## Mini Chapter Two

# Unwind Value of swaps

Swap unwinds are computed as the present value of the cash flows (positive or negative) reflected in the difference between the traded fixed rate and the current market fixed rate. As the swap ages and market movement changes the projected floating rate (the current par rate) it results in a non-zero present value relative to the original fixed rate. In addition to the fixed rate differential, the unwind value also needs to be adjusted for any short stub valuation i.e. the residual current floating rate period that uses the updated interpolated floating rate vs the original floating rate to calculate the stub unwind value.

As an example of an **aged interest rate swap** – Consider a received 5y swap at a fixed rate of 5% against a 3m floating index. The swap has aged by a month since the start date of the swap and the first floating rate was fixed at 4%. Iâ€™ll discuss two different methods for the unwind:

## Method One

- Since the original swap now behaves like a fixed short stub cash flow for 2 month tenor and a 2m forward 4y9m fixed float swap – the unwind PV would have two components to it.

- First component – Assume that the current 2m forward 4y9m rate is at 4.5%. Then the PV of the forward starting component of the original swap is nothing but PV of net cash flows of 50bps every progressive 3 months after the effective start date; first reset in 2 months and first cashflow 5 months from today.

- Second component – please note that since the first fix was already set the net cash flow amount is already known. Itâ€™s the changing discount factor that would change the PV of the residual tenor. After a month therefore, the known net cash flow of 1% (payable for the 3m period) for the front short stub (2 months) would need to be discounted by the current 2m floating rate to obtain the PV.

- The total unwind value is the sum of the two unwind PV components above.

## Method Two - the more popular/widely observed

- Letâ€™s think of the original swap which now has a tenor of 4yr 11 month which is unwound by trading a live 4y 11 month swap in the opposite direction at 4.4% with a short front stub of 2m. Assume the interpolated 2 month fix is at 3.5%.

- First component – the differential of the fixed rates amounts to a present value of 60bps of the swap notional, starting in 2 months for every 3 months thereafter. Please note that this unwind value already incorporates the interpolated 2m stub since 4y 11mnth rate was traded to unwind the original swap.

- Second component – the difference in the front stub fixings will need to be adjusted. We have made 60 bps on the original fixed rate swap for 4y11m tenor but we have lost 50 bps on the 1st fixing for the residual 2 month tenor (paid 4% original fix received 3.5% on unwind). This cash flow discounted at the 2m rate of 3.5% will have to be deduced from the first component PV.

- Third component – The first month accrual of 1% as part of the final payout at the end of 2 months from today would also be discounted by the 2 month interpolated rate of 3.5% and added to the overall unwind PV.