Multiscale Intensity Models for Single Name Credit Derivatives

Work partially supported by NSF grants DMS‐0306357 and DMS‐0456195.

Abstract

We study the pricing of defaultable derivatives, such as bonds, bond options, and credit default swaps in the reduced form framework of intensity‐based models. We use regular and singular perturbation expansions on the intensity of default from which we derive approximations for the pricing functions of these derivatives. In particular, we assume an Ornstein‐Uhlenbeck process for the interest rate, and a two‐factor diffusion model for the intensity of default. The approximation allows for computational efficiency in calibrating the model. Finally, empirical evidence on the existence of multiple scales is presented by the calibration of the model on corporate yield curves.

Work partially supported by NSF grants DMS‐0306357 and DMS‐0456195.

Keywords:

• Defaultable bond
• credit default swap
• defaultable bond option
• asymptotic approximation
• time scales
• JEL classification: G12
• G13

Notes

Work partially supported by NSF grants DMS‐0306357 and DMS‐0456195.

1. Since r = (r_t ) _{t ≥0} is a Gaussian process, the random variable has moments of all orders. Also the Laplace transform of the positive random variable is finite, and the rest follows from the inequality |ab|≤a ²/2+b ²/2, for a, b ∈ ℝ.