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Pricing Defaultable Bonds in a Markov Modulated Market

Banerjee, Tamal and Ghosh, Mrinal K and Iyer, Srikanth K (2012) Pricing Defaultable Bonds in a Markov Modulated Market. In: STOCHASTIC ANALYSIS AND APPLICATIONS, 30 (3). pp. 448-475.

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Official URL: http://dx.doi.org/10.1080/07362994.2012.668442

Abstract

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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Taylor and Francis
Keywords: Credit spread;Defaultable bond;Minimal martingale measure;Quadratic hedging;Structural approach.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 16 Jun 2012 10:31
Last Modified: 23 Jun 2012 03:34
URI: http://eprints.iisc.ernet.in/id/eprint/44617

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