Pricing, implementation and calibration of credit derivatives in incomplete market
par Régis Houssou
After the financial crisis of 2UU8. it is observed that tlie liquidity of many credit derivatives has dried up. The existence of illiquid credit derivatives that can not be perfectly hedged means that the market is incomplete. Therefore. the classical risk-neutral approach to valuing the credit derivatives will not take account, the risks that remain after the hedging. In this thesis, we address these issues by modifying the classical intensity-based models for credit derivatives by embedding them into the framework of optimal portfolio problems, a methodology that, takes into account; the investor's risk aversion. Through stochastic optimal control methods, we use indifference pricing with exponential utility function to determine tlie defaultable bond prices and Credit Default Swap (CDS) spreads. The Hamilton-Jacobi-Bellman (HJB) equations for the value functions are derived. The bid and ask spreads are numerically solved based on the indifference between the investor's two utility maximization problems. We examine how these quantities are affected clualitatively by the risk aversion, the default intensity, the correlation coefficient and the recovery rate. Moreover, the asymptotic behavior of the spread curves is studied. The calibration of tlie indifference pricing model of CDS spreads in the context of CIR-intensity is investigated. This gives rise to nonlinear inverse problems since the price of tlie CDS spreads depends in a non-linear way on the intensity's parameters and tlie risk aversion coefficient. In a first step using the data of CDS spreads from Markit, the estimates of time series for tlie default intensity for a given rating class are obtained. In a, second step, including the default intensities constructed in the first step, the parameters of the CIR intensity model and the absolute risk aversion coefficient are estimated. The estimation results reveal that during the subprime crisis, more risk averse investors prefer to buy the protection against the default of low credit quality firms. In addition, estimates for the parameters of CIR-intensity are in general significant and are increasing when the credit quality is decreasing. Credit Risk models ; Credit Derivatives ; Indifference Pricing ; Poisson processes ; PDE ; Finite difference method ; Nonlinear regression
Year of publication: |
2011
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Authors: | Houssou, Régis |
Publisher: |
Neuchâtel : Univ. |
Subject: | Derivat | Derivative | Portfolio-Management | Portfolio selection | Kreditrisiko | Credit risk | Stochastischer Prozess | Stochastic process | Modellierung | Scientific modelling | Nichtlineare Regression | Nonlinear regression | Kontrolltheorie | Control theory |
Saved in:
freely available
Extent: | Online-Ressource (PDF-Datei: 159 S., 948 KB) graph. Darst. |
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Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Hochschulschrift ; Thesis ; Graue Literatur ; Non-commercial literature |
Language: | English |
Thesis: | Neuchâtel, Univ., Diss., 2011 |
Notes: | Zsfassung in engl. und franz. Sprache Systemvoraussetzungen: Acrobat Reader |
Source: | ECONIS - Online Catalogue of the ZBW |
Persistent link: https://www.econbiz.de/10009523460
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