In this study we use a three-step procedure that relates the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the transition law of such processes. Based on this procedure and the results of Qu, Dassios, and Zhao (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins, Kiely and Murphy (2017, 2018).

Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. To this end, in this paper we present a few fast and efficient methodologies for the exact simulation of the spot price dynamics modelled as the exponential of the sum of a Gaussian Ornstein-Uhlenbeck process and an independent pure jump process, where the latter one is driven by a compound Poisson process with (bilateral) exponentially distributed jumps. These methodologies are finally applied to the pricing of Asian options, gas and hydro storages and swing options under different combinations of jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized.

We investigate the distributional properties of two Lévy-driven Ornstein–Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to the self-decomposable gamma and bilateral gamma laws, and their densities and characteristic functions are here given in closed form. Algorithms for the exact generation of such processes are accordingly derived with the advantage of being significantly faster than those available in the literature and therefore suitable for real-time simulations.

The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong [J. Derivatives, 2008, 15, 81–91]. As mentioned in the seminal paper by Longstaff and Schwartz [Rev. Financ. Stud. 2001, 113–147], the convergence of the Least Squares Monte Carlo algorithm depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the optimization is more complex and its convergence is of fundamental importance in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence, and hence of the reliability of the algorithm, has not been performed yet, in our opinion this is because the apparent infeasibility and complexity uses a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges in contrast to Dutt and Welke [J. Derivatives, 2008, 15 (4), 29–47] that considers time-reversal Itô diffusions and subordinated processes. In particular, we show that in the case of Cox-Ingersoll-Ross and Heston models, the bridge approach has the advantage to produce exact simulations even for non-Gaussian processes, in contrast to the time-reversal approach. Our methodology permits performing a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory. Generally, in the valuation of energy facilities, one is also interested in the forward recursion. We then design backward and forward recursion algorithms such that one can produce the same random trajectories by the use of multiple independent random streams without storing data at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages.

The aim of this study is to present algorithms for the backward simulation of standard processes that are commonly used in financial applications. We extend the works of Ribeiro and Webber and Avramidis and L'Ecuyer on gamma bridge and obtain the backward construction of a gamma process. In addition, we are able to write a novel acceptance–rejection algorithm to simulate the Inverse Gaussian (IG) bridge and consequently, the IG process backward in time. Therefore, using the time-change approach, we can easily derive the backward generation of the compound Poisson with infinitely divisible jumps, the Variance-Gamma the Normal-Inverse-Gaussian processes and subsequently the time-changed version of the Ornstein–Uhlenbeck process introduced by Li and Linesky. We then compare the performance of the forward and backward construction of all these processes and show that the latter one is the preferable solution in the context of pricing American options or energy facilities like gas storages.

Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called thea-remainderof their self-decomposable stationary laws. In the present study we fully characterize the Lévy triplet of these $$a$$a -remainders and we provide a general framework to deduce the transition laws of the finite variation Ornstein–Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein–Uhlenbeck processes related to such distributions, with the further advantage of adopting procedures which are tens of times faster than those already available in the existing literature.