Overview
The Gibson Schwartz commodity model, models the price of a commodity using a two factor model.
see Fanelli chpt 2
Gibson Schwartz
The Gibson Schwartz model proposes that the spot commodity price follows a geometric brownian motion.
{% dS(t) = \mu S(t) dt + \sigma_s S(t) dW_1(t) %}
In addition, the
convenience yield
follows a mean reverting
Ito process.
{% dy(t) = \alpha(k-y(t))dt + \sigma_y dW_2(t) %}
{% dW_1(t) dW_2(t) = \rho dt %}
Schwartz
Schwartiz proposes the following extension to the Gibson Schwartz model
{% dS(t) = (\mu - y(t) )S(t) dt + \sigma_s S(t) dW_1(t) %}
That is, the spot price includes the convenience yield in its drift.