Local Parametric Analysis of Derivatives Pricing and Hedging

The authors present a novel methodology for the analysis of derivatives pricing in incomplete markets. Unlike existing procedure, they do not commit to a particular model for the prices of the underlying asset(s). Instead they locally fit the hedge ratios from a parsimonious complete-market model to changes in the prices of options and underlying securities. The authors then compute prices from the locally estimated parameters. Thus, they extract information from the local co-movement of prices of several securities, as opposed to the standard procedure, which obtains parameter values either from time series estimation or by implying them from option prices directly. The authors illustrate the methodology on a dataset of DAX index options and futures transactions from the computerized German Futures Exchange, over the period 1992-94. They form their estimates entirely on the basis of lagged information. While they predict final payoffs with a precision that matches that of market prices, their prices often deviate substantially from synchronous market prices. Moreover, self-financed delta hedges based on their estimates of the hedge ratios perform worse than those with hedge ratios computed from market-implied volatilities. All this is caused by anomalous behavior of the locally fitted hedge ratios. For instance, the hedge ratios of in-the-money options are sometimes estimated to be so low that they imply volatility above 200% (per year). Since a typical estimation is based on 5% of the "training" sample, with a minimum of 50 observations, sampling error cannot explain the anomalous behavior.