Option-Implied Equity Premium Predictions via Entropic Tilting

Abstract

We propose a new method to improve density forecasts of the equity premium using information from options markets. We tilt the predictive densities from standard econometric models suggested in the stock return predictability literature towards the second moment of the risk-neutral distribution implied by options prices. In so doing, we use a simple regression-based approach to remove the variance risk premium. By combining the backward-looking information contained in the econometric models with the forward-looking information from the options prices, tilting yields sharper predictive densities. Using density forecasts of the U.S. equity premium in Rapach and Zhou (2012), we find that tilting leads to more accurate predictions, both in terms of statistical and economic performance.

Quantile regression forecasts of inflation under model uncertainty

“…Table 3 provides diagnostics related to calibration of predictive densities, and is similar to Table 1 of Metaxoglou, Pettenuzzo and Smith (2016). Entries are p-values, and values lower than 0.05 signify rejection of the null hypothesis of the test at the 5% level.…”

Modeling and forecasting stock return volatility using the HARGARCH model with VIX information

“…Obviously, if $$g(R{V}_{t+1})=R{V}_{t+1}$$ or $$g(R{V}_{t+1})={(R{V}_{t+1}-E[R{V}_{t+1}| {{\rm{ {\mathcal F} }}}_{t}])}^{2}$$, then $${\bar{g}}_{t}$$ represents the mean or variance of the random variable $$R{V}_{t+1}$$. Moreover, $${\bar{g}}_{t}$$ can take other forms, such as those based on the Euler equations (Giacomini & Ragusa, 2014), survey forecasts (Altavilla et al, 2017; Krüger et al, 2017), or option‐implied information (Metaxoglou et al, 2019).…”

“… , then g ¯t represents the mean or variance of the random variable RV t+1 . Moreover, g ¯t can take other forms, such as those based on the Euler equations (Giacomini & Ragusa, 2014), survey forecasts (Altavilla et al, 2017;Krüger et al, 2017), or option-implied information (Metaxoglou et al, 2019).…”

“…Therefore, it is essential to eliminate the influence of the risk premium before adjusting for baseline density. According to the hypothesis of Metaxoglou et al (2019), a straightforward linear relationship exists between the estimators under the risk-neutral and physical measures as follows:…”

“…The entropic tilting technique is an effective means of incorporating valuable external information into existing models and gaining popularity in various fields. For example, it is applied to forecast yield curves (Altavilla et al, 2017), predict macroeconomic variables such as the gross domestic product, unemployment rate, and interest rate of treasury bonds (Krüger et al, 2017), and forecast stock premiums (Metaxoglou et al, 2019). Drawing inspiration from these findings, we use the entropic tilting technique to incorporate forward-looking information into the baseline volatility model and propose a straightforward method for volatility prediction.…”