Locally minimizing the credit risk

Lotz, Christopher (1998) Locally minimizing the credit risk. Financial Markets Group Discussion Papers (281). Financial Markets Group, The London School of Economics and Political Science, London, UK.

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Abstract

The aim of this paper is the valuation and hedging of defaultable bonds and options on defaultable bonds. The Heath/Jarrow/Morton-framework is used to model the interest rate risk, and the time of default is determined by the first jump time of a point process. In the first part, we consider valuation and hedging of a defaultable bond. The firm value process is modelled explicitly, and is used to determine the default intensity or the payout ratio after default. This means that default intensity or payout ratio are not exogenously given, but determined implicitly by the specification of the firm value process. Incompleteness of markets arises naturally, and therefore we apply the local risk-minimizing methodology introduced by Fäollmer, Schweizer and Sondermann to determine a martingale measure and to calculate hedging strategies. In incomplete markets, the total risk of a contingent claim can be divided into traded risk and totally non-tradeable (intrinsic) risk. Therefore, a contingent claim cannot be hedged perfectly. We can only reduce the risk to the intrinsic component. In our model, we can hedge partly against the risk of default because we assume that the ̄rm value is a traded asset. In the second part, we consider the valuation and hedging of options on default- able bonds. Again, we are in an incomplete market. In addition to the traded assets, we introduce a virtual asset to the market which represents non-hedgeable risk. We derive the partial differential equation which is satis ̄ed by the value process of the option and show how the risk-minimizing strategy can be computed.

Item Type:	Monograph (Discussion Paper)
Official URL:	https://www.fmg.ac.uk/
Additional Information:	© 1998 The Authors
Divisions:	Financial Markets Group
Subjects:	H Social Sciences > HC Economic History and Conditions H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Date Deposited:	05 Jun 2023 12:36
Last Modified:	11 Dec 2024 19:48
URI:	http://eprints.lse.ac.uk/id/eprint/119160

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