189Introduction
In Chapter 11 we discussed that the risk neutral probabilities of merger can
be evaluated from the value of the spread as observed in the marketplace.
The reasoning was that market forces that affect the value of the spread take
into account the risk of deal completion. It is probably true that in most
cases the deal completion risk is the predominant factor affecting the spread
dynamics. However, the spread is also subject to idiosyncratic movement on
the part of any one of the two stocks in question. This movement can be due
to a variety of reasons that have nothing to do with the deal completion risk
and hence contributes to what we shall term noisein the evaluation of the
spread-implied probabilities. This fact is rather evident from the raw plot of
the spreads.
Some of the reasons for this behavior could be due to the bid-ask spread
of the individual stocks and the order of the buys and sells as they occur on
each individual stock. It could also be due to the market maker, looking to
adjust inventory. The market maker may move the price sufficiently higher
or lower albeit on a temporary basis to produce the desired supply or de-
mand in the stock and thereby adjust his inventory levels. Another reason
for the spread movement could be attributed to short covering on the target
stock especially right after the merger announcement. Therefore, when at-
tempting to evaluate the deal break probabilities, we need to bear in mind
that the observed spread is not a consequence of the deal risk alone.
However, if the deal risk is the predominant driver of the spread dy-
namics, the other effects may be treated as noise and filtered using classical
filtering methods. In this chapter, we propose the Kalman filter for the task.
The primary reason for proposing the Kalman filter is that it is robust and
easy to use. Unlike Weiner filtering methods, which are valid only for sta-
tionary stochastic signals, the Kalman filter may be applied to a wide vari-
ety of situations without restriction. This property conveniently precludes us
from coming to any conclusions on the stationarity of the spread and makes
it a suitable candidate method.
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