I would like to use the following model in QuantLib:
$\frac{dF(t,T)}{F(t,T)} = \sigma_se^{-\beta(T-t)}dW_{t}^{1} + \sigma_L\left(1-e^{-\beta(T-t)}\right)dW_{t}^{2}$
This is a reformulation of the Schwartz Smith model (Schwartz-Smith). $F(t,T)$ is the commodity future price and the model is to be calibrated to American option prices (options on futures).
I plan to proceed in the following way:
- Derive a class from StochasticProcess for the process.
- Implement a PricingEngine for the analytical formula of european options.
- Implement a PricingEngine for American Options. I will use the Barone-Adesi/Whaley approximation. I have adapted the algorithm to use it with this model. I cannot use the provided implementation in the library though. My implementation will follow the lines of the one in the library I just have to plug-in 3 things: the analytical formula for the european option, the delta and the term that multiplies the second derivative wrt $F$ in the pricing PDE (the first two coming from the european pricing engine and the last one coming from the process).
- Implement a CalibratedModel.
- Implement a CalibrationHelper.
My problem is with point number 1. Is it OK to use the StochasticProcess class ? or should I implement a different class because in fact I'm modelling a family of processes, one for each T?
Thank you for any help and thoughts.