Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein–Uhlenbeck Type

In this study, we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY-driven Ornstein–Uhlenbeck process. To this end, we first calculate the characteristic function of the transition law of such processes in closed form. This result is instrumental for the derivation of nonarbitrage conditions such that the spot dynamics is consistent with the forward curve. Moreover, we also conceive efficient algorithms for the exact simulation of the skeleton of such processes and propose a novel procedure when they coincide with compound Poisson processes of Ornstein–Uhlenbeck type. We illustrate the applicability of the theoretical findings and the simulation algorithms in the context of pricing different contracts, namely strips of daily call options, Asian options with European style and swing options

Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein–Uhlenbeck Type

In this study, we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY-driven Ornstein–Uhlenbeck process. To this end, we first calculate the characteristic function of the transition law of such processes in closed form. This result is instrumental for the derivation of nonarbitrage conditions such that the spot dynamics is consistent with the forward curve. Moreover, we also conceive efficient algorithms for the exact simulation of the skeleton of such processes and propose a novel procedure when they coincide with compound Poisson processes of Ornstein–Uhlenbeck type. We illustrate the applicability of the theoretical findings and the simulation algorithms in the context of pricing different contracts, namely strips of daily call options, Asian options with European style and swing options

Exact simulation of normal tempered stable processes of OU type with applications

We study the Ornstein-Uhlenbeck process having a symmetric normal tempered stable stationary law and represent its transition distribution in terms of the sum of independent laws. In addition, we write the background driving Levy process as the sum of two independent Levy components. Accordingly, we can design two alternate algorithms for the simulation of the skeleton of the Ornstein-Uhlenbeck process. The solution based on the transition law turns out to be faster since it is based on a lower number of computational steps, as confirmed by extensive numerical experiments. We also calculate the characteristic function of the transition density which is instrumental for the application of the FFT-based method of Carr and Madan (J Comput Finance 2:61-73, 1999) to the pricing of a strip of call options written on markets whose price evolution is modeled by such an Ornstein-Uhlenbeck dynamics. This setting is indeed common for spot prices in the energy field. Finally, we show how to extend the range of applications to future markets.Peer reviewe

Convenient Multiple Directions of Stratification

This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. Several choices have been proposed but, even if they provide variance reduction, their implementation is computationally intensive and not applicable to realistic payoffs, in particular not to Asian options with barrier. Moreover, all these previously published methods employ orthogonal directions for multiple stratification. In this work we investigate the use of algorithms producing convenient directions, generally non-orthogonal, combining a lower computational cost with a comparable variance reduction. In addition, we study the accuracy of optimal allocation in terms of variance reduction compared to the Latin Hypercube Sampling. We consider the directions obtained by the Linear Transformation and the Principal Component Analysis. We introduce a new procedure based on the Linear Approximation of the explained variance of the payoff using the law of total variance. In addition, we exhibit a novel algorithm that permits to correctly generate normal vectors stratified along non-orthogonal directions. Finally, we illustrate the efficiency of these algorithms in the computation of the price of different path-dependent options with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross markets.Comment: 21 pages, 11 table