Can you help me understand the One-Factor Model (general form)? drt = k(theta-rt)dt + sigma*rt*dzt I am basically looking for some guidance/intuition as to how to learn/remember the model in reference to Vasicek, Cox Ingersoll Ross and Lognormal model. Any practical scenario/example would also help.
Well, I think that’s a Vasicek model because of the (theta - rt) term. The idea is that the short rate mean reverts back to theta and the farther it gets from theta, the more drift there is back to theta. CIR is just an improvement on this so that interest rates don’t go negative and the lognormal model is a silly model that says interest rates evolve like stock prices. These are all “one-factor” models because ther is one source of randomness (that dZ[t]). I don’t know exactly what you mean by a practical scenario/example. These models are pretty fanciful. For one thing, they can’t usually be made to fit observable rates. For another they say that the correlation of forward rates is 1 though that is certainly not true in the real world. You can do things like price a call option on a stock with interest rates following a Vasicek model which is sort-of practical/example but it’s not something I could do on AF (Heston, 1993 I think is the reference for that). People use Vasicek for simulating interest rates and then pricing stuff like MBS (bad plan I think but rating agencies did it a lot). Maybe if you told me what you didn’t understand I could help you more with it. Edit: and I’m sure Maratikus and others can help too.
Exactly what I was looking for. Thanks a lot. p.s.: I tried to read the text and couldn’t make a head or tail out of it. Really there was nothing in particular that I was looking forward to (or could have asked). Wanted just a basic familiarity with the model. After having read the explanation here, everything feels like breeze.