How to simulate CMS 10y

linlibj · February 3rd, 2005, 10:04 pm

Starting with a short rate model, say H-W, how do I simulate CMS 10Y rate month by month?

prettyspecific · February 3rd, 2005, 10:39 pm

what's CMS

mghiggins · February 4th, 2005, 12:49 am

You simulate the short rate under your HW model; then the spot CMS rate is just a function of that short rate (that you can express in terms of zero-coupon bonds, which are analytic under HW given the short rate).

linlibj · February 4th, 2005, 1:50 pm

Thanks, mghiggins! What you said is applicable to each path in MC simulation. How about lattice? Starting from H-W, you can build a binary tree of short rates, how do I get CMS 10Y on each node?

dicesare · February 4th, 2005, 2:03 pm

You have analytic formula for zero-coupon bond as function of the short-rate : P(t,T) = A(t,T) exp(-B(t,T)*r(t) )and CMS 10y (t) = [ P(t,t_0) - P(t, t_0+10Y) ] / A(t)with A(t) be the annuity

linlibj · February 4th, 2005, 3:54 pm

Got it. Thanks!

Raul85 · February 26th, 2009, 6:25 pm

Church · February 28th, 2009, 12:00 pm

Well, you could try a 2-factor Hull-White model (G2++).Note that there are very good (and easy to implement) approximations for options on CMS-rates given underlying n-factor Gaussian models, see http://ssrn.com/abstract=1093710