Currently, we support pricing of a ZeroCouponBond with the HJM framework. There are 2 ways of calculating the price of a ZCB at maturity \(t\), via the short rate and the forward curve. Importantly, the forward rate method is an analytical formula depending only on the present forward curve and the time to maturity, so we can use it to calibrate and validate the results from the MonteCarlo HJM framework in order to get confidence for pricing other path-dependent options.
The forward rate ZCB price can be calculated with:
This will give our reference price, which can be compared with the average of \(N\) prices calculated with the short rate of each path via:
After enough iterations, the average values from all the short rate calculations should converge to the value obtained with the forward curve method.