Risk Premia, Volatilities, and Sharpe Ratios in a Non-Linear Term Structure Model
London Business School
London Business School - Department of Finance
Philipp K. Illeditsch
University of Pennsylvania - Finance Department
May 13, 2013
In this paper we propose an expansion of Gaussian term structure models where the short rate and market prices of risk are non-linear in the state variables. We provide closed-form solutions for bond prices and since the latent factors are Gaussian the expanded model is as tractable as the Gaussian model. We estimate a three-factor expanded model and find that the model matches the time variation in both expected excess returns and yield volatilities of U.S. Treasury bonds. Comparing Sharpe ratios in the Gaussian and expanded model, the expanded model implies that Treasury bonds are more attractive investments in periods with low volatility. A significant part of expected excess returns in the expanded model is not spanned by the cross section of yields. This suggests that more information than previously thought is contained in the yield curve, but in a non-linear way.
Number of Pages in PDF File: 42
Keywords: Affine term structure models, non-linear term structure models, time-varying term premiums, time-varying investment opportunities, stochastic volatility, Sharpe ratios, hidden factors
JEL Classification: D51, E43, E52, G12working papers series
Date posted: April 1, 2013 ; Last revised: October 14, 2013
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