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
  • License: BSD
  • Language: C# (tested in VS Express 2013 for Desktop)
  • Model: Hull-White and Black-Karasinski one-factor short rate trees
  • Dependence: ALGLIB numeric library (for optimisation code)

Click Here to Download

Benchmarking with Euro Bond ETF

Bond ETF is now an important investment vehicle for US based high yield investors with the top 5 HY Bond ETF accounting for a total market cap of exceeding $40bn at the time of writing (24/6/14). While it is still just a small fraction of the $1.5tn US high yield market, the leading ETF iShares iBoxx $HY Corp Bond ETF (HYG – $13.5bn market cap) and SPDR Barclays HY Bond ETF (JNK– $9.8bn market cap) are closely following by many investors as the passive investment style of the ETFs makes them ideal benchmark (either when comparing with other funds or other asset classes). Moving across the Atlantic, HY bond ETF also enjoys phenomenal growth. The market cap of the biggest iShares iBoxx Euro HY Corp Bond ETF (IHYG) has grown more than 10-fold since Dec 2010 and reaches a market cap of EUR3.2bn. Continue reading “Benchmarking with Euro Bond ETF”

Credit migration matrix – use and misuse

A rating is supposed to be a stable long term predictor of the creditworthiness of a borrower. Every once in a while, the Credit Rating Agencies (CRAs) would release their analysis upon rating migration and, more importantly, how their ratings compare with realised default frequencies. The information is often summarised in form of a credit migration/transition matrix.  It is a useful tool but sometimes be misused. Continue reading “Credit migration matrix – use and misuse”