Final_1.pdf

APPENDIX

Notation

Price of security A on the eve of merger announcement

Price of security B on the eve of merger announcement

Price of combined entity at time T

Price of security A in case of deal break at time T

Price of security B in case of deal break at time T

psuccess Probability of successful merger

pfailure Probability of deal break

g Ratio

We now construct Table 11.2 similar to Table 11.1.

TABLE 11.2

Investment Initial

Payoff (Price at Time T)

Scenario Price Merger Successful Merger Failed

Risk-Free e–rT 11

Buy Stock A

Buy Stock B

The Arrow-Debreu equations that need to be satisfied written in matrix
form is as follows:

Solving for the values of and normalizing so that they add
up to 1, we have

πγ γfailure=−+ −+[(eprT 00 A pB)cash]/[(pTA pTB)cash]

ππ′′success and failure

11

0

0

pp

pp

e

p

p

T

AB

T

A

T

AB

T

B

rT

A

+ B





















′

′











=





















−

cash

success

γ failure

π

π

γp 0 B pTAB+cash γpTB

p 0 A pTAB pTA

pTB

pTA

pTAB

p 0 B

p 0 A

The Market Implied Merger Probability 187