Z Spread Post
William Carpenter / April 2024 (104 Words, 1 Minutes)
Z-Spread
This project and source code is available on github here
Introduction
In fixed income markets, investors rely on various ‘spread’ measurments to help provide a more informative metric of incremental yield they are receiving vs. a benchmark instrument (ex: Treasury bonds that are often considered to be ‘riskless’). This spread would represent compensation for various risks in a given bond that are not in a riskless, benchmark instrument, such as: prepayment risk, credit risk, liquidity risk, etc. Spreads can be readily calculated given a bond cash flow and price and will also give investors a tool to compare relative value between bonds that could have different characteristics. This project focuses on the calculation Z-Spread, which assumes zero-volatility in cash flows and interest rates - it is considered to be a ‘static’ valutaion tool, but still more informative than a simple yield spread.
Objectives
Use Treasury data to calculate daily spot rate curves over a given time span.
Generate mortgage cashflows that have flexibility to handle various prepayment assumptions.
Calculate a bond’s Z-Spread for a given cash flow provided a price, or vice-versa
Procedure
Obtain U.S. Treasury Par-Yield Data
Interpolate Semi-Annual Treasury Par Yield Rates
Bootstrap Semi-Annual Zero Coupon Rate Curves
Generate a Bond Cash Flow
Calculate Price Given a Bond Z-Spread
Calcuate Z-Spread Given a Bond Price
Mathematical Background
Code Examples?
And here is some inline code!
Here is a nice code block:
def crr_trinomial_tree(S, K, r, t, T, vol, call, american)