A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives

• Published in: Management science Vol. 46; no. 1; pp. 46 - 62
• Main Authors: Das, Sanjiv Ranjan, Sundaram, Rangarajan K
• Format: Journal Article
• Language: English
• Published: Hanover, MD., etc INFORMS 01.01.2000; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Algorithms; Arbitrage; Cash flow; Corporate bonds; Corporate debt; Credit; Credit default swaps; Credit Risk; Debt; Derivatives; Economic models; Management science; Martingales; Modelling; No-Arbitrage; Pricing; Recursion; Risk; Studies; Term structure; Yield curves
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.46.1.46.15124

This paper develops a framework for modelling risky debt and valuing credit derivatives that is flexible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. Rather than follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, we work directly with the evolution of spreads. The risk-neutral drifts in the resulting model possess a recursive representation that facilitates implementation and makes it possible to handle path-dependence and early exercise features without difficulty. The framework permits embedding a variety of specifications for default; we present an empirical example of a default structure which provides promising calibration results.