SFB 303 Discussion Paper No. B - 433
Author: Lotz, C.
Title: Locally Minimizing the Credit Risk
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 F\"ollmer, 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 firm value is a traded asset.
In the second part, we consider the valuation and hedging of options on
defaultable 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
satisfied by the value process of the option and show how the
risk-minimizing hedging strategy can be computed.
Keywords: Credit Risk, Incomplete Markets, Risk Minimization
JEL-Classification-Number: G12, G13
Creation-Date: May 1998
URL: ../1998/b/bonnsfb433.pdf"
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