Final_1.pdf

Lett 1 andt 2 be points in the interval [0,T] and t 2 >t 1. We denote the
probabilities of failed merger at times t 1 andt 2 by, and the
spreads by , respectively. See Figure 11.2.
Applying the one-step model, we have

(11.4)

(11.5)

Dividing one by the other, we have

(11.6)

To get a better feel for what the equation signifies, let us consider the situa-
tion of a pure stock-for-stock deal without a cash component. Making the
cash to zero, the equation in this case reduces to

ππfailurett^12 /( )/( )failure=+eSert t()^21 −−−t 1 rT t()^1 cash Set 2 +−−rT t()^2 cash

πfailuret^2 =+eSerT t()−−−^2 ()/()t 2 rT t()^2 cash ST +cash

πfailuret^1 =+eSerT t()−−−^1 ()/()t 1 rT t()^1 cash ST+cash

SStt 12 ,

ππfailuret^1 , failuret^2

178 RISK ARBITRAGE PAIRS

FIGURE 11.2 Multistep Model.

St 1

Spread=0

(^0) T
ST
πt (^1) success
πt (^1) failure
πt (^2) success
πt (^2) failure
St 2