### Swap Market

#### LIBOR Curve

Also known as the Swap Curve, "interbank credit risk" or "interest rate swap curve"

An interest rate curve is often referred to as a swap curve

The Libor curve is also known as the Swap Curve ??

Banks with high credit ratings lend and borrow money at the LIBOR interest rates

These rates are typically slightly higher than government curves

The LIBOR curve is also known as the **Swap Curve**.

Another set is based on sterling interbank rates (LIBOR) and on yields on instruments linked to LIBOR, short sterling futures, forward rate agreements and LIBOR-based interest rate swaps.

These commercial bank liability curves are nominal only.

The relationship between the swap rates and time

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

The most popular being for the US dollar

The LIBOR without any qualification means the US dollar LIBOR rate

The US dollar LIBOR rate gives the interest rate for borrowing dollar deposits held in banks outside the United States

Dollar deposits held in bank outside of the United States are referred to as EuroDollars

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

#### Comparing to Treasury Yield Curve

LIBOR is richer at the short end

LIBOR does not extend to 30 years

#### LIBOR inc Short Sterling Futures

#### Bond Yields / Gilts

#### Overnight Interest Swaps

#### LIBOR

LIBOR stands for London International Bank Offer Rate.

This is the annual interest rate banks charge when lending money to one another in the International / eurocurrency markets.

This interest rate changes frequently and is determined by the supply and demand in the international market

This interest rate can be thought of as the interest rate for loans in the international Financial-Markets.

1 month LIBOR - The annual interest rate charged to borrow money for 1 month

3 month LIBOR - The annual interest rate charged to borrow money for 3 months

6 month LIBOR - The annual interest rate charged to borrow money for 6 months

When a floating rate interest rate is applied to loans it if often quoted in terms of LIBOR.

#### PRIME

Prime is the interest rate used for floating rate loans in the domestic financial market.

#### 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)

#### Types of Interest Rate

1) Deterministic

2) Stochastic - Processes where one state does not fully determine its next state (there is some randomness)

Financial models use stochastic models to value options on stock prices, bond prices and on interest rates (see Markov models)

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 Paris we have PIBOR, Frankfurt FIBOR etc

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 ?

Thery 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

LIBOR obv flucuates during the day.

LIBOR rate used is usually quoted as the average of the LIBOR rates given by the nominated banks at 11:00am on that day.

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

You also use this curve for discounting

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)

#### EURIBOR

Published for a range of maturities for the EUR interest rate

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