Forward Curve

[msinghs]

Hi there, I am looking for a accurate way to model a forward curve of a spot price of WTI oil. I know the formula where their is a constant convinience yield and interest rate : FT(t)=S(t)e(r-y)(T-t).

However is this accurate? Could anybody please give me a accurate method of modelling a Oil forward curve.

Best wishes,

Msinghs

 

[aaronhotchner]

That is the method for pricing a forward contract. The only more "accurate" version is to actually know the risk-free interest rate and convenience yield for the relevant time period. Basically, you're trying to predict the future. The equation is more like a no-arbitrage identity, not a predictive model.

 

[msinghs]

Ok but is their a model which would assume a stochastic convenience yield and interest rate?

 

[aaronhotchner]

Interest rates tend not to be random, so I would shy away from modeling them that way (maybe use future spot interest rates?). The convenience yield, as a catch-all parameter for market forces, is theoretically similar to a stock price, so you could try applying a stock model. I can't speak to the effectiveness of this, but it's something to consider.

 

[quotes]

It is impossible to determine a commodity forward price function with respect to time, spot price and cost of carry.

The convenience yield is determined by the difference between real forward spot spread and cost of carry. The former is suspect to volatile supply and demand.

 

[msinghs]

Ok thank you for your reply. It seems if one were to try to model a forward curve for lets say Brent Oil it would be very hard as determining the parameters of the convenience yield would be difficult?

 

[physEcon]

Modeling a forward curve is non-trivial. Even modeling the spot price alone for a commodity curve can be pretty daunting. I recomend looking here first. That presentation is a good intro on different frame works. Even if that particular presentation is too basic for you check out the other posts on that blog. Next I recommend getting Lacima's white papers. They're pretty straight-forward. They aren't a rigorous discussion of theory though.

It all depends what you are trying to do. Price a derivative? Develop a trading algo? What's your time horizon? If you have a shorter time horizon then try basically doing a Black-76 inspired correlated GBM simulation. If you are doing longer then I think you need some sort of economic component (which need not be explicitly economic, it could just be Markov regime switching). Look into PCA. The oil curve tends to maintain a shape for a while.