Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

Abstract

Summary.A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework the market filtration is modelled explicitly, and is assumed to be generated by one or more independent market information processes. Each such information process carries partial information about the values of the market factors that determine future cash flows. For each market factor, the rate at which true information is provided to market participants concerning the eventual value of the factor is a parameter of the model. Analytical expressions that can be readily used for simulation are presented for the price processes of defaultable bonds with stochastic recovery. Similar expressions can be formulated for other debt instruments, including multi-name products. An explicit formula is derived for the value of an option on a defaultable discount bond. It is shown that the value of such an option is an increasing function of the rate at which true information is provided about the terminal payoff of the bond. One notable feature of the framework is that it satisfies an overall dynamic consistency condition that makes it suitable as a basis for practical modelling situations where frequent recalibration may be necessary.

Pricing of Defaultable Bonds with Random Information Flow

“…Before we proceed to investigate the properties of the model with a random σ in detail, let us first comment on the meaning of the information process (1). In general, in a financial market, even if we accept the simplifying assumption implicit in (1) that the only relevant market factor is the cash flow X T , there are plenty of information sources available for X T , each being obscured by noise.…”

“…However, since noise terms are independent of X T , they make no contribution towards the pricing of that asset entailing the cash flow X T . We can therefore discard them altogether and represent the totality of 'relevant' information in the form of a single information process (1).…”

“…In the information-based asset pricing framework of Brody, Hughston and Macrina (hereafter the BHM framework) the starting point is the specification of a model for the market filtration, along with the cash flow of the asset [1][2][3][4]. The market filtration, more specifically, is generated by a market information process that takes the form of a superposition of a 'signal' component associated with the cash flow of the asset (or, more generally, market factors relevant to the actual cash flow) and an independent 'noise' component that obscures the value of the cash flow.…”

“…The market filtration, more specifically, is generated by a market information process that takes the form of a superposition of a 'signal' component associated with the cash flow of the asset (or, more generally, market factors relevant to the actual cash flow) and an independent 'noise' component that obscures the value of the cash flow. The simplest model for the information process within the BHM framework was introduced in the context of modelling credit-risky discount bond price process [1]. Specifically, we fix a probability space (Ω, F t , Q), where Q denotes the risk-neutral measure, and let X T denote the random variable representing the impending cash flow of a credit-risky bond, with maturity T .…”

“…In this way, price process can be derived as an emergent phenomenon, rather than postulated from the outset. Motivated by this, here we analyse in detail properties of a specific model that corresponds to the simplest stochastic-volatility extension of the original BHM model introduced in [1].…”