Implied merger probability in R

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Implied merger probability in R

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I am trying to solve for the implied merger probability by using the method introduced by Lewellen and Ferri (1983). Have managed to solve it correctly in solver, but with a big dataset it would take forever to change the constraints for every single trading day, so I was hoping there was a way to do this in R.

It is just a simple system of equations, where one evaluates the implied merger probability of a stock offer where company A looks to acquirer company B trough a stock offer.

(1) P`A = %PA + (1-%)Pa

(2) P`B = %PB + (1-%)Pb

(3) PB=X*PA

Explanation of the equations:

P`A and P`B is the prevailing market prices (closing price), these needs to be changed every day to the new trading price for stock A and B until completion of the deal or withdrawal. KNOWN.

% is just the probability. UNKNOWN! This is what I am looking to find the answer to.

PA and PB just denotes the market prices that would prevail immediately if success were assured. This is unknown but not of interest for my paper.

Pa and Pb is the 1 day before announcement prices of the two stocks. These are fixed at those levels, and do not change.

X is the exchange offer, this is also fixed.

Appreciate if someone can help me with a explanation or code!