Pricing and Evaluating a Bond Portfolio Using a Regime Switching Markov Model

43 Pages Posted: 11 Feb 2008

See all articles by Leela R. Mitra

Leela R. Mitra

CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications; OptiRisk Systems; Brunel University

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

Rogemar Mamon

Department of Statistical & Actuarial Sciences, University of Western Ontario

Date Written: September 2007

Abstract

We apply a regime switching Markov chain model to determine bond prices. Our work builds upon the work of Thomas, Allen & Morkel-Kingsbury (2002) and Jarrow, Lando & Turnbull (1997). The interest rate process and credit rating migration process are considered. Our aim is to study the price evolution of a portfolio of defaultable bonds. We are interested in determining the density process to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) a year ahead. Whereas Thomas et al. describe a model under the pricing measure only, our model takes into consideration both the physical and pricing measures. We also describe the whole (risk free) forward rate curve, with appropriate conditions for the absence of arbitrage, while Thomas et al. describe the spot rate process. Most bond models make use of zero coupon bond prices. By using bond stripping we are able to discover zero coupon bond prices for bonds of different ratings. We use a mathematical programming approach to strip coupons and minimise squared error, subject to no arbitrage constraints.

Keywords: Credit risk, Markov model, regime switching, risk measures, Value at Risk (VaR), Conditional Value at Risk (CVaR)

JEL Classification: G12, G13

Suggested Citation

Mitra, Leela R. and Mitra, Gautam and Mamon, Rogemar, Pricing and Evaluating a Bond Portfolio Using a Regime Switching Markov Model (September 2007). Available at SSRN: https://ssrn.com/abstract=1092042 or http://dx.doi.org/10.2139/ssrn.1092042

Leela R. Mitra (Contact Author)

CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications ( email )

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

OptiRisk Systems ( email )

UNICOM R&D House
One Oxford Road
Uxbridge, UB9 4DA
United Kingdom

Brunel University ( email )

United Kingdom

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications ( email )

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

Rogemar Mamon

Department of Statistical & Actuarial Sciences, University of Western Ontario ( email )

London, Ontario N6A 5B8
Canada

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