Swap Curve

It is possible to create a spot curve using market swap rates.
Often thought of as the swaps equivalent of the treasury bonds spot curve.

Constructing the Swap Curve

We need to find the equivalent of a zero-coupon bond at certain maturities.
Once we have this information we can apply the bootstrap method to create a curve.
The LIBOR without any qualification means the US dollar LIBOR rate

The market instruments used are the most liquid and dominant interest rate products to certain time horizons
A curve is usually divided into three parts:
Short End - using determined using LIBOR
Middle Part - using Eurodollar futures or Forward rate agreements
Far End - using Mid Swap Rates

Short Term (Deposit) : < 3 months

Derived using overnight, 1 week, 1 month, 2 month and 3 month
Each deposit instrument pays out a single payment at the end of its term.
These are quarterly compounding

Unsecured Deposits from the money markets
You can use LIBOR
EURIBOR
EONIA
In Paris we have PIBOR, Frankfurt FIBOR etc
Federal Funds Rate

we can use the following formula
SS

Middle Term (Future) : 3 months < > 2 years

Forward Rate Agreements (Interest Rate Forwards)
OR
Eurodollar futures (EDF) - linked to 3 month LIBOR rates / short term interest rate futures - also needs a convexity bias adjustment

Long Term (Swaps) : 2 years <> 10 years

Swaps Market
using par swap rates derived from the Interest Rate Swap market
You can use LIBOR based interest rate swaps

Banks with high credit ratings lend and borrow money at the LIBOR interest rates
These rates are typically slightly higher than government curves

The swap rate is the weighted arithmetic average of forward rates for the term to maturity.

The "swap rate" curve shows the fixed-rate leg of a plain vanilla swap against the floating leg of a six month LIBOR

The Swap curve and the treasury spot curve are often drawn together
When a swap curve is different to the yield curve you have Swap Spread

Comparing to Treasury Yield Curve

LIBOR is richer at the short end
LIBOR does not extend past 1 year

Example

Lets imagine a 6 year loan with a floating interest rate of LIBOR + 0.5% per annum and lets assume the interest must be paid every 6 months.

Therefore every 6 months the interest rate is defined as 0.5% above the 6 month LIBOR rate and is set at the beginning of the 6 month period.

The interest rate is typically set at the beginning of the 6 month period, but payment is not due until the end of the 6 month period.

This is the interest rate at which banks are able to borrow funds from one another
It is used for short-term lending transactions
The rate is published at 11:30am GMT

Banks submit the rate which they are willing to offer deposits to other banks
The libor rate remains fixed for 24 hours
There are at least 8 banks contributing for each currency
The submitted rates are then ranked and the average rate is taken from the middle two quartiles

10 major currencies
15 borrowing periods (overnight to 1 year)

Discount Rate/Lombard Rate
This is the rate at which the bank will discount eligible bills of exchange (i.e. top quality bills) for other banks.
The maturity of these bills must not exceed 3 months. As this rate is below other rates there is a quota for each bank or life would be too easy. If we could discount a bill at 9.5% and then finance ourslevs at 8 3/4% at the central bank we would soon make lots of money.

Interest Rates - The terms "bid rate" and "offer rate" are usually met in securities markets.
The offer is always higher than the bid and the difference is called the "spread" (typically quite small)

When it comes to wholesale money, the banks deposit rate is called the "bid rate" and their lending rate is called the "offer rate"
The interbank lending rates in London are therefore

In the US the interbank rate is called the "Federal Funds Rate"

Interest rates vary with time and so the interbank rates for 1 month, 3 months, 6 months and 12 months will probably all be different.

What is the Sterling LIBOR rate today ?
There will always be referring to the 3 month rate
The interbank market in London deals in all currencies and the wholesale rates offered by different banks could be different.
If we say Sterling LIBOR is 10 1/16 % we mean the average of all the major banks in the market.

Lending rates are typically quoted as LIBOR + or - ? basis points

Pre-Crisis
Interest rates derivatives are priced using a single curve (LIBOR curve or Swap Curve)
This curve was used to project Forward LIBORs of all tenors and obtain discount rates
This one curve was used for both discounting and forecasting
Overnight Index Swap (OIS) rates could be projected using this curve
Swaps were simple to value using this curve

Crisis (2007)
There was a significant divergence of the different Libor tenors
The cross currency basis also diverged
Banks CDS spreads increased dramatically

Post Crisis
Collaterised trades should be discounted at OIS (which is less than LIBOR)
Uncollaterised trades should be discounted at Banks Unsecured Funding Rate (which is greater than LIBOR)
LIBORs of different tenors cannot be projected off the same curve
Rolling a 3 month deposit is not the same as a 6 month deposit
Need to have separate curves for (OIS, LIBOR of all tenors, Unsecured Funding, etc)