Pricing and forecasting of sovereign CDS premium with stochastic risk-free rate and default intensity

• Project/Area Number: 18K01707
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 07060:Money and finance-related
• Research Institution: Musashi University
• Principal Investigator: Kagraoka Yusho 武蔵大学, 経済学部, 教授 (40328927)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: ソブリンCDS / quanto CDS / Fractional Step Methods / 国債 / リスクフリー・レート / デフォルト強度 / 相関 / Radial Basis Functions / CDS / 有限差分法 / Fractional Step法 / 動径基底関数 / Nelson=Siegelモデル / ソブリンCDSプレミアム / 国債金利 / CDSプレミアム / 確率微分方程式 / 予測

Outline of Final Research Achievements

A unified model that consistently evaluates sovereign credit default swap (CDS) quanto and government bonds is developed. By product, a new procedure is proposed to calibrate stochastic processes for the risk-free interest rate and the sovereign default intensity to sovereign CDS quanto spreads and government bond yields. Fractional step methods are applied to solve a partial differential equation (PDE) for derivative prices, which cannot be solved using a standard finite difference method due to a cross derivative term. An empirical study is conducted on United States, German and Portuguese CDS quanto spreads in the midst of the European sovereign debt crisis and reveals that sovereign CDS quanto spread differentials are partially explained by introducing a correlation between the risk-free interest rates and the sovereign default intensity.

Academic Significance and Societal Importance of the Research Achievements

米国，ドイツなどの国債は重要な投資対象であり，ソブリン危機が発生するまでは無リスク資産と見なされてきた．しかしながら，ソブリン債務危機は国債のクレジット・リスクを顕在化した．その結果，投資家は，国債のクレジット・リスクをヘッジするために，ソブリンCDSを購入している．国債とソブリンCDSは共にリスクフリー・レートとデフォルト強度を原資産とするデリバティブと解釈できるが，別々に価格評価がされてきた．本研究成果により，国債とソブリンCDSを統一的にリスク評価と管理を可能にし，さらに，クォートする通貨によって異なるソブリンCDSプレミアム差を説明できる．

Research Products

• [Int'l Joint Research] Universite de Nante(フランス)
• [Journal Article] A unified model of sovereign CDS quanto spreads and government bond yields (2021)
  • Author(s): Yusho Kagraoka
  • Journal Title: Musashi University Discussion Paper Series Volume: 99 Pages: 1-19
• [Journal Article] The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes (2020)
  • Author(s): Yusho Kagraoka
  • Journal Title: International Journal of Financial Studies Volume: 8 Issue: 4 Pages: 77-77
  • DOI: 10.3390/ijfs8040077
  • Peer Reviewed / Open Access
• [Journal Article] Are the Risk-Free Interest Rates Correlated with Sovereign Default Intensities? (2019)
  • Author(s): Yusho KAGRAOKA
  • Journal Title: The Journal of Fixed Income Volume: 28-4 Issue: 4 Pages: 91-103
  • DOI: 10.3905/jfi.2019.1.068
  • Peer Reviewed
• [Journal Article] The Changing Shape of Sovereign Default Intensities (2019)
  • Author(s): Yusho Kagraoka, Zakaria Moussa
  • Journal Title: Theory and Applications of Time Series Analysis: Selected Contributions from ITISE 2018, Springer Volume: 2018 Pages: 203-216
  • DOI: 10.1007/978-3-030-26036-1_14
  • ISBN: 9783030260354, 9783030260361
  • Peer Reviewed / Int'l Joint Research
• [Presentation] On the changing shape of the sovereign default intensities (2018)
  • Author(s): Yusho Kagraoka, Zakaria Moussa
  • Organizer: International Conference on Time Series and Forecasting (ITISE 2018)
  • Int'l Joint Research