Examples

Discount Factor

A loan starts in one year and lasts for 2 years.
The 1 year spot rate is 6%.
The 3 year spot rate is 8%.

Calculate the 1 year discount factor
=1/(1+6%)^1 = ??

Calculate the 3 year discount factor
=1/(1+8%)^3 = ??

Calculating Forward Rates from Spot Rates

We have three zero coupon bonds.
They have a maturity of 1 year, 2 year and 3 year.
The spot rates for these three bonds are shown below
Bond 1, Maturity 1 Year, Spot Rate = 9%
Bond 2, Maturity 2 Years, Spot Rate = 10%
Bond 3, Maturity 3 Years, Spot Rate = 11%

Calculate the forward rate for a 1 Year zero-coupon bond that is issued 1 year from today

Calculate the forward rate for a 2 Year zero-coupon bond that is issued 1 year from today

For a vanilla swap you need at least one forward curve (3M libor) for cash flow generation and a discount curve (OIS) for calculating present values