Swap

Exchange of cash flows from fixed interest for floating interest. Several types: interest rate swap, currency swap, equity swap, volatility swap, commodity swap, …

Example of a plain vanilla interest rate swap using bonds: discount fixed rate cash flows, discount floating rate cash flows and take difference. fixed rate=6%,semiannually, floating rates=(5.4%,5.6%,5.8%), 1M notional, every 6 months, for 1.5 years. $B_{fixed} = 30'000 e^{-(0.054*0.5)} + 30'000 e^{-(0.056*1)} + 1'030'000 e^{-(0.058*1.5)} = 1'001'744.42$ $B_{floating} = 1'000'000 * (1 + \frac{0.05}{2}) e^{(-0.054*0.5)} = 997'695.27$ $V_{swap} = (B_{fixed} - B_{floating}) = 4'049.15$

Example of currency swap valuation using forwards: paid rate for USD: 5%, received rate for GBP: 6% GBPUSD = 1.50, interest rates in USD: 2%, GBP: 4%, time: 2 years, annually paid.

Time	USD CF	GBP CF	forward rate	$ per GBP	Net CF	PV of Net CF
1	7.5	6	1.47	8.82	-1.32	-1.294
2	7.5	6	1.441	8.646	-1.146	-1.101
2	150	100	1.441	144.1	5.9	5.669
Total						3.274

Forward rate calculation: $F_1 = 1.5 e^{(2{\%}-4{\%})*T)}$