Interpreting the implied SPD as the SPD used by
investors to price options, the historical density as the `real'
underlyings' SPD and assuming that no agent but one know the
underlyings' SPD one should expect this agent to make higher
profits than all others due to its superior knowledge. That is
why, exploiting deviations of implied and historical density
appears to be very promising at a first glance. Of course, if all
market agents knew the underlyings' SPD, both would be equal
to
. In view of the high net cash flows generated by both
skewness and kurtosis trades of type
, it seems that not all
agents are aware of discrepancies in the third and fourth moment
of both densities. However, the strategies seem to be exposed to a
substantial directional risk. Even if the dataset contained
bearish and bullish market phases, both trades have to be tested
on more extensive data. Considering the current political and
economic developments, it is not clear how these trades will
perform being exposed to `peso risks'. Given that profits stem
from highly positive cash flows at portfolio initiation, i.e. profits result from possibly mispriced options, who knows how the
pricing behavior of agents changes, how do agents assign
probabilities to future values of the underlying?
We measured performance in net EUR cash flows. This approach does not take risk into account as, for example the Sharpe ratio which is a measure of the risk adjusted return of an investment. But to compute a return an initial investment has to be done. However, in the simulation above, some portfolios generated positive payoffs both at initiation and at maturity. It is a challenge for future research to find a way how to adjust for risk in such situations.
The SPD comparison yielded the same result for each period but
one. The implied SPD was in all but one period more
negatively skewed than the time series SPD
. While
was
in all periods platykurtic,
was in all but one period
leptokurtic. In this period the kurtosis of
was slightly
greater than that of
. Therefore, there was no alternating
use of type
and type
trades. But in more turbulent market
environments such an approach might prove useful. The procedure
could be extended and fine tuned by applying a density distance
measure as in Ait-Sahalia, Wang and Yared (2000) to give a signal when to set up
a portfolio either of type
of type
. Furthermore, it is
tempting to modify the time series density estimation method such
that the monte carlo paths be simulated drawing random numbers not
from a normal distribution but from the distribution of the
residuals resulting from the nonparametric estimation of
, Härdle and Yatchew (2001).