User FAQs

1) What is Curve Building ?
This is the process of extracting market information to find out what the market consensus thinks about projected interest rates.

2) What is Bootstrapping ?
This is a method that can be used for curve fitting.

3) Bootstrapping can be split into two categories
Exact Methods - market rates can be replicated exactly but need assumptions on the interpolation
Non-Exact Methods - requires calibration/testing and then needs to be checked for consistency / validated

4) What is the Spot Yield Curve ?

5) What is a Spot Curve used for ?

6) What is the Forward Yield Curve ?

7) What is a Forward Curve used for ?

8) What is the equation (or relationship) that connects spot rates and forward rates ?
Fabozzi, pg 134

9) What is the Swap Curve ?

10) What is a Swap Curve used for ?

11) What is an Inverted Yield Curve ?

12) If the spot rate for a Treasury Bill with a maturity date in 3 months time (91 days) is 8.91%, what is its price today ?
The yield to maturity for zero coupon bonds is referred to as the spot rate, so Yield to Maturity is 8.91
The face value of a Treasury Bill is $1,000,000
The day count convention is Actual/360
price = 1000000 / (1 + (8.91/100))^(91/360) = $978,656.1

13) I am receiving £100 in 6 months time, How much is that worth today ?
You can calculate this using the Spot Curve.

14) I need to pay £100 in 6 months time. How much is that worth today ?
You can calculate this using the Forward Curve.

15) Once we get the Swap Curve we can infer all the other curves
You can infer the Spot Curve and Forward Curve from the Swap Curve

16) If the spot rate for a Treasury Bill with a maturity date in 6 months time (182 days) is 11.56%, what is its price today ?
price = 1000000 / (1 + (8.91/100))^(182/360) = $946,197.5

17) What is the annualized bank discount yield for this 6 month Treasury Bill (expressed as a decimal) ?
Treasury Bills are traded in the secondary market, and are quoted based on their bank discount yield.
This is the approximate annualized return the buyer should expect when holding to maturity.
discount yield = (dollar discount from face value / face value) * 360 / (days until maturity)
discount yield = (946,197.5 / 1,000,000) * (360/182)
discount yield = 1.8716 %

18) Can you describe the term Holding-Period Yield ?

19) Can you describe the term Effective Annual Yield ?
Also known as Effective Interest (Quant page)
This converts an interest rate to an interest rate that is compounded every year.
This allows investments that have different compounding frequencies to be compared.

20) What is Arbitrage Pricing ?
This is thought to be an improved alternative to its predecessor Capital Asset Pricing
By extracting the discount factors used from currently traded instruments we can use the same discount rates to price other instruments.

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)