Journal of Computational Finance

Variance optimal hedging with application to electricity markets

Xavier Warin

  • Existence and uniqueness of the solution of the mean variance hedging problem incorporating illiquidity constraints.
  • Development of effective algorithms to solve the problem.
  • Test on a real case from energy market showing that constraints can have a high impact on strategies.
  • Numerical study of the convergence of the algorithms.

In this paper, we use the mean–variance hedging criterion to value contracts in incomplete markets. Although the problem has been well studied in continuous and even discrete frameworks, very few works that incorporate illiquidity constraints have been undertaken, and no algorithm is available in the literature to solve this problem. We first show that a valuation problem incorporating illiquidity constraints with a mean–variance criterion admits a unique solution. We then develop two least squares Monte Carlo algorithms based on the dynamic programming principle to efficiently value these contracts. In these methods, conditional expectations are classically calculated by regression using a dynamic programming approach discretizing the control. The first algorithm calculates the optimal value function. The second algorithm calculates the optimal cashflow generated along the trajectories. Next, we provide an example of the valuation of a load curve contract coming from an energy market. In such contracts, incompleteness comes from the uncertainty surrounding a customer’s load, which cannot be hedged, and very tight illiquidity constraints are present. We compare the strategies given by two algorithms and by a closed formula ignoring constraints. Finally, we show that hedging strategies can be very different. A numerical study of the convergence of the algorithms is also given.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here