Clewlow and Strickland Commodity one factor spot model

Commodity one factor spot price model

Introduction
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This code simulates commodity spot prices using the Clewlow and Strickland one factor daily spot model using a Monte Carlo approach. The derived stochastic differential equations (SDEs) are solved using several finite difference schemes.

The paper detailing the equations is available online in ref 1 below.

The example requires a commodity forward curve and assumes a one factor volatility model of the form sigma = A exp(-c(T-t)), where A is the cash volatility, c is the mean reversion rate and T is the maturity.

The code highlights several different finite difference schemes to solve the spot equation applied using a Monte Carlo appraoch.

Numerical finite difference schemes
1 = Euler log transformation
2 = Euler scheme
3 = Semi implicit Euler log transformation
4 = Weak predictor/Corrector on log transformation

Accuarcy can be improved by increasing the number of simulations (nSims) or increasing the number of discrete strips per days (Strips).

Validation
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The spot price paths can be validated using european call and put option valuations based on the analytical formula. Validation assumes an Asian option based on the last 729 days. Analytical formula for a standard European call and put option from Black
and Scholes - see equation 3.6 in ref [1].

References
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Reference 1 details the derivation of the one factor model that is detailed further in Clewlow and Strickland's book referenced in 2. This books is available in pdf from www.lacimagroup.com and the website has available many papers to freely download discussing commodities.

1. http://ideas.repec.org/p/uts/rpaper/10.html
2. "Energy Derivatives: Pricing and Risk Management," Clewlow and Strickland, Lacima Group, 2000.