We analyze the time series and cross-sectional properties of variance risk premia (VRP) in the interest rate swap market. The results presented show that the term structure of variance risk premia displays non-negligible differences in a low interest rate environment, compared to normal times. Variance risk premia have on average been negative and economically significant during the sample. In a low interest rate environment, the variance risk premium tends to display more frequent episodes where it switches sign. We extend these findings by exploring the effects of macro-economic announcements on variance risk premia.

• MATLAB 2020a with the following toolboxes (Econometrics, Optimization, Financial)
• Bloomberg Professional Services for historical data
• MATLAB system environment with at least 3 GB of memory

All project code is stored in the /Code folder for generating figures and performing analysis. Refer to the headline comment string in each file for a general description of the purpose of the script in question.

• /.../lib/ stores functions derived from academic papers or individual use to compute statistical tests or perform complex operations

Folder for all unfiltered, raw input data for financial time series.

• yeildCurve.csv historical timeseries data of the 1y, 5y and 10y UST, taken from the Federal Reserve
• sp500.xlsx historical timeseries data of the S&P 500, last_px taken from Bloomberg
• bloomberg_economic_releases.csv historical data of economic announcements, including forecast average, standard deviation, etc.
• swaptionIV.xlsx historical timeseries ATM swaption implied volatility, using a Black-Scholes volatility model
• swapRates.xlsx historical timeseries of USD swap data for select maturities

Folder for storing data files after being read and cleaned of missing/obstructed values.

• DATA.mat stores the downloaded data from input files (e.g., swap rates, swaption implied volatility)
• FSigmaF.mat stores the daily, not annualized GARCH(1,1) volatility forecasts, including 95% lower and upper bounds
• SigA.mat stores the annualized GARCH(1,1) volatility forecasts, including 95% lower and upper bounds

Folder and sub-folders are provided to store graphs and tables for forecasts, regressions, etc.

• /.../autocorrelations/ stores all autocorrelation figures associated with each swaption security's VRP measure. For a detailed overview of the code responsible for constructing these measures refer to vrpGraphs.m under the header Figure (5) Autocorrelation Function for Variance Risk Premia.

• /.../garch-forecasts/ stores all GARCH forecasts for each swap tenor against implied volatility levels, for each term. For a detailed overview of the code responsible for constructing these measures refer to vrpGraphs.m under the header Figure (3) Swaption Implied Vol vs. Forecasted Real Vol.

• /.../macro-announcements/ stores .csv files that perform analysis against economic announcements (e.g., CPI)

  • /.../buckets/ stores graphs of changes in volatility conditioned by the standard deviation of each economic forecast and interest rate regime. For more detailed overview of the code responsible for constructing these measures refer to macroBucket.m.
  • /.../regressions/ stores coefficients for changes in volatility measures regressed on macro-economic announcements. For more detailed overview of the code responsible for constructing these measures refer to macroRegress.m.
  • /.../responses/ stores graphs illustrating cumulative returns against macroeconomic variables. For more detailed overview of the code responsible for constructing these measures refer to macroAggregate.m.

The following steps are necessary for gathering data, prior to executing the main.m file.

Data Fields that are automatically updated from HTML connections

• Effective Federal Funds Rate, taken from FRED website (stored under variable fedfunds)
• NBER based Recession Indicators for the United States (USRECD), taken from FRED website (stored under variable recessions)
• CBOE Volatility Index: VIX, taken from FRED website (stored under variable vix)
• The U.S. Treasury Yield Curve: 1961 to the Present, taken from Federal Reserve website and stored under the yeildCurve.csv file in the Input folder

Data Fields that are semi-manually updated

1. Login into your Bloomberg Professional Service account, you will need it to retrieve historical data.

2. Open the following excel files sp500.xlsx, swaptionIV.xlsx, and swapRates.xlsx on your local machine. Go to the Bloomberg tab on Excel and click the Refresh Worksheets icon to update the Bloomberg formulas, populating the data fields. Note if working on a separate server or cluster, these refreshed worksheets will need to be transferred to the designated workstation

3. To update the data series entitled bloomberg_economic_releases.csv, refer this repo. Simply transfer the Output series from the BBG-ECO-EXCEL project to the Input folder of this repo.

4. Once all data has been updated you are free to run the entire project base. You may opt to run the main.m file in a MATLAB interactive session or via terminal on your local machine or HPC cluster.

   % %    e.g., running code via batch on the FRBNY RAN HPC Cluster
   $ matlab20a-batch-withemail 5 main.m 
   

• Work on potentially updating Bloomberg data without manually opening files.

• Rajesh Rao (Sr. Research Analyst)