Stochastic modeling for commodity prices and valuation of commodity derivatives under stochastic convenience yields and seasonality [Elektronische Ressource] / vorgelegt von Sanae Rujivan

INAUGURAL-DISSERTATION zur Erlangung der Doktorwürde der Naturwissenschaftlich-Mathematischen Gesamtfakultät der Ruprecht-Karls-Universität Heidelberg vorgelegt von M.Sc..- Sanae Rujivan aus Thailand Tag der mündlichen Prüfung : 23.01.2008 Stochastic Modeling for Commodity Prices and Valuation of Commodity Derivatives under Stochastic Convenience Yields and Seasonality Gutachter: Prof. Dr. Dr. h.c. mult. Willi Jäger Gutachter: Prof. Dr. Markus Rei β Abstract In this dissertation, we develop a two-factor model of the stochastic behavior of commodity prices. The first factor is the commodity spot price which follows a geometric Brownian motion with a time-varying volatility. The second factor is the instantaneous convenience yield which follows an extended Cox-Ingersoll-Ross (CIR) process by adding a time-dependent function into the drift term of the process in order to describe seasonal variations in commodity prices. The time-varying volatilities of the commodity spot prices and the instantaneous convenience yields are proportional to the square root of the instantaneous convenience yields. Our modeling concerns about two important things: a link between price volatilities and convenience yields as suggested by the theory of storage, and the seasonality in commodity prices and convenience yield volatilities.