This year's winter issue of The Journal of Computational Finance is focused around novel stochastic differential equation (SDE) discretization schemes and variance optimal hedging for time processes with independent increments. Three papers propose improved SDE discretization schemes. We encounter Lévy jump processes, as well as stochastic volatility models. In the first paper in the issue, "Exact simulation pricing with Gamma processes and their extensions" by Lancelot F. James, Dohyun Kim and Zhiyuan Zhang, an exact path simulation is presented for a stochastic volatility asset price model in which the instantaneous volatility process is driven by a Gamma process. An infinite activity volatility process is employed. The quality of fit of the presented stochastic volatility model to market data is discussed.
Our second paper, "Simulation of Lévy processes and option pricing" by El Hadj Aly Dia, shows how to approximate an infinite activity Lévy process by either truncating the small-sized jumps or replacing them with a Brownian motion. Options are priced using the resulting approximate Lévy process, and errors are examined.
In "Variance-optimal hedging for discrete-time processes with independent increments: application to electricity markets", Stéphane Goutte, Nadia Oudjane and Francesco Russo discuss mean-variance hedging, based on the well-known Föllmer-Schweizer decomposition, for a two-factor model that appears in the electricity market. They present the impact of the choice of rebalancing dates on hedging errors
The last paper in this issue again focuses on a discretization scheme for SDEs. In "High-order discretization schemes for stochastic volatility models", Benjamin Jourdain and Mohamed Sbai propose a second-order weak convergence scheme for a stochastic volatility asset price process. When the volatility of the asset price is driven by an Ornstein-Uhlenbeck process, improved convergence properties are presented, both theoretically and numerically.
I wish you very enjoyable reading.
Cornelis W. Oosterlee
Delft University of Technology
Variance–optimal hedging for discrete-time processes with independent increments: application to electricity markets