Research Papers

Working Papers

Internal Rationality, Stochastic Variance and Return Predictability (Submitted)

This paper develops a general equilibrium asset pricing model featuring internal rationality and endogenous learning about stochastic variance. Investors form subjective beliefs about risk-adjusted capital gains using a constant-gain Kalman filter, treating volatility innovations as following a GARCH(1,1) process. While investors behave rationally given their subjective information, an econometrician under the objective measure observes predictable variation in returns, volatility clustering, and momentum effects. The model generates an endogenous leverage effect—where negative price shocks raise perceived volatility—and simultaneously implies a positive relationship between the VIX premium and future returns, in contrast to traditional RE-based models. This joint behavior arises because the VIX premium reflects belief distortions induced by learning, rather than pure compensation for objective risk. Empirically, I show that the VIX premium predicts momentum factor returns, and propose conditional trading strategies (MOMVP, WMLVP) that significantly outperform their unconditional benchmarks. The model quantitatively matches key features of U.S. equity and option markets from 1990 to 2019, including the magnitude and variability of the VIX premium, the persistence of volatility. These results provide a unified explanation for the joint behavior of volatility risk premia and time-varying momentum premiums, highlighting the essential role of investor learning and subjective risk perceptions.

Expectations and Option Implied-Variance

Abstract

I show that a simple asset pricing equilibrium model can explain many salient features of index option prices if one allows for small deviations from rational expectations. A representative investor holds subjective beliefs about the underlying asset returns, which he optimally learns from past returns. I derive a closed form European call-option price formula in this setup. I show that given this belief structure, investor's subjective expectations about next period underlying's price growth are priced in an option, creating a wedge between option implied-variance and realized variance. Time variation in the agent's subjective expectations link this wedge to realized stock returns, helping explain its power to predict stock returns. Further, these subjective expectations also help generate different shapes of option implied-volatility curve. The model can quantitatively replicate key features of index returns and index options with very reasonable parameter values. The findings in this paper suggest that measures of option-implied variance such as VIX are not capturing the true uncertainty expected by agents but are biased in the direction of the investors expectations of future capital gains on the underlying asset.

Presentations at: 

2022: University of Leicester School of Business

2021:WORKSHOP ON DYNAMIC MACROECONOMICS, University of VIGO, VIGO Spain; Systemic

Risk Center, London School of Economics

2020: UAB Macro Club, Barcelona, Spain; Spanish Economic Association (SAEe) Meeting

2019: Barcelona GSE Summer Forum, Barcelona, Spain; ENTER Jamboree, Tilburg University, Netherlands; UAB Macro Club, Barcelona, Spain.

2018: UAB Macro Club

Internal Rationality and the Term Structure of Equity Returns (Draft available on request)

Standard rational expectations models struggle to replicate the downward-sloping  term structure of equity risk-premia and the countercyclical behavior of the equity term premium. This paper proposes a parsimonious resolution: investors are rational but learn about future capital gains on the stock from historical price movements. Optimistic beliefs inflate spot stock prices and  its futures prices, but leave short-term dividend futures prices relatively undervalued due to no-arbitrage condition, causing short-duration assets to  earn anomalously high returns versus the long term dividend futures. During pessimistic periods the mechanism reverses, leaving short-end dividend futures overvalued relative to fundamental. Both puzzles are thus unified as consequences of the same endogenous belief dynamics rather than fundamental cash flow risk.

Option Implied Expectation of Returns (Draft coming soon)