Retrieving Risk Neutral Moments and Expected Quadratic Variation from Option Prices

This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange (CBOE)