# 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
bad day convention: Modified Following
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: