Extracting Information from Options Markets; Smiles, State-Price Densities and Risk-Aversion

In this paper, recent techniques of estimating implied information from derivatives markets are presented and applied empirically to the French derivatives market. We determine nonparametric implied volatility functions, state-price densities and historical densities from a high-frequency stock index option dataset. Moreover, we construct an estimator of the risk-aversion function implied by the joint observation of the cross-section of option prices and time-series of underlying asset value. We report a decreasing implied volatility curve with respect to the moneyness of the option, which holds true whatever the time-to-maturity considered. The estimated relative risk-aversions function are positive over the largest part of the considered range of levels of the stock index, implying a concave utility function, and are globally consistent with the decreasing relative risk-aversion (DRRA) assumption. However, once the tails of the state-price density and of the historical density left out, we observe that the relative risk-aversion function fluctuates around its mean attesting that the constant relative risk-aversion assumption (CRRA) may be locally accepted. Finally, the average level of relative risk-aversion is in accordance with the results reported by other studies using option data. However, this value is dramatically lower than the figures reported by studies based on consumption data, such as Mehra and Prescott (1985)