A unified approach to pricing and risk management of equity and credit risk

Abstract

We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intensity, while maintaining full analytical tractability. We characterise all riskneutral measures which preserve the affine structure of the model and show that risk management as well as pricing problems can be dealt with efficiently by shifting to suitable survival measures. As an example, we consider a jump-to-default extension of the Heston stochastic volatility model.

On Multicurve Models for the Term Structure

“…With the Fourier transform method the price in t = 0 of the Caplet can then be obtained in the form (see [8]) where M T +∆ X (•) is the moment generating function of X under the (T + ∆)−forward measure and R is such that M T +∆ X (R + iv) is finite. This moment generating function would have to be computed for each of the various forward measures, but it can be directly expressed in terms of the Q−characteristics of the factors: the Radon-Nikodym-derivative to change from Q to Q T +∆ can in fact be expresses in explicit form and it preserves the affine structure, see Corollary 10.2 in [10] (For a recent account on conditions for an absolutely continuous measure transformation to preserve the affine structure see [12]).…”

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

“…Duffee 1999, Duffie and Singleton 1999, Madan and Schoutens 2008, Schoutens and Cariboni 2009, Fontana and Montes 2014 the default event is modelled as the first jump of a counting process whose intensity, termed intensity of default, is not assumed to be firm-specific but is prescribed exogenously. This allows one to take into account the possible occurrence of a sudden (unpredictable) default event and henceforth the high credit spreads that are often experienced for short debt maturities can be recovered.…”