The recent deregulation of electricity markets has led to the creation of energy exchanges, where the electricity is freely traded. In this paper, we study the most salient statistical features of electricity prices with a particular attention to the European energy exchanges. These features can be adequately reproduced by the sum-OU model: a model representing the price as a sum of Lévy-driven...

This addendum provides a detailed proof of Theorem 6.1 in Glasserman and Merener [1], establishing the convergence order of a discretization scheme.

Abstract: Thresholded Realized Power Variations (TPV) are one of the most popular nonparametric estimators for general continuous-time processes with a wide range of applications. In spite of their popularity, a common drawback lies in the necessity of choosing a suitable threshold for the estimator, an issue which so far has mostly been addressed by heuristic selection methods. We address this...

In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, t...

generally, exponential Lévy models to a finite set of observed option prices. We show that the usual formulations of the inverse problem via non-linear least squares are ill-posed and propose a regularization method based on relative entropy: we reformulate our calibration problem into a problem of finding a risk-neutral exponential Lévy model that reproduces the observed option prices and has ...

In this paper, we consider a mixed diffusion version of the stochastic target problem introduced in [3]. This consists in finding the minimum initial value of a controlled process which guarantees to reach a controlled stochastic target with a given level of expected loss. It can be converted into a standard stochastic target problem, by increasing both the state space and the dimension of the ...

In this paper we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged position in a continuous time, regime-switching jump-diffusion market, by using Fourier Transform methods. However, the analysis of this hedging strategy, as well as the computational technique for its implementation, is fairly general, i.e. it can be applied to any dynamical model...

The quality spread differential is defined to be the difference between the default premiums demanded for fixed rate and floating rate risky debts. The risky debt model based on Merton’s firm value approach is used to examine the behaviors of the quality spread differential of fixed rate and floating rate debts. We extend earlier result by adopting Geometric Brownian diffusion process with jump...

A model for a set of stock prices is said to be convexity preserving if the price of any convex European claim is convex as a function of the underlying stock prices at all times prior to maturity. As is well-known, this property is intimately connected to certain monotonicity properties of the option price with respect to volatility and other parameters of the model. Generally speaking, if the...