Indifference of Defaultable Bonds with Stochastic Intensity models

Abstract

The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi-Bellman (HJB) equations for the value functions is derived. A finite difference method is used to solve this problem. The yield-spreads for both buyer and seller are extracted. The behaviour of the spread curve given the default intensity is analyzed. Finally the impacts of the risk aversion and the correlation coefficient are discussed.

Bond indifference prices and indifference yield curves

“…Utility indifference pricing (see Carmona (2009) for an overview) provides a framework for deducing bond prices uniquely. A number of authors have analyzed indifference prices of corporate bonds under the assumption of constant interest rates and stochastic default intensities; see Bielecki and Jeanblanc (2006); Sigloch (2009); Houssou and Besson (2010); Jaimungal and Sigloch (2012). By contrast, in this note, we deduce indifference prices of government bonds under the assumption of a stochastic short-rate and no default.…”

European Option Pricing With Liquidity Shocks

“…This aspect of our model connects with the growing literature on Markov-modulated financial markets driven by the recognition that the economic environment is not stable. Some of the pertinent analyses include [3,6,11,15,23]. The model of Blanchet et al [3] effectively corresponded to the case where the liquidity shock was permanent, while Siu et al [23] and Leung [15] studied valuation of options using Esscher and minimal entropy martingale measures, respectively.…”

“…Some of the common candidates for EMMs include minimal martingale measure [7], minimal entropy martingale measure [8,19], varianceoptimal martingale measure [22], and empirical martingale measure [3]. Second, one may use a utility maximization criterion to obtain indifference prices that take into account the risk aversion of the investor [2, 10,11,12,15,20,26]. Given the widely reported crash-ophobia of liquidity crises, this is a useful nonlinear pricing rule complementing the classical expectations-based approach.…”