By Serge Darolles, Christian Gourieroux

Much study into monetary contagion and systematic hazards has been inspired through the discovering that cross-market correlations (resp. coexceedances) among asset returns raise considerably in the course of problem sessions. is that this raise as a result of an exogenous surprise universal to all markets (interdependence) or as a result of particular types of transmission of shocks among markets (contagion)? Darolles and Gourieroux clarify that an try to express contagion and causality in a static framework may be unsuitable as a result of id difficulties; they supply a extra certain definition of the idea of concern to bolster the answer inside of a dynamic framework. This booklet covers the normal pracitce for outlining shocks in SVAR types, impulse reaction capabilities, identitification matters, static and dynamic types, resulting in the demanding situations of size of systematic possibility and contagion, with interpretations of hedge fund survival and industry liquidity risks

- Features the traditional perform of defining shocks to types that can assist you to outline impulse reaction and dynamic consequences
- Shows that id of shocks may be solved in a dynamic framework, even inside a linear perspective
- Helps you to use the types to portfolio administration, possibility tracking, and the research of monetary stability

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**Example text**

We have: Cov(η1 , η2 ) = E(η13 ) − E(η1 )E(η12 ) = 0. Therefore, these variables are uncorrelated. 7). Due to the symmetry of the standard normal distribution and the parabolic form of the support, the regression line is parallel to the x−axis, that is, the correlation coefﬁcient is equal to zero. This example is rather extreme, since these uncorrelated variables are in a deterministic relationship. In particular, we cannot shock η1 without shocking η2 = η12 , even if the variables are uncorrelated.

The pattern of this term structure depends on the ˆ The eigenvalues have a modulus eigenvalues of matrix Φ. strictly smaller than 1 in our basic speciﬁcation. They can be real or complex. 1). 1. 2. 3). 2. 3. 3. Interpretation in terms of contagion and network Even if a shock only concerns the error of the ﬁrst equation, that is if Δ1 = 0, Δi = 0, i ≥ 2, we generally observe at horizon h an effect on several variables, not only on the ﬁrst one. To analyze these effects, we have to look at the ˆ in particular at the zero structure of matrix Φ (or Φ), elements of this matrix and of its different powers.

11] V (vt ) = IdK . 1] is a vector autoregressive (VAR) model with partial observability. This model admits a state space representation. More precisely, let us introduce the state variable Zt = (Yt , Ft ) . 11], we have: State equation: Zt = ΨZt−1 + wt , where Ψ= C BA 0 A , wt = ut + Bvt vt , V (wt ) = Ω + BB B B IdK . where Ω = V (ut ). Measurement equation: Yt = (Id, 0)Zt . Consistent estimators of matrices A, B, C and associated variances of the speciﬁc factors can be obtained by Common Frailty versus Contagion in Linear Dynamic Models 55 maximizing a Gaussian pseudo-likelihood2.