Lognormal multifactor HJM

Picco · February 5th, 2002, 4:31 pm

Can anyone give me a hint how to implement a lognormal multifactor HJM model. In the actual low interest environment, a basic multifactor HJM model (volatility factors estimated by PCA)is quite likely to give negative forward rates. Thus, I tried to implement the non-infinitesimal short rate modification of the HJM (laid out in Wilmott), but got some troubles. Has anyone done this before?

johnnorman · March 5th, 2002, 6:40 am

HiOne thing comes to my mind - and that is an earlier article by Heath, Jarrow and Morton (1990), where a log-normal version in connection with PCA are discussed. I can find out til tomorrow what the title of the article is - as I do not have it with me here.Does this help?

Picco · March 5th, 2002, 1:36 pm

Thanks,In the meantime, I found some articles (Goldys/Musiela/Sondermann, Sondermann/Sandmann) which describes in more detail the non-infinitesimal compounding approach. With the help of this article (and some creative scaling of the volatility factors) I was able to code up a log-normal HJM model, which gives quite reasonable results (positivity and finiteness of the rate is guaranteed. But anyway, thank you for your help.Regards,Picco

Pat · March 5th, 2002, 2:00 pm

Another alternative are the BGM models, which are essentially discrete HJM models.Also, need some care because low rates are where log normal models break down(!). For example, in Japanese Yen one is almost forced to use a normal of square root model because the log normal volatility varies dramatically by how close rates get to zero.