Can you explain to me in details step by step how to work this out --- We suppos

Question

Can you explain to me in details step by step how to work this out

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We suppose that the 2-month zero rate (CC) is 3.1%, the 5-month zero rate (CC) is 3.6%, the 8-month zero rate (CC) is 3.7% and the 11-month zero rate (CC) is 3.8%.

There is a swap with maturity 5 months that pays every 3 months (the fixed leg and the floating leg have same frequency). The rate of the fixed leg of the swap is 3.6% (given on an annual basis and the nominal is 100 as usual). One month ago the 3-month Libor rate was 3.4% (given on an annual basis). Compute the value of the swap paying the floating leg and receiving the fixed leg.

Explanation / Answer

Answer- Swap value => Vswap = Vfix - Vfloating

Vfix = value of receiving the fixed leg

Vfloating = value of paying the floating leg

Vfix = (3.6/4)e-r22/12 + ( 3.6/4 + 100 )e-r55/12 = 100.2931567

[ rate of fixed leg of swap is 3.6% pa and it pays every 3 months so quarterly rate is 3.6/4 ]

Vfloating = ( 100 + 3.4/4 )e-r22/12

= 100.3302854

[one month ago rate of 3-month Libor was 3.4% pa, swap pays every 3 months so quarterly rate is 3.4/12 and 2 months are remaining. ]

Value of swap (Vswap) = Vfix - Vfloating = 100.2931567 - 100.3302854 = -0.037128721

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