ISyE8900 Project
Chi Zhang
Georgia Institute of Technology
Abstract
This project proposes a nonparametric approach for the modeling and forecasting of weekly interest rate spread curves by using nonlinear dimension reduction, such as the locally linear embedding (LLE). We mainly focus on two objective spread curves: Swap Spread (LIBOR substract Treasury) and Basis Spread (LIBOR substract SOFR). Benchmarking on its linear dimension reduction counterparty -- principle component analysis (PCA) -- we show the LLE-based framework yields a higher out-of-sample forecast accuracy for specific underlying tenors as well as a better profit and loss (PnL) profile in backtesting various systematic term structure trading strategies.
Data
The following dataset are stored in corresponding .xlsx files. The current experiement is based on the period 2018.10 - 2020.10. New data will be kept adding.
Original:
Parameters of Treasury Term Structure Models -- feds200628_till210319.xlsx;
US 3m LIBOR/Swap Zero+Forward Yield Curve -- WklyLIBOR.xlsx;
3m SOFR Zero+Forward Yield Curve -- WklySOFR.xlsx;
USD OIS Zero+Forward Curve -- WklyOIS.xlsx;
fed funds rate time series -- FFR_daily;
1yr breakeven inflation rate time series -- inflation_daily;
Cleaned:
US Treasury Zero Yield Curve -- Treasury_clean.xlsx;
US 3m LIBOR/Swap Zero Yield Curve --LIBOR_clean.xlsx;
3m SOFR Zero Yield Curve -- SOFR_clean.xlsx;
USD OIS Zero Curve -- OIS_clean.xlsx;
Programs
CurveBuild.ipynb:
(1) Data cleaning and re-sampling
(2) Curve building
DmnsRdct_StateFrcst.ipynb:
(1) Data visualization of low-dim embedding using various dimension reduction methods
(2) Toy model of Kalman filter implementation (require Kalman_filter.py)
(3) Randomness test for univariate low-dim embedding
(4) Implementation of LLE transform and inverse-transform
(5) Backtesting engine for systematic trading strategies using PCA+ARMA and LLE+ARMA models
NumerExperim.ipynb:
(1) Calculate credit risk premium 3m LIBOR- 3m SOFR, liquidity risk premium EFFR – inflation
(2) Regress swap spd on the two risk factors for each tenor
(3) Simulate the residual as O-U process for each tenor
(4) Recover the simlulated swap spd curve
(5) Run multi-stage forecasting framework for swap spd curve from script 2
Problem formulation
(1) Dimension reduction
(2) Forecasting in the reduced dimension
(3) Mapping back to the original space
(4) Performance evaluation
Report:
Submission to INFORMS finance best student paper -- Template_for_Management_Science_Journal.pdf
Paper:
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