Pricing of Oil Derivatives: With the SABR and Schwartz models

Mark S√łndergaard Pedersen & Alex Rusanov

Student thesis: Master thesis


The aim of this paper is to introduce and analyse the main characteristics of the commodity market, namely the crude oil segment due to its importance in the world economy, large market share and simple price evolution as compared with other com- modities. The commodity market is very di erent from the regular and mature money market. The crude oil market is predetermined by the crude oil logistics. As a result of delivery limitations there is no centralized spot market for crude oil, and one has to model the future oil prices instead. For the above purpose the Black model is introduced. This model is almost identical to the more famous Black-Scholes model, but with futures prices instead of spot prices. The Black model provides easy formulas for the future oil prices and common derivatives. Nevertheless the assumptions of this model, especially the one about constant volatility, are not realistic and there is only one source of uncertainty (one-factor model). Next the two-factor model from Schwartz (1990) [11] is presented. Schwartz proposes a stochastic process for convenience yield, which is a measure of the bene t associated with physically owning crude oil. A closed formula for the future crude oil prices is calculated analogously to Bjerksund(1991) [3]. The model is used for pricing oil futures contracts and analysing di erent aspects of the futures price curves. However Schwartz' method cannot cope with the changing dynamics of the futures price curve towards large maturities, and consequently it is shown that the model is not suitable for practical purposes. For this reason, and also since the Black assumptions are not realistic, the two-factor SABR model from Hagan et al. (2002) [6] is applied, in order to price options on crude oil. The SABR model has an independent process for volatility. The dynamic SABR model, which is an extension of the SABR model with time varying parameters, is also studied. The model is used for pricing calls and puts with crude oil as the underlying asset. Finally, the SABR model is used for hedging crude oil risks in accordance to Bartlett (2006) [2]. Based on the aforesaid, and as proved by the conclusions of the paper, the SABR model, and its development dynamic SABR, may serve as a precise and e ective tool for assessing the market price of crude oil derivatives.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
Publication date2014
Number of pages123