Ornstein-Uhlenbeck Process

Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions ArXiv ID: 2402.09243 “View on arXiv” Authors: Unknown Abstract This study proposes a new exact simulation scheme of the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path following the Ornstein-Uhlenbeck process is expressed as a sine series, and the time integrals of volatility and variance are analytically derived as the sums of independent normal random variates. The new method is several hundred times faster than Li and Wu [“Eur. J. Oper. Res., 2019, 275(2), 768-779”] that relies on computationally expensive numerical transform inversion. The simulation algorithm is further improved with the conditional Monte-Carlo method and the martingale-preserving control variate on the spot price. ...

Risk valuation of quanto derivatives on temperature and electricity ArXiv ID: 2310.07692 “View on arXiv” Authors: Unknown Abstract This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian Lévy process, which allows to include dependence between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD). ...

Monte Carlo Simulation for Trading Under a Lévy-Driven Mean-Reverting Framework ArXiv ID: 2309.05512 “View on arXiv” Authors: Unknown Abstract We present a Monte Carlo approach to pairs trading on mean-reverting spreads modeled by Lévy-driven Ornstein-Uhlenbeck processes. Specifically, we focus on using a variance gamma driving process, an infinite activity pure jump process to allow for more flexible models of the price spread than is available in the classical model. However, this generalization comes at the cost of not having analytic formulas, so we apply Monte Carlo methods to determine optimal trading levels and develop a variance reduction technique using control variates. Within this framework, we numerically examine how the optimal trading strategies are affected by the parameters of the model. In addition, we extend our method to bivariate spreads modeled using a weak variance alpha-gamma driving process, and explore the effect of correlation on these trades. ...