Alternative Defaultable Term Structure Models

Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios (christina.nikitopoulos@uts.edu.au), Eckhard Platen (eckhard.platen@uts.edu.au) and Erik Schlogl

No 242, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Keywords: defaultable forward rates; jump-diffusion processes; growth optimal portfolio; real-world pricing (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2009-01-01
New Economics Papers: this item is included in nep-cmp
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Published as: Bruti-Liberati, N., Nikitopoulos-Sklibosios, C. and Platen, E., 2009, "Alternative Defaultable Term Structure Models", Asia-Pacific Financial Markets, 16(1), 1-31.

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