I have two questions relating to the title.1. I need to model the Libor using the risk neutral measure instead of the terminal or spot measure. I have been looking everywhere but there seems to be a lack of literature on it. I do have the brigo theory and practice text book, but it just states the dynamics without much description or how they derived it. Can someone help me out on how to get the risk neutral dynamics?2. When simulating the libor rate, one needs to discretize it. originally the euler or milstein methods were used but , i have seen that some on wilmott suggest the leif anderson method. where can i find the method and also I may need help applying it to the risk neutral dynamics discussed above.thanksfor the help

For your first questionHave a look in the literature of LMM with Spot Measure in mind instead of risk neutral measure I think you should find plenty of reference Regards

TheBridge, so you are saying that the RN and Spot measure are often found together? okay I will look for that.

You can check out the LMM chapter from our book, available for free in the downloads section hereVladimir

@VladimirWhen is the book going on sale?*impatient fan*

what do you mean by risk-neutral measure?If you mean using the continuously compounding money market account as numeraire, then the reason you won't find much on this is that part of the point of the LMM was that it abolished the need to have a short rate and continuously compounding money market account. If you want to use the discretely compounding money market account as numeraire then this is pretty standard.

QuoteOriginally posted by: katastrofa@VladimirWhen is the book going on sale?*impatient fan*mid-summer, with any luck

Have a look at Erik Schlögl "A Multicurrency Extension of the Lognormal Interest Rate Market Models" Lemma 3.3. If the volatility of zero bonds to the next tenor date is assumed to be zero, risk neutral and spot measure coincide!

Here it might be the right time to ask the question: what is the date 0 definition of thae call option payoff? Actually date 0 does not relevent to this question. Is there 1) max [ S_mu ( T ) - K , 0] or 2) max [ S_r ( T ) - K , 0]. In BS setting that generated risk neutral world it should be the 2) though by definition payoff should be 1) ?