by
Allen M. Poteshman
Department of Finance
University of Illinois at Urbana-Champaign
Abstract
Although it is widely believed that option prices provide the best possible
forecasts of the future variance of the assets which underlie them, a large
body of empirical evidence concludes that option prices consistently yield
biased forecasts of future variance. The prevailing interpretation of these
findings is that option investors may be forming unbiased forecasts of
the future variance of underlying assets but that these unbiased forecasts
fail to get impounded into option prices because of either (1) the difficulty
of carrying out the necessary arbitrage strategies that would force the
prices to their proper levels, or (2) the availability to market makers
of lucrative alternative strategies in which they simply profit from the
large bid-ask spreads in the options markets. This interpretation has significant
consequences for nearly the entire range of option pricing research, since
it implies that non-continuous trading, bid-ask spreads, and other market
imperfections substantially influence option prices. This implication is
important, both because incorporating these types of market imperfections
into option pricing models is much more difficult than, for example, altering
the dynamics of the underlying asset and also because it suggests that
researchers cannot learn about option investor expectations by filtering
option prices through available option pricing models. The present paper
studies the variance forecasting ability of SPX option prices against the
backdrop of the prevailing interpretation of the findings in the variance
forecasting literature. The paper presents two main empirical findings.
First, approximately one third of the usual bias is eliminated when high
frequency futures data rather than daily closing data is used to construct
measures of realized variance. Second, roughly another third of the bias
disappears when forecasts of future variance are extracted from option
prices via an option pricing model that – unlike the commonly employed
model – permits a non-zero market price of variance risk and a non-zero
correlation between innovations to the level and variance of the SPX index.
Furthermore, the remaining bias is no longer significant. In addition to
the empirical results, Monte Carlo simulations are performed to study the
impact on the results of model misspecification and errors in the futures
and options data. The simulations indicate that failure to account for
a non-zero market price of variance risk produces a forecasting bias similar
to that found in the previous literature when the conventional option pricing
model is employed but that errors in the variables do not produce appreciable
bias.