I’m valuing some callable muni’s using backwards induction. Can someone tell me the differences in the assumptions of the Hull-White model v. the Black-Karasinski model?
I don’t think there is any difference in the assumptions, just that BK models the log instead of HW modelling the rate. Both assume parameters are deterministic functions of time only. However, I don’t think there is an analytical solution for the price of the bond using BK.
wyantjs Wrote: ------------------------------------------------------- > I don’t think there is any difference in the > assumptions, just that BK models the log instead > of HW modelling the rate. Both assume parameters > are deterministic functions of time only. > However, I don’t think there is an analytical > solution for the price of the bond using BK. Thank you for your response. I am under the impression that under the HW model interest rates can go negative and under the BK model they can not. I’m not stating this as a fact, because I’m not sure, but that is my current understanding. I haven’t done anything with logs since business calculus in 01 or 02, but I don’t think the Log would prevent a rate from going negative so… a. Is my negative rate assumption incorrect b. Does the Log prevent the rate from going negative c. Is this a difference in model assumptions d. Other
if you model the log of X, then to recover X you need to exponentiate from the modeled variable. Only Chuck Norris can find real values for Y s.t. e^Y<0.
Using the log does prevent negative rates. A log can be negative, but you cannot take the log of a negative number. That was the main purpose of BK, and the main difference between the two models. Not to be condescending, but if you have not taken anything other than business calculus 7 years ago, are you sure you really know what you are doing? Using this model requires knowledge of stochastic PDE’s.
wyantjs Wrote: ------------------------------------------------------- > Using the log does prevent negative rates. A log > can be negative, but you cannot take the log of a > negative number. That was the main purpose of BK, > and the main difference between the two models. > Not to be condescending, but if you have not taken > anything other than business calculus 7 years ago, > are you sure you really know what you are doing? > Using this model requires knowledge of stochastic > PDE’s. Ouch! My muni’s are one product (out of several hundred) and that assumption only relates to market value, which is a very small part of what I’m doing. I appreciate your non-condescending concern and thank you again for the explanation.
Sorry dude. I didn’t mean to sound harsh. My point is that using a simpler model that you understand better can often give better results than misusing a model that you don’t clearly understand.