ABSTRACT
A joint model of commodity price and interest rate risk is constructed analogously to the multicurrency LIBOR Market Model (LMM). Going beyond a simple ‘re-interpretation’ of the multicurrency LMM, issues arising in the application of the model to actual commodity market data are specically addressed. Firstly, liquid market prices are only available for options on commodity futures, rather than forwards, thus the dierence between forward and futures prices must be explicitly taken into account in the calibration. Secondly, we construct a procedure to achieve a consistent t of the model to market data for interest options, commodity options and historically estimated correlations between interest rates and commodity prices. We illustrate the model by an application to real market data and derive pricing formulas for commodity spread options.
