Expectations and the Option Implied-Variance

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 option price formula for a European call option in this set up. I show that given this belief structure, investor's subjective expectations about next period 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.