# Valuation of Swaps

- There are 2 ways to value a swap.
- Considering it as a difference of two bonds
- Considering it as a portfolio of FRAs

- Value using bonds
- Consider an example in which the swap lasts for n years. If the payments are made at the end of each year then :
- If the principal is exchanged between the 2 parties at the end of the swap, then Party 1â€™s cash flow suggests that itâ€™s long a fixed rate bond and short a floating rate bond.
- Party 2 is short a fixed bond and long a floating rate bond.
- We can value the swap by looking at the pay offs of either party.

- Hence the value of the swap can be given as:
**V = B**_{fix}â€“ B_{fl}- Where:
- B
_{fix }= PV of payments - B
_{fl}= (P+AI)e^{-rt}

- B

- Value of a floating bond is equal to the par value at coupon reset dates and equals to the Present Value of Par values (P) and Accrued Interest (AI)

**Value using portfolio of FRAs**

- In this case we assume that each payment at a future date is a forward rate agreement.
- For payment at time t, the rate used is the rate for the period between t-1 and t. This rate would be FRA at t-1