Science of term structure CMT swap

[enjofaes]

Hi David,

I have a question relating sheet 29_7_CMS in the spreadsheets. Maybe a stupid one. The probabilities q & 1-q, are these normally given for this example?
I'm maybe overthinking it, but as we are given the interest rate process we should firts derive it assuming a zero-coupon security and then calculate the value of the swap?

 

[gsarm1987]

@enjofaes The example on page 27 in the notes, shows real-world probabilities on the tree (50/50) but if its risk neutral probability, then you may need to calculate the p and q (page 28). Just sharing for info, RN probability = (1 + rf - down)/(up - down). up for higher rate, down for lower rate. This one may not necessarily be 50-50. its done by calibrating with the market price. I've seen a question of such nature in my exam. sometimes just knowing the formula can save you a score