Model based Monte Carlo pricing of energy and temperature quanto options

Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the Black-Scholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.