I have implemented the Black-Karasinski model using trinomial trees and calibrated following Brigo (2007) page 29. However, the results do not fit the interest rate curve practiced in the market. As I could verify, there are something around 30 to 60bps of difference in the 10Y tenor.
Is this due to the fact that I have not used the "market price of risk" to correct my drift in the calibration? In the way I am implementing, both drift and volatility are constant for the whole simulation.
Edit1: moreover, if I analyse the outcome of these "non-adjusted by the mpr" simulations, is my analysis useless?