Default and determinacy under quantitative easing

We show that the path of inflation under quantitative easing policies that target interest rates, is determinate in the presence of default. We achieve this through different payoff profiles that a collateralised defaultable bond achieves in different states of nature with distinct default outcomes. In the model, heterogeneous households trade this bond and other shorter maturity risk-free bonds to maximize their intertemporal utility of consumption and labour. The differentiated payoffs of the collateralised bond, in an equilibrium with active default, span the full state space giving determinacy of prices and inflation as an outcome. This, implies that quantitative easing as implemented by the ECB in the recent years, can control the stochastic path of inflation.

The Dynamic Spread of the Forward CDS with General Random Loss

We assume that the filtrationFis generated by ad-dimensional Brownian motionW=(W1,…,Wd)′as well as an integer-valued random measureμ(du,dy). The random variableτ~is the default time andLis the default loss. LetG={Gt;t≥0}be the progressive enlargement ofFby(τ~,L); that is,Gis the smallest filtration includingFsuch thatτ~is aG-stopping time andLisGτ~-measurable. We mainly consider the forward CDS with loss in the framework of stochastic interest rates whose term structures are modeled by the Heath-Jarrow-Morton approach with jumps under the general conditional density hypothesis. We describe the dynamics of the defaultable bond inGand the forward CDS with random loss explicitly by the BSDEs method.

Valuation of Credit Derivatives with Multiple Time Scales in the Intensity Model

We propose approximate solutions for pricing zero-coupon defaultable bonds, credit default swap rates, and bond options based on the averaging principle of stochastic differential equations. We consider the intensity-based defaultable bond, where the volatility of the default intensity is driven by multiple time scales. Small corrections are computed using regular and singular perturbations to the intensity of default. The effectiveness of these corrections is tested on the bond price and yield curve by investigating the behavior of the time scales with respect to the relevant parameters.