Hull White Calibration

kv · June 11th, 2004, 4:55 pm

Hi,I'm a student in financial engineering in an french engineering school specialized in informatics and Applied Mathematics. I would like to implement the calibration of Hull White model with a mean reversion rate time-dependent and a spot volatility time-dependent.Let's say that we have : is known.So as to determine my parameters, I will use for example enough prices of caplets. I've read an article by John Hull who said that the best way to calibrate is to use the Levenberg-Marquardt algorithm that I've found on Numerical Recipes. But the thing is that I need a pricing formula for caplets for THIS model to apply the best fit procedure implied by the LM algorithm. I have found some formulas but they were all for constant. Does someone know if there are some formulae for pricing caplets for this model?Thanks

kv · June 15th, 2004, 7:29 am

Come on, please...Doesn't someone have a clue? I'm completely stuck...Thanks...

doublebarrier2000 · June 15th, 2004, 8:09 pm

be careful as to which vanillas you use to calibrate the modelps. try using least squares minimisation with an iterative process

doublebarrier2000 · June 15th, 2004, 8:12 pm

just remembered that I have a spreadsheet that I downloaded from a past thread that calibrates the HW model

kv · June 15th, 2004, 8:50 pm

I'm going to see that and give you feedback as soon as possible... Hope it will help me...Anyway, thanks for your help!

kv · June 17th, 2004, 3:15 pm

I've briefly read the spreadsheet you gave me... It's very useful as it gives me a good environment... I don't know if you have a really good knowledge about the code underneathj this spreadsheet but it's calibrating Hull-White model for only two parameters (the drift and the spot volatility) which are supposed constant. But I would like to calibrate this model with piecewise constant functions for these parameters. Do you think it would be easy to adapt this VB code for my problem? I think so but as a student I can't be a 100% that I'm on a good way.Please tell me what you think about... Thanks

kv · June 21st, 2004, 4:24 pm

Hi again,So, I succeeded in adapting this spreadsheet for piece-wise constant mean-reversion rate and spot volatility but there are still little problems... If someone is interested, I can put it on the forum when it will be complete.If you could just tell me who wrote this code so I could join him and discuss about the ameliorations I brought...For example, I would like to know why the model is more accurate with Market Caps volatilities close to 100% whereas all the quotes I have found for caps (with 3 months tenor) are around 20%. By the way, what is the tenor of the caps considered in this spreadsheet?Anyway, thanks again for the help...

nparaschos · July 29th, 2004, 8:03 pm

Hey KV,I don't know who posted the original spreadsheet. It may be worthwhile asking a member by the name davidjn. He's quite knowledgeable about HW and calibration methodologies. He's also a nice chap.You may want to post your spreadsheet with the amended code anyway.Regards,

entpl · August 25th, 2004, 3:09 pm

I have tried calibrating with this spreadsheet and have severe problems with v. low yield curves ( forwards in the range of 0.01 - 0.03). Has any1 on this thread encountered them?

domilar04 · October 15th, 2004, 9:14 am

HiI am also new to this quants world and have a question about implementation of Hull-White Tree with unequal time steps. "Using Hull-White Interest-Rate Trees" provides a roughly introduction about it. But it doesn't mention how to decide the boundary (Jmax=0.184/(a*dt) in equal time steps model).Anyone can help me? Thanks in advance.Chris

Za · October 27th, 2004, 2:46 pm

KV,I'm interested in your spreadsheet. Could you post it ?I'd like to compare your calibration with mine.Thanks,Za.

calculator · December 27th, 2004, 5:54 am

Hi domilar04,The value Jmax=0.184/(a*dt) is calculated so that you can switch from a "(up/stable, down) configuration" to a "(stable, one up/down, two up/down) configuration" and still getting positive probability of transition. It is important to switch as quick as possible to that configuration to limitate the calculation time.RegardsC

computedrisk · December 29th, 2004, 2:49 pm

Hi there,I am just like some of you, a new-comer in this quants world. Recently, I was given a project to creat interest rate paths using Hull-White model. I took a look at the spreadsheet that you guys posted, it is very useful, however, it looks pretty complicated to me, especially, when I was trying to step into the vb codes. Would you please tell me a little bit (any helpful web info will be appreciated) on the least square method, LB method or the Brent method.Thanks in advance.cr

hunting · December 29th, 2004, 4:41 pm

As a side note, when calibrating, is it typical to fix theta(t)? If so, what is it fixed to?Thx

computedrisk · January 3rd, 2005, 7:18 pm

In Hull's book, it says that that theta function can be calculated from the intitial term structure, is theta supposed to be a function of time, so how is theta (t) calibrated?thanks,cr