Brigo&Mercurio`s lognormal model

LesleYLyu · February 5th, 2015, 2:17 am

Hello,please help. I am working on Brigo&Mercurio 2002 lognormal mixture model. And I am a little confused about their "shifted model"--see section 4, shifting the distributionIn figure 5, they provide an example, the calibration to a caplet data. And finally they obtain the parameters for lambda,eta, and alpha, but no information on A_0Is this a typo or A_0 is actually not a parameter to be determined?Any experience and hints on this model are truly welcomeThanks

Orbit · February 5th, 2015, 6:31 pm

Isn't it this?[$]A_0=\frac{S_0}{(1-\alpha)}[$](from equation 20)

LesleYLyu · February 10th, 2015, 1:16 am

Thanks Orbit, I got it, so basically the shifted model has only one additional parameter, alpha. A0 could be derived from S0 and alphaanother question, have you tried to implement their model. I did, and found 2 problems bother me:1. I tried to product figures in their paper, but my results are always a little bit smaller than theirs2. for some almost flat market curve, their model performs badly. If only limited strikes exist in the market (maybe 5 or 6), model did badly. I decided to use only cubic spline in this situationAny suggestions?

Orbit · February 10th, 2015, 8:10 pm

LesleYLyuI implemented this but it was years ago when I worked at a different place. I will try to find my model or maybe just re-do it. Not sure if I have the time. I remember it being a cool model conceptually but I seem to remember there were some challenges fitting certain market situations.If I get time I will post thoughts here. If you don't see me then it means I was putting out fires