Financial risk management with integration of multi-cuve models and XVA

• Project/Area Number: 17K01261
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Social systems engineering/Safety system
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: Tanaka Keiichi 首都大学東京, 経営学研究科, 教授 (00381442)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
• Keywords: マルチカーブ / 遷移確率 / レジームスイッチ / 金利期間構造モデル / ファイナンス / マルチカーブモデル / XVA

Outline of Final Research Achievements

We assume that a change of credit rating is a regime switch and then we have developed a bond pricing method based on a regime-switching model where the stochastic differential equation for an interest rate is switched among, for example, Vasicek type and CIR type. Although the bond pricing formula is not expressed in an analytic form, it is shown as a series of multiple integral. The second result is that we have developed a credit-rating model where the possibility of a change of the credit-rating of a firm is affected by a change of the credit-rating of the firm and other firms. The development of the self-exciting and the contagion is based on a Hawkes process.

Academic Significance and Societal Importance of the Research Achievements

自己励起・感染の有無により、債券価格に特徴的な影響を与えることが判明した。これらの結果を各モデルに適用すればマルチカーブモデルによる評価が可能となる。金融機関のポートフォリオにおける信用リスクの評価において、各社の格付推移は独立ではなく各社の格付推移の遷移確率を支配する状態変数の変化に自己励起と感染を導入した債券価格付けやデリバティブ評価が可能である。