## Nelson-Siegel Yield Curve Model

(Yield curves are obtained by bootstrapping the interest rate information contained in a range of risk-free/ near risk-free fixed income instruments (deposit rate, LIBOR, FRA, interest rate futures, interest rates wap, OIS swap, government bond…).  Rather than treating each data point as separate, many are more interested in the term structure of the yield curve. Nelson-Siegel (and its extension Nelson-Seigel-Svensson) exponential components framework is one of the most popular yield curve models.  The forward rates are readily available once a Nelson-Siegel model is obtained.  As shown by Diebold & Li, the three time-varying components in Nelson-Siegel can be interpreted as factors corresponding to level, slope and curvature.   These factors have also been shown by Diebold & Li to have some forecasting power. We will go through the meaning of various components of Nelson-Siegelmodel, its implementation and other alternatives in yield curve modelling. ` Continue reading “Nelson-Siegel Yield Curve Model”

## Nelson Siegel Model – Python Source Code

This program implements Nelson-Siegel and Nelson-Siegel-Svensson Yield Curve models.  Grid-based OLS is chosen as the parameter estimation algorithm.  Last update: change OLS to weighted OLS to improve model fitting performance.
• Author: David Y
• Date of release: 2019-11-13
• Date of last update: 2019-12-01
• Version: 1.1.0
• Language: Python (tested in python 3.7.1)

## Hurst Exponent – Python Source Code

The calculation of Hurst Exponent.  It is ported from Matlab to Python based on Rafal Weron’s code.
• Maintainer: David Y
• Date of release: 2019-11-05
• Version: 1.0.0
• Language: Python (tested in python 3.7.1)

## Volatility Cone – C# Source Code

While the generation of volatility cone[1] [2] can be done via e.g. a spreadsheet, the calculation is a bit repetitive and is thus more convenient to code it in C#.

• Author: David Y
• Date of first release:2014-08-30
• Version: 1.0.0
• Language: C# (tested in VS Express 2013 for Desktop)

## Demystify the Volatility Cone

Volatility cone is a visualisation tool for the display of historical volatility term structure. It was introduced by Burghardt and Lane[1] in early 1990 and is popular in the option trading community. Using the same methodology, we can extend the use of such chart for periodic return data. I find these charts useful not only for options but also for the general market. Continue reading “Demystify the Volatility Cone”

## One Factor Interest Rate Model – C# Source Code

I have looked into the analytics for callable bonds lately [1][2].   The involves the use of an interest rate tree.  I thus implemented the Hull-White and Black-Karasinski one-factor short rate trees illustrated in Hull’s Options, Futures and Other Derivatives 6th Ed.  Ch28.7.   I included procedures to calibrate the rates tree using the premium of interest rate cap.   Once a tree is generated, it can be used to price and calculate the OAS for callable bonds (both fixed and floating rate with flexible call schedule).

• Author: David Y
• Date of first release:2014-08-03
• Version: 1.0.0