Consider a swap contract with parties B and C in which B will pay (to C) a LIBOR spot rate and C will pay (to B) a fixed

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Consider a swap contract with parties B and C in which B will
pay (to
C) a LIBOR spot rate and C will pay (to B) a fixed rate R. To be
more
specific, the payment dates will be Ti = i,i = 1,2,...,n, where n ≥
2 is
a natural number. So T := Tn is the expiry date of the contract.
The
contract is written at time T0 = 0. Party B will pay K.L(Ti−1,Ti)
at time
Ti,i = 1,2,...,n while party C will pay K.R at these n time points.
Derive
a formula for the swap rate R, if it is given that R is determined
such that
the contract has zero value for both parties at time T0 = 0.
(b) Suppose now that, in an otherwise equal situation as described
in part
(a), the value of the principal diminishes by K/n at each time
point Ti,i =
1,...,n−1. Note that the payments at time Ti are based on the value
of the
principal over the period [Ti−1,Ti) for each i = 1,2,...,n. Derive
a formula
for the swap rate R for this contract, if it is given that R is
determined such
that the contract has zero value for both parties at time T0 =
0.