Numerical Methods of Option Pricing for Two Specific Models of Electricity Prices

In this work, two models are proposed for electricity prices as energy commodity prices which in addition to mean-reverting properties have jumps and spikes, due to non-storability of electricity. The models are simulated using an Euler scheme, and then the Monte-Carlo method is used to estimate the expectation of the discounted cash-flow under historical probability, which is considered as the option price. A so called random variable simulation and a control variate method are then used to decrease, the discretization error and the Monte-Carlo error, respectively. As the option prices satisfy PDE's associated with the models, by solving these PDE's, numerically, we can find the option prices by a second method, thereby being able to make comparisons.