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Question: Suppose IBM pays a dividend D on their shares S at time τ. Show that S(τ+) = S(τ−) − D. Actually, to be precise, τ should be what is called the ex-dividend date. You should again argue your solution from the assumption of no arbitrage. S(τ+) means the value of S just after τ, and S(τ−) the value just before. – Free Chegg Question Answer

Suppose IBM pays a dividend D on their shares S at time τ. Show that S(τ+) = S(τ−) − D. Actually, to be precise, τ should be what is called the ex-dividend date. You should again argue your solution from the assumption of no arbitrage. S(τ+) means the value of S just after τ, and S(τ−) the value just before.

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Answer:

Answer


We know, the change of the stock price (S) after declaring a dividend (D) is calculated as:

D*(1-TD S = 1- TCG

 ………….(1)

Тр = tax rate payable on dividend

Tca CG= tax rate payable on capital gain

In case of no-arbitrage possibility there will be no tax payable, i.e., Td = 0

 and TCG = 0

So from (1)

OS=

But OS

 = price before dividend paid (value before ex-dividend)- price after dividend paid (value after ex-dividend) = S(T-) – S(T+)

So D = S(T-) - S(T+

So ST+) = S(T-)-D


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