Modeling electricity forward prices using the multivariate normal inverse Gaussian distribution

The Multivariate Gaussian Distribution

A vector-valued random variable X = X 1 · · · X n T is said to have a multivariate normal (or Gaussian) distribution with mean µ ∈ R n and covariance matrix Σ ∈ S n ++ 1 if its probability density function 2 is given by p(x; µ, Σ) = 1 (2π) n/2 |Σ| 1/2 exp − 1 2 (x − µ) T Σ −1 (x − µ). We write this as X ∼ N (µ, Σ). In these notes, we describe multivariate Gaussians and some of their basic prope...

Modeling day–ahead electricity prices

Introducing a production–based approach, we take into account different attitudes and liabilities of market participants to discuss the equilibrium day–ahead prices on electricity. Conditions ensuring the existence of the equilibrium are given and price distribution is considered. We include a discussion of reasons for high price volatility.

The Complex Multivariate Gaussian Distribution

Here I introduce package cmvnorm, a complex generalization of the mvtnorm package. A complex generalization of the Gaussian process is suggested and numerical results presented using the package. An application in the context of approximating the Weierstrass σ-function using a complex Gaussian process is given.

American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution ∗

In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model using the Generalized Local Risk Neutral Valuation Relationship of Duan (1999) and we derive approximation proce...

Screening for a Multivariate Mixture Normal Distribution