Pricing of Commodity and Energy Derivatives for Polynomial Processes

Abstract

Operating in energy and commodity markets require a management of risk using derivative products such as forward and futures, as well as options on these. Many of the popular stochastic models for spot dynamics and weather variables developed from empirical studies in commodity and energy markets belong to the class of polynomial jump diffusion processes. We derive a tailor-made framework for efficient polynomial approximation of the main derivatives encountered in commodity and energy markets, encompassing a wide range of arithmetic and geometric models. Our analysis accounts for seasonality effects, delivery periods of forwards and exotic temperature forwards where the underlying “spot” is a nonlinear function of the temperature. We also include in our derivations risk management products such as spread, Asian and quanto options.

Wind Put Barrier Options Pricing Based on the Nordix Index

“…Weather derivatives are used to manage the economic consequence of non-catastrophic weather events on companies' performance [1][2][3][4][5][6][7][8][9][10][11][12][13]. Given there is no standardised pricing model for weather derivatives, recent studies have developed different pricing models using underlying indices derived from climatic variables like temperature [2,4,5,8,[10][11][12][14][15][16], irradiance [17], rainfall [3,6] and wind [18][19][20][21]. The derivatives most used are options [3][4][5][6][7][8]11,15,16,22,23], futures [2,10,12] and swaps [15,24].…”