how to caclulate fair value of interest rate swap

how to caclulate fair value of interest rate swap

Online Interest Rate Swap Calculator

tipical example of interest rate swap contract between A and B:

example of swap

init date: 1/5/2012
maturity date: 1/5/2014
notional: 1 000 000 Eur
payments: annually
day counting convention: Actual/360
calendar: TARGET
A pays: fixed rate 4%
B pays: Euribor 12m

this contract can be represented by following cashflow diagram:

swap cashflows

Euribor rates generally are fixed at the beginning of the period (in our case one year before payment)

how to calculate fair value?

valuation algorithm

1. calculate net cashflow at every paydate
2. discount each cashflow to valuation date
3. sum all net discounted cashflows
payment 1 (1/5/2013)
A pays 4% on 1 000 000 = 40000 eur
we must multiply this quantity by year fraction with base Act/360 = frac(1/5/2012 -> 1/5/2013) = 1.014
so finally A pays 40000*1.014=40560 eur
B pays euribor 12m fixed on 1/5/2012 [  1.321 % ] i.e. B pays 1000000*0.01321*1.014 = 13394 eur
net pay1 = 40560 – 13394 =  27166 eur
this cashflow we must discount with EUR discount curve caclulated on 31/12/2012
suppose that discount factor for 1/5/2013 is 0.9
so discounted cashflow 1 will be 27166*0.9 = 24449 eur
payment 2 (1/5/2014)
A pays 4% on 1 000 000 = 40000 eur
multiply it by year fraction 1.014
A pays 40000*1.014=40560 eur
B pays euribor 12m fixed on 1/5/2013
this date is in the future so we must estimate it (=calculate euribor forward) with forwarding yield curve Euribor 12m on 31/12/2012
we can calculate this forward by formula:
$$F= \frac{1}{YearFrac(1/5/2013 -> 1/5/2014)}(\frac{ DF(1/5/2013)}{DF(1/5/2014)}-1)$$
here the year fraction is calculated with the convention of the discounting curve  (suppose its the same act/360 convention)
if DF(1/5/2013)=0.8
and DF(1/5/2014)=0.85
then B would pay 1000000*0.058*1.014 = 58812 eur
net pay1 = 40560 – 58812 =  -18252 eur
this cashflow we must discount with the discounting yield curve with reference date 31/12/2012
suppose that discount factor( 1/5/2014)= 0.7
so discounted cashflow1 is -18252*0.7 =-12776.4 eur
So , this swap’s fair value on 31/12/2012 is -12776.4 eur
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