Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models

Notation and List of Symbols

Probabilities and expectations

• Risk-neutral probability.

• Risk-neutral expectation.

• pX : Risk-neutral probability density function of the random variable X:

• ϕ_X : Risk-neutral characteristic function of the random variable X, namely the Fourier transform of the probability density function:

• h_X: Risk-neutral intensity of the process X, namely the density of the absolutely continuous compensator of X:

• ϕ: Probability density function of the standard n-variate Gaussian distribution with correlation matrix C:

In particular for the case n = 1, 2 we define:

• Φ: Cumulative distribution function of the standard n-variate Gaussian distribution with correlation matrix C:

In particular, for the case n = 1, 2 we define:

• f: Probability density function of the ...