Hi,I'm simulating the evolution of an interest rate using the Black Karasinski model. My aim is to simulate the evolution from today to thirty year.After the simulation I checked the distribution that I obtained in the different time step and I noticed a vey strange(for me) behaviour.If I use a certain set of parameter the mean and variance of the distribution obtained via montecarlo simulation match the mean and variance expected by the model; but with another set of parameter this fact doesn't happen.Is there some region of parameters in which this model doesn't work?The set of parameters that I used are: TEST1-[OK]: Initial condition=log(0.0011); mean reversion speed=0.4; mean reversion level=-2.5; vol=0.91; Simulation number=2000; Variance expected by the model for the rate at 12775=0.0344 Variance from Montecarlo for the rate at 12775=0.0294 TEST2-[FAILED]: Initial condition=log(0.0011); mean reversion speed=0.03; mean reversion level=-5.5; vol=0.91; Simulation number=2000; Variance expected by the model for the rate at 12775=2.26e+05 Variance from Montecarlo for the rate at 12775=25.93Thank you for your time!!!Bye

It is basically an OU modeldX = (a - b X) dt + dWFor a > 0, the critical value is b=0. The model has completely different behavior for b > 0 vs b < 0.So, likely you are seeing the onset of that with smaller b.

Hi,thanks for your answer... When you speak about "b", is the mean reversion speed? right?My problem is that after calibration I obtained the parameters of TEST2 and with these parameters if I notice that the distribution obtained via Montecarlo simulations is different from the expected distribution that the Black Karansinski should create. What can I conclude? Should I have to change model?The mean reversion speed very close to zero maybe suggests that this rate is not so mean reverting......Bye

mean reversion speed=0.03 might be too low. Can you check sensitivity? Increase mean reversion and increase sample?

QuoteOriginally posted by: MagnumpiHi,thanks for your answer... When you speak about "b", is the mean reversion speed? right?...rightMy problem is that after calibration I obtained the parameters of TEST2 and with these parameters if I notice that the distribution obtained via Montecarlo simulations is different from the expected distribution that the Black Karansinski should create. What can I conclude? Should I have to change model?... Assuming correctly coded simulation, I would conclude I need smaller step size and larger sample size.