swap rate on zero coupon swap

[archived_user]

How do I find a swap rate of a zero coupon swap? I know that the determining equation is value_of_floating_leg = value_of_fixed_leg. What should be the unknown in the equation, the discount rate in the denominator of the zero coupon or the face value in the numerator? But then the face values of both legs should be equal, shouln’t they?

 

[archived_user]

tsodoreti wrote:
But then the face values of both legs should be equal, shouln’t they?
How do I find a swap rate of a zero coupon swap? I know that the determining equation is value_of_floating_leg = value_of_fixed_leg. What should be the unknown in the equation, the discount rate in the denominator of the zero coupon or the face value in the numerator?

I think this rate is equal to (1- Z(T) ) /Z(T) with Z(T) - the price of T-year zero coupon bond at t = 0.
I note the swap rate is C.
The value at t = 0 of fixed leg is : C* Z(T)
The value at t = 0 of variable leg is : 1 - Z(T) (you can find it in the CFA books)
because the value of fixed leg = variable leg, so C = (1- Z(T) ) /Z(T)
It is the first time i hear about Zero Coupon Swap. Is it in the CFA books?

 

[archived_user]

This topic is in the reading on term structure of interest rates. The goal is to establish interconnection between swap rates and spot rates. For that (they say) they use zero coupon fixed leg, but (as usual) lack any elaborate explanation.
In your answer I am not sure about the value of the floating leg, as it usually has periodic floating payments in all IRS, making the value (1+coupon_set_at_the_last_coupon_date)/(1+current_one_period_discount_rate).
More detailed calculations are done in the derivative section, but i am not sure there is any zero coupons.

 

[archived_user]

A zero coupon swap (if it already exists) would be the same as a forward contract, right? That wouldn’t be a swap then. A swap, as the name states, is the exchange of positions more than 1 time.

 

[archived_user]

The way it is explained if googled, a zero coupon swap is “an exchange of income streams in which the stream of floating interest-rate payments is made periodically, as it would be in a plain vanilla swap, but the stream of fixed-rate payments is made as one lump-sum payment when the swap reaches maturity instead of periodically over the life of the swap.” The question is, what is the swap rate?