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

“…whereM T +∆ X (·) is the moment generating function of X under the (T + ∆)−forward measure and R is such thatM 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]).…”

A revised version of the Cathcart & El-Jahel model and its application to CDS market

“…The mechanism that triggers default is different in a reduced-form model. Fully embracing the hypothesis of incomplete information and neglecting any knowledge about the capital structure of a firm, bankruptcy occurs as the first jump of a counting process, see, e.g., Jarrow and Turnbull ( 1995 ), Lando ( 1998 ), Duffee ( 1999 ), Duffie and Singleton ( 1999 ), Madan and Schoutens ( 2008 ), Schoutens and Cariboni ( 2009 ), and Fontana and Montes ( 2014 ). The possibility to replicate high credit spreads even for short-term maturities and the mathematical tractability are the main advantages of this approach.…”