Pricing Defaultable Floating-Rate Bonds with Correlated Rate and Intensity Factors

Summary

This document frames a pricing problem for defaultable bonds when default intensity is stochastic and correlated with the risk-free interest rate. The proposed setup uses a two-factor Gaussian model, with one factor for rates and one for default intensity, and asks whether a standard floater can be priced in closed form when its reference and interest periods coincide. It also identifies bond options as a longer-term pricing interest.

The document offers no derivation, formula, or answer to the question. It points to tree-based credit-spread modeling as existing literature, but gives no comparison of methods or numerical evidence. Its value is mainly in defining the modeling challenge: correlation between rates and default intensity, and whether that dependence permits tractable valuation. Any claim that a closed formula exists, or that a particular model handles the problem, would need support from sources beyond this text.

Key ideas

• The pricing problem concerns defaultable bonds with stochastic default intensity.
• The proposed two-factor setup allows correlation between interest rates and default intensity.
• The initial target is a standard floater with matching reference and interest periods.
• Tree methods are mentioned, but the document supplies no closed-form solution or pricing evidence.
• Bond options are identified as a possible extension of the inquiry.

Tags

# Are there closed formulas for non-callable defaultable floating rates in a reduced form models?


# Are there closed formulas for non-callable defaultable floating rates in a reduced form models?












currently, I am evaluating for my company the possibility to price defaultable bonds with stochastic default intensity. Precisely, I am considering using the G2++ model where one factor is the riskless rate and the other the default intensity. Hereby, it is an essential goal to allow correlation between the two factors. While it is rather easy to find literature on tree models for this situation (e.g. the article A TREE IMPLEMENTATION OF A CREDIT SPREAD MODEL FOR CREDIT DERIVATIVES by Schönbucher) so far I failed to find any closed formulas. For the beginning, I would already be happy to know if there is a closed formula for a standard floater (i.e. reference period is interest rate period) under this situation, although in the long term I am also interested in pricing bond options in this models.

Does anybody know any literature where this matter is discused?

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