I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates.
Is there a way (e.g. a benchmark) to compare these results or a test to choose the best model?
I also noted that the result of the model which has stochastic interest rates depends on the (chosen) initial value of the simulation. Since it is reasonable to use for this the last observable value of the interest rate time series, what would be the right value to assume constant for the other model (taking into account that this is a long-term option)?