Generalization of Put-Call Symmetry Method and Its Applications

• Project/Area Number: 24840042
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Ritsumeikan University
• Principal Investigator: IMAMURA Yuri 立命館大学, 理工学部, 助教 (40633194)
• Project Period (FY): 2012-08-31 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 数理ファイナンス / 静的ヘッジ / タイミングリスク / 漸近展開 / Put－Call対称化 / ノックアウトオプション / 社債 / Put - Call 対称化 / Ｐｕｔ－Ｃａｌｌ対称化

Research Abstract

Firstly, I have fully determined the Put-Call type symmetrizations for generic multi-dimensional diffusion processes. The results were published as a joint paper with Prof. Jiro Akahori at Ritsumeikan University. Secondly, I have obtained an asymptotic static hedge formula for a timing-risk under a one-dimensional diffusion model by collaborating with Jiro Akahori, and Flavia Barsotti from Unicredit(Milan).

Research Products

• [Journal Article] Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion (2013)
  • Author(s): Y.Imamura、K.Takagi
  • Journal Title: Asia-Pacific Financial Markets Volume: 20 Pages: 71-81
  • Peer Reviewed
• [Journal Article] On a Symmetrization of Diffusion Processes (2013)
  • Author(s): J.Akahori、Y.Imamura
  • Journal Title: Quantitative Finance Volume: (Published online)
  • Peer Reviewed
• [Journal Article] On a Symmetrization of Diffusion Processes (2013)
  • Author(s): Jiro Akahori and Yuri Imamura
  • Journal Title: Quantitative Finance Volume: online first Pages: 0-0
  • Peer Reviewed
• [Presentation] A diffusion approximation of a stochastic model of metastasis formation (2013)
  • Author(s): J.Akahori、Y.Imamura、T. Nakai、A.Naganawa、T.Shibutani
  • Organizer: The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学(沖縄県)
  • Year and Date: 2013-11-02
• [Presentation] An Asymptotic Static Hedge of a Timing Risk and its Error (2013)
  • Author(s): Y.Imamura
  • Organizer: Stochastic processes and their statistics in Finance
  • Place of Presentation: 沖縄青年会館(沖縄県)
  • Year and Date: 2013-11-01
• [Presentation] Earthquake Insurance Reserves Implied by a Coherent Risk Measure (2013)
  • Author(s): J.Akahori、Y.Imamura、H.Ohgaki、K.Uchida
  • Organizer: The 45^<th> ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学(沖縄県)
  • Year and Date: 2013-11-01
• [Presentation] The Put-Call Symmetry Method by a Higher-Order Scheme (2013)
  • Author(s): R.Akimoto、Y.Imamura、N.Shimizu
  • Organizer: The 45^<th> ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学(沖縄県)
  • Year and Date: 2013-11-01
• [Presentation] タイミングリスクの静的ヘッジ (2013)
  • Author(s): 今村悠里
  • Organizer: 日本応用数理学会2013年度年会
  • Place of Presentation: アクロス福岡(福岡県)
  • Year and Date: 2013-09-11
• [Presentation] Static hedging of timing risk (2013)
  • Author(s): Y.Imamura
  • Organizer: The First International Workshop on Quantum Information Theory and Related Topics
  • Place of Presentation: ダナン(ベトナム)
  • Year and Date: 2013-08-20
• [Presentation] An Asymptotic Static Hedge of a Corporate Defaultable Bond (2013)
  • Author(s): Y.Imamura
  • Organizer: The Fifth Florence-Ritsumeikan Workshop on Stochastic Processes and Applications to Finance and Risk Management
  • Place of Presentation: フィレンツェ(イタリア)
  • Year and Date: 2013-03-12
• [Presentation] Static hedging of timing risk
  • Author(s): 今村 悠里
  • Organizer: The First International Workshop on Quantum Information Theory and Related Topics
  • Place of Presentation: Duy Tan University (ベトナム，ダナン)
• [Presentation] タイミングリスクの静的ヘッジ
  • Author(s): 今村 悠里
  • Organizer: 日本応用数理学会2013年度年会
  • Place of Presentation: アクロス福岡（福岡県）
• [Presentation] An Asymptotic Static Hedge of a Timing Risk and its Error
  • Author(s): 今村 悠里
  • Organizer: Stochastic processes and their statistics in Finance in Okinawa
  • Place of Presentation: 沖縄青年会館（沖縄県）
• [Presentation] Earthquake Insurance Reserves Implied by a Coherent Risk Measure
  • Author(s): 内田 慧一朗
  • Organizer: The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学（沖縄県）
• [Presentation] The Put-Call Symmetry Method by a Higher-Order Scheme
  • Author(s): 秋元 亮
  • Organizer: The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学（沖縄県）
• [Presentation] A diffusion approximation of a stochastic model of metastasis formation
  • Author(s): 長縄 篤
  • Organizer: The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学（沖縄県）
• [Presentation] An Asymptotic Static Hedge of a Corporate Defaultable Bond
  • Author(s): 今村 悠里
  • Organizer: the Fifth Florence-Ritsumeikan Workshop on Stochastic Processes and Applications to Finance and Risk Management
  • Place of Presentation: フィレンツェ イタリア