9.1 Introduction

In recent years a number of methods have been developed to infer implied state price densities (SPD) from cross sectional option prices, Chapter 7 and 8. Instead of comparing this density to a historical density extracted from the observed time series of the underlying asset prices, i.e. a risk neutral density to an actual density, Ait-Sahalia, Wang and Yared (2000) propose to compare two risk neutral densities, one obtained from cross sectional S&P $ 500$ option data and the other from the S&P $ 500$ index time series. Furthermore, they propose trading strategies designed to exploit differences in skewness and kurtosis of both densities. The goal of this article is to apply the procedure to the german DAX index. While the option implied SPD is estimated by means of the Barle and Cakici, Barle and Cakici (1998), implied binomial tree version, the time series density is inferred from the time series of the DAX index by applying a method used by Ait-Sahalia, Wang and Yared (2000). Based on the comparison of both SPDs the performance of skewness and kurtosis trades is investigated.

We use options data included in M D *BASE . This is a database located at CASE (Center for Applied Statistics and Economics) of Humboldt-Universität zu Berlin. The time period is limited to data of the period between $ 01/01/97$ and $ 12/31/99$ for which M D *BASE contains daily closing prices of the DAX index, EUREX DAX option settlement prices and annual interest rates which are adjusted to the time to maturity of the above mentioned EUREX DAX options.

While Section 9.2 applies the Barle and Cakici implied binomial tree algorithm which estimates the option implied SPD using a two week cross section of DAX index options, Section 9.3 explains and applies the method to estimate DAX time series SPD from $ 3$ months of historical index prices. Following, in Section 9.4 we compare the conditional skewness and kurtosis of both densities. Section 9.5 and 9.6 complete the chapter with the investigation of $ 4$ trading strategies and Section 9.7 completes with some critical remarks.