LGM Models: implementation and calibration

NY153 · January 12th, 2007, 4:13 pm

Hi All,This subject was probably already treated in previous posts but I didn't find any post.I am interested by the LGM models (1 upto 3 factors). Does anybody have some experience with these models? Apart the Hagan paper, I did'nt find any documentation about the implementation and calibration of these models. Can anybody help me with some references?Regarding the fact that this model is equivalent to the HW model in an HJM framework; is it usually used with tree/PDE (like the HW) or strictly with MC (like the HJM)?Thanks in advance for your help.NY153

Joshua2004 · January 12th, 2007, 5:00 pm

I implemented LGM up to 2 factors, maybe will go to 3 factor but not right now.LGM is equivalent to extended HW model, but it is much easier to calibrate. you have analytic fomular for the option instrument, and very good proximation works also.About the techniques, I used gauss convolution in 1-D as suggested by Pat. and FFT in 2-D. I am thinking research the gauss-hermit integration method (in 1-d it is not as good as convolution, but probably it has advantage in hight than 2-D case)

gjk77 · January 12th, 2007, 5:55 pm

Chp 17 of Hunt and Kennedy book, "Financial Derivatives: In theory and practice" describes an implementation of the HW model which is similar to the method in Hagan's LGM papers

germoz · January 13th, 2007, 7:48 am

Where can I find Hagan's LGM papers ?

gjk77 · January 13th, 2007, 10:18 pm

There are 2 papers I am familiar with were the term LGM is used'Accrual swaps and range notes''Methodology for callable swaps and Bermudan "exercise into" swaptions'These papers are on these forumsIt also helps to look at "Markov interest rate models", Applied Math Finance, 6, 233-260 (1999) by Hagan and Woodward.

NY153 · January 14th, 2007, 11:02 am

Thank you for the reference of for the comments. I will give a look at the Hunt and Kennedy chapter.I would like to highligth the advantages of the LGM model wrt to the HW model. What are the advantages and the drawbacks?Secondly, I am interested by using this model (with 2 factors) to price bermudan callable swaps. What's your experience on this point?Thanks in advance

westwood23 · March 19th, 2007, 11:28 am

Does anyone have any information about the 2 factor version of LGM? Papers, SDEs etc would be very much appreciated.