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
  • License: BSD
  • Language: Python (tested in python 3.7.1)

click here to download

Does Taking Higher Risk Lead to More Return In Bonds?

The low volatility anomaly is well-known in equity.  Holding a basket of shares with the highest beta does not generate the highest return.  It has been shown in many different regions and periods.  A similar mechanism may be in action in bonds as well.  The yield is higher when going down the rating spectrum.  But that does not fully compensate the credit quality deterioration beyond a certain point.  Examined 20 years of Bloomberg Barclays bond indices for US and European corporate, buy-and-hold the riskiest credit did not generate a good return.  There seems to be a sweet spot when going down the credit spectrum. Continue reading “Does Taking Higher Risk Lead to More Return In Bonds?”

Pairs Trade – Practice

In the last post, we had reviewed some theory related to pairs trade.  In this post, we will go through a textbook case of arbitrage to show how various test-statistics should look like.  We also introduce the half-life of mean-reversion and the Hurst Exponent as performance indicators.  We then look into a possible implementation for mean-reversion strategy before discussing the real-world issue in pairs trade. 

Continue reading “Pairs Trade – Practice”

Pairs Trade – Theory

Pairs trade is one of the simplest market-neutral statistical arbitrage strategies.  The goal is to find a pair of securities which historically move up and down in highly correlated fashion but the price differential between them is temporarily at an extreme.  We then long the relatively cheap security and simultaneously short the other.  Hopefully, the price differential would promptly revert back to normal such that we can realise some profit.  We would review some useful statistical concept (such as co-integration, stationary process) and discuss the types of securities that are likely to form good trading pairs.   Continue reading “Pairs Trade – Theory”

Callable Bond – Part 3: Perpetual Subordinated Capital Note

Perpetual subordinated capital note does not have a maturity date. It has a pre-negotiated coupon (which can be fixed, floating or switches from fixed-to-float in its lifetime) to the holder periodically but the coupon can be switch off if no dividend is being distributed to the ordinary shares at the time. The deferred coupon might be cancelled (non-cumulative) or pay back all at the same time in arrear (cumulative). Continue reading “Callable Bond – Part 3: Perpetual Subordinated Capital Note”

Callable Bond – Part 2: Callable HY in Practice

In this article, I focus on bonds comes with callable features when issued and look into why the bonds are structured the way it is. The callable bonds tend to be from HY issuers. Bond options structured thru fixed income desk of investment bank would not be considered here as these are largely interest rate investment and hedging derivative products with government bond or highly liquid investment bonds as underlying instrument.   The consideration can be different when compared with the cash HY bonds (e.g. the payoff of bond derivatives follow mechanical rule whereas the strategic financing decision at the company level would determine whether a HY bond be called – not just bond price in comparison with the strike). Continue reading “Callable Bond – Part 2: Callable HY in Practice”

Callable Bond – Part 1: YTW vs OAS

Callable bond: a credit perspective – Part 1: YTW vs OAS

Bonds with callable feature are very common in the HY space with close to 65% and 35% of all new US and European HY bonds are callable. These bonds tend to have a call schedule (rather than a single call date and price) with credit component more of a concern than the fluctuations in interest rate. This is a topic falls in an area somewhere between quants and fundamental analysts and tends to ignore by many. I intend to look closer to it in this series of articles. Yield-to-worst (YTW) and option-adjusted spread (OAS) are the commonest analytics being used. In part one, I will explain how to calculate YTW and OAS and how should we interpret them. Continue reading “Callable Bond – Part 1: YTW vs OAS”