Fixed Income Flashcards
What is bootstrapping?
Where Spot rates can be derived from the par curve.
100 = Y3 Par / 1+y1Spot + Y3 Par / 1+y2spot^2 + Y3 Par + 100 / 1+Y3spot^3
You will be given the par rate in year three and spot rates in Y1 and Y2 and you solve for Y3 par.
Are spots arithmatic or geometric means of forward rates?
Spot rates are geometric means of forward rates.
YTMs are weighted average spot rates.
YTMs are weighted average spot rates
Upward sloping curve relationship of Forward, Spot and YTM?
Fingers, Strap Yelbows
Forwards steepest
Swaps middle
YTM shalloweest
Swap spread =
Z spread =
TED spread =
LIBOR OIS spread =
I spread =
Swap spread = swap rate of govt bond
Z spread = spread over govt bond
for callable bonds z spread = OAS spread + call option
TED spread = T-Bill vs Eurodollar future. General economy health indicator.
LIBOR OIS spread = LIBOR Vs Overnight Indexed Swap risk in money market securities.
I spread = Corp bond - Swap rate
Liquidity preference theory =
Yield curve reflect future expected zeros plus a risk/liquidity premium
Cox-Ingersoll-Ross Model =
Vasiceck Model =
Cox-Ingersoll-Ross Model =Interest rate movements are based on individuals choosing between Current consumption vs future consumption. Interest rates are mean reverting mean reverting to long term interest rates. Volaitilty increases as interest rates increase.
Vasiceck Model = Same as CIR but it holds volatility constant. Meaning there is no increase in volatiltiy as interest rates increase.
Pure expectations aka unbiased expectations theory =
We hypothesis that it is investor expectations that determine the shape of interest rate term structure.
Normally you’d expect longer periods to pay a risk premium but this is not the case with pure expectations / unbiased expectations theory which states forward rates are a function of spot rates. Ie a 5 year bond will pay exactly the same as a 3 year bond held to maturity and then buying a 2 year bond to maturity.
Risk neutrality is the key word as investors don’t require a risk premium.
Local preference theory =
Similar to pure expectations theory except investors deem risk neutrality only holds in the ‘local’ years short term. Over longer periods a risk premium should exist.
Ho Lee Model =
Observed market prices use binomial approach. Market prices calibrate the model to generate an arbitrage free model.
Interest rate volatility =
SD Annual = SD Monthly x no months in a year ^0.5
Shaping risk =
Sensitivity of a bond price to changes in shape of yield curve.
Main driver of short term interest rate volataility =
Monetary policy.
Binomial interest rate tree assumptions:
Volatility
Forward interest rates
Most useful for
Volatility = constant
Forward interest rates = lognormal random walk
Most useful for = Option-embedded options
Binomial tree
Callable bonds £99 and £101
Putable bonds £99 and £101
Callable bonds £101 becomes £100 as the company call the bond if it gets too expensive
Putable bonds £99 become £100 because the holder would sell at £100 if the price drops below this level.
Convexity of callable bonds ina falling interest rate environment.
Negative convexity.
