Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in...

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Bibliographic Details
Published inStochastic analysis and applications Vol. 30; no. 3; pp. 448 - 475
Main Authors Banerjee, Tamal, Ghosh, Mrinal K., Iyer, Srikanth K.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 01.05.2012
Taylor & Francis
Subjects
Credit spread
Defaultable bond
Exact sciences and technology
Mathematics
Minimal martingale measure
Probability and statistics
Probability theory and stochastic processes
Quadratic hedging
Sciences and techniques of general use
Stochastic analysis
Stochastic processes
Structural approach
Stochastic analysis
Risk rate
Price
Interest rate
Pricing
Incomplete market
Boundary condition
Partial differential equation
Martingale measure
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Summary:We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2012.668442