My calculation is 35/36 and I verified this with 1000000 simulations.{(1+2+3+4+5)/6 + (1+2+3+4)/6 + (1+2+3)/6 + (1+2)/6 + 1/6} *1/6

Step1: simulate a Brownian process W(t) between time 0 and 1Step2: Let W_b (t) = W(t) - t*W(1)You got a Brownian Bridge.

Your guys made this way too complicated. Here is my answer: pi*3*2*1/3 = 6.8mile/min which is 408mile/hr.

What exactly is CMS 10Year Rate? Think of 10Year CMS Swap, the floating leg is 10Y Swap rate, is so called CMS 10Y rate the fixed rate which gives zero value to this swap?

Got it. Thanks!

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?

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