Valuation of SWAPs and SWAPTIONs

Summaries

1. Plain Vanilla SWAP
1. To valuate a swap, find the net cash flows and discount to the present values.
2. However, it is not easy to find the cash flows without knowing the future interest rates for the floating part.
3. Therefore, one can use bond valuation approach. For the fixed rate, use a fixed rate paying bond. For the floating rate, use a floating rate paying bond.
4. At the initiation, the term structure is given. Use this term structure to valuate the floating bond and find the fixed rate (swap rate) such that the value of the swap is zero.
5. In the future, valuate the swap by using the new term structure on the fixed bond (payment is fixed already but PV is not) and floating bond.
6. Swap does not involve principal payment. But in the bond-valuation approach, we have to include the principal payment
7. *** For floating bond, the value is set to par value each settlement. This simply the valuation when valuation is done between the settlement date.

2. Currency Swap:
1. Principal is exchanged at the termination of swap!
2. Fixed DC with Fixed FC
3. Fixed DC with Floating FC
4. Floating DC with Fixed FC
5. Floating DC with Floating FC
6. 2 systems (DC and FC); Use the spot exchange rate to find the notional amount in DC and FC systems; in each system, find the swap rates; in the future, to valuate the swap, determine which swap is used (10-13); Then just calculate the PV of cash flow in each system and use the spot exchange rate to find the value.

3. Equity SWAP:
1. Fixed with Equity
2. Floating with Equity
3. Equity with Equity
4. Value of Equity is found by the %change of value (new index/old index) X notional principal = change of total value in equity side (NOT treating the % change as interest rate); Fixed and Floating are calculated as in Plain Vanilla; Then find the net PV.

4. SWAPTIONS:
1. Options give holders the right to enter into swap
2. Notation same as FRA 1X3: mature in 1 year to enter 2 years swap
3. payer swaption: right to enter as fixed rate payer
4. receiver swaption: right to enter as fixed rate receiver
5. Can be American or European
6. a) Lock in fixed rate b)interest rate speculation c) swap termination

5. SWAP credit risk:
1. Current credit risk
2. Potential credit risk
3. Highest at the middle of the swap (for currency swap, later stage)