Let Ti, i=1, … ,n be a set of dates, on which payments of thefloating leg of an interest
rate swap occur. The payoff of the floating leg of the swap attime Ti is Fi + s where Fi is
the reference rate of the floating leg and s is a constantspread. For simplicity, let’s
assume that the floating and fixed payments happen on the samedates. Also, ri is the
risk-free rate on the same tenor. Let N be the notional of theswap.
1) What is the fixed semiannual swap rate calculated from therisk-free rates? Please
specify mathematical formula (no need for exact numerical resultat this point).
2) Let the semiannual swap rate calculated in 1) be the fixedleg payment of the
swap. What is the constant spread s which sets the present valueof the swap
position to be zero? Please specify mathematical formula (noneed for exact
numerical result at this point).
How to address the question ?2?
