Fixed Income (1)
The Term Structure and Interest Rate Dynamics
Spot Rates, Forward Rates, and the Forward Rate Model
The spot curve: the annualized return of an option and default risk free zero coupon bonds of various maturities
The forward curve: the curve of forward rates over a range of maturities from a specified start date
The par curve: the curve of YTM on coupon-paying government bonds priced at par over a range of maturities.
Bootstrapping: a technique for deriving the zero coupon yield curve from the par curve
An inverted yield curve reflects market expectation of declining future inflation rates. They are often observed before recessions.
Yield-to-Maturity in Relation to Spot and Forward Rates
The YTM is the expected rate of return for a bond held to maturity, assuming that all promised coupon and principal payments are made in full when due and that coupons are reinvested at the original YTM.
Summary
Z Spread: The constant spread that equates the price of a security to the present value of its cash flows when added to the yield at each point on the spot curve
Arbitrage Free Valuation
Intro
Value Additivity: The sum of the whole must equal the sum of the parts. ex. buy portfolio sell individual holdings
Dominance: A risk free payout must have a positive price in the future. ex. two risk free assets of different rates having the same price.
Arbitrage-free valuation for an option free bond
definitely need to review pathwise valuation