y.Miyahara
    • Journal Title

      The Institute of Statistical Mathematics, Cooperative Research Report 184

      Pages: 24-37

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The [GLP & MEMM] Pricing Model and Related Problems,2006

    • Author(s)
      Y.Miyahara
    • Journal Title

      Proceedings of the 5th Ritsumeikan International Symposium "Stochastic Processes and Applications to Mathematical Finance (eds. J. Akahori et al.)"

      Pages: 125-156

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Variance minimal martingale measures for geometric Levy processes,2006

    • Author(s)
      M.Jeanblanc, Y.Miyahara
    • Journal Title

      Discussion Papers in Economics, Nagoya City University No. 444

      Pages: 1-22

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Empirical analysis of the [Geometric Stable Process & MEMM] model. (in Japanese)2006

    • Author(s)
      N.Moriwaki, Y.Miyahara
    • Journal Title

      Discussion Papers in Economics, Nagoya City University No. 454

      Pages: 1-18

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Marginal value approach to pricing Temperature options and its empirical example on daily temperatures in Nagoya2006

    • Author(s)
      Y.Emoto, T.Misawa
    • Journal Title

      Discussion Papers in Economics, Nagoya City University #450

      Pages: 1-13

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Similarity Analysis of Time Series Data by WISAM2006

    • Author(s)
      T.Mori, T.Misawa
    • Journal Title

      Journal of the Japanese Society of Computational Statistics vol. 19

      Pages: 15-26

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] From the minimal entropy martingale measures to the optimal strategies for the exponential utility maximization : the case of geometric Levy processes,2006

    • Author(s)
      T.Fujiwara
    • Journal Title

      Asia-Pacific Financial Markets Vol.11

      Pages: 367-391

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On Modeling U. S. Product Liability Risk - An Empirical Analysis-2005

    • Author(s)
      Y.Maeda, N.Moriwaki, Y.Miyahara
    • Journal Title

      Working Paper (Center for Risk Research, Shiga University) B-5

      Pages: 1-20

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On Modeling U.S. Product Liability Risk-An Empirical Analysis-,2005

    • Author(s)
      Y.Maeda, N.Moriwaki, Y.Miyahara
    • Journal Title

      Working Paper No. B-5, Center for Risk Research, Shiga University

      Pages: 1-20

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The[GLP & MEMM]Pricing Model and its Calibration Problems2004

    • Author(s)
      Y.Miyahara
    • Journal Title

      Discussion Papers in Economics, Nagoya City University 397

      Pages: 1-30

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The [GLP &MEMM] Pricing Model and its Calibration Problems,2004

    • Author(s)
      Y.Miyahara
    • Journal Title

      Discussion Papers in Economics, Nagoya City University, " No. 397

      Pages: 1-30

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2008-05-27  

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