I setup a HW 1F model using Monte Carlo simulation with constant mean reversion and volatility factors. When I calibrate to a series of swaptions ( 1x4yr;2x3yr;3x2yr;4x1yr),the last three swaption prices match the market quite well, but the price of first (1x4yr) swaption from the MC Simulation is much higher than market price, the model also can recover initial term structure. Hope someone can help me on the following questions.
- how many swaptions are typically used in calibration of a HW1F model with constant factors.
- what is the acceptable pricing error (%) in HW1F calibration
- To calculate CVA for a stand-alone 10 yr IRS using HW1F, is it appropriate to focus on the around the max exposure area when I calibration the model, i.e. 3-5 year, rather than the whole scope?
- I also setup a HW1F trinomial tree (exact Theta), and it's calibrated to swaptions much better than the MC simulation, does that indicate my MC Simulation has issues (Euler discretization, theta function from forward)?