The Stochastic Differential Equations (SDEs) that models the price processes are solved numerically by simulating many sample paths and forming a probability distribution. This is called Monte Carlo simulation. We implement a 1st order Euler method with a dynamic mesh for the time step to prevent divergence. Indeed electricity spot prices are highly volatile and sometimes require a finer mesh.

The Monte Carlo engine automatically builds or simulates the spot and forward curves together in a coherent term structure. The differential equations linking the spot and forwards have been solved for every SDE Model provided. A Market Price of Risk is estimated for every forward position.

You can set the following parameters of a simulation run:

• Stochastic model to be used,
• Curve fitting to be used for expected values,
• Number of sample paths, and
• Time horizon in days, months or years.

For every sample path of the spot, the system simulates all corresponding forwards with different maturities. This is how we jointly and coherently build the Term Structure of forward markets, where nearby forwards are as volatile as the spot and far out forwards have decaying volatility.

Suppose we simulate 5,000 sample paths 1 year into the future. Then what we mean is that 12 monthly forward rates will also be simulated, each with 5,000 sample paths. We do this by solving the partial differential equations generating the term structure of the forward markets by relating the spot and the various forwards, so the only data that is stimulated are the spot prices.

We usually simulate daily values. However, we can and do simulate hourly, ½ hourly and ¼ hourly for electricity loads and prices.

You can set the following parameters of a Monte Carlo simulation run: Comprehensive display of Monte Carlo sample paths, distribution and statistics.