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 option data and the other from the S&P
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 and
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 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
trading strategies and Section 9.7 completes with some
critical remarks.