the successful completion of the merger are small, then we can expect that
the players would put on a large position causing the spread to narrow. If,
however, the value of the spread narrows disproportionate to the risks, then
we can expect some profit taking causing the spread to widen. If there are
sufficient players in the marketplace engaging in risk arbitrage, the spread
would then in some sense represent the consensus estimate of the risk in-
volved in the deal and thereby the odds of successful completion of the
merger. Therefore, it makes sense to construct models to estimate the odds
of merger success taking the value of the spread into account.
In this chapter, we discuss a method to assess the probabilities of merger
as reflected by the spread between the stock prices of the merging compa-
nies. The method is based firmly on the classical results of the Arrow-Debreu
theory of contingent claims. The probabilities derived are called risk neutral
probabilities.
Risk neutral probabilities calculated for a merger are in many ways sim-
ilar to the implied volatility parameter encountered in option pricing. For
purposes of option pricing, stock price movement is modeled as a log-
normal process. One of the important parameters of the log-normal process
is its standard deviation. This standard deviation is commonly termed
volatility. The volatility of the underlying stock plays a crucial role in the
pricing of an option. Conversely, the price of an option quoted in the mar-
ketplace implies a certain volatility that when plugged into the option pric-
ing model results in the quoted option price. This volatility implied by the
option price is called the implied volatility.
In an analogous fashion, the probability of merger success as implied by
the observed spread may be calculated. Note that both implied volatility and
the merger probability specify probability distributions. Furthermore, they
are both calculated from values observed in the marketplace, and therein lies
the similarity between the two constructs. A key question, however, pertains
to the premise of the chapter. What is the value in knowing the market im-
plied probability of merger? Well, if one has a view based on independent re-
search that the true chance of merger success is better than the implied
probability, then entering into a trade may have a good risk–reward profile.
Thus, knowing the probability of merger can provide value in making in-
vestment decisions.
The implied probability of deal success can also prove useful in the area
of risk management. The risk manager is typically charged with assessing the
risk in multiple portfolios running multiple strategies. Unlike the risk arbi-
trage traders, risk managers are not disposed to know the intimate details of
every deal in the risk arbitrage portfolio. Using the market-implied proba-
bilities, the risk manager will be able to design meaningful value at risk
(VAR) measures for such deals. The VAR plays a key role in determining the
172 RISK ARBITRAGE PAIRS