Maple for Commodity Finance 

Igor Hlivka 

MUFJ Securities International, LONDON 

In this application we show how Maple can handle financial options models that have become popular in commodity finance. The financial trading of commodities has dramatically increased over past years as finance community started to look for non-standard instruments uncorrelated with the traditional financial products such as stocks, bonds, rates and currencies. Commodities, unlike their financial counterparts, require different approach to the process modeling: (i) commodities exhibit seasonality effects, (ii) commodity futures are exposed to many deformation modes, (iii) futures volatility is driven by the "Samuelson" effect that causes its drop as the expiry time shortens.

To accommodate these features into the option pricing we propose a two-factor Markov model with deterministic volatility. A reader familiar with financial products will recognise its patterns as two-factor Heath-Jarrow-Morton [HJM] model adapted to commodities. Similar to HJM setting, the stochastic object here is the commodity future rather than the spot price that allows us ignoring the "convenience yield" that is a systemic feature of commodities pricing. This approach has become quite popular amongst energy traders and the model has been recently implemented by Murex - a leading provider of financial trading systems. 

Multi factor models, where two-factor is a particular case, are not easily handled due to complex dependencies. Maple with its powerful symbolic engine can handle this task with ease and the analytical approach presented below provides an interesting insight into the underlying stochastic process. 

Model specification 

Implementation 

Conclusion