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Effect of Dividends in Two-Step Binomial Model [Tutorial 4] [Question 7]

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asked Apr 2 in BUS 4028F - Financial Economics by Daniel (420 points)


How does one go about drawing the binomial lattice for a question as shown above?

This was my thinking, but perhaps I have misunderstood the question:

  • Management says now at t=0 that they are going to pay a dividend of 10% of the value of the share at t=1/2  only if the value of the share has risen at that point 
  • The payment of this dividend happens after the market has closed, including the exercising of any options
  • This means that if you were to exercise a call option at t=1/2, you would receive that dividend immediately at the outset of ownership of the share or in other words the dividend would form part of the value of your share
  • This is where some confusion comes in - how does this affect the price of the share at t=1/2?
  • Firstly, is the lattice a snapshot of the share price at the moment in time corresponding to the timing of the exercising of an option?
  • Would the share price thus rise immediately after t=1/2 or has it already been internalised by the market previously?
  • Does market efficiency come into play here?
  • Do we say that there is a degree of market efficiency and that this dividend having been announced at t=0, has already been internalised into the market price and hence that the price of the share would be unaffected by this dividend payout?

Not sure as to why the memo goes to t=1, increases the value of the share normally over t=1/2 and then strips out the value of the dividend at the final nodes.

commented Apr 3 by adam (240 points)

I think the question wording is ambiguous and that at t=0.5 the management announce there will be a dividends in 6 months ie at t=1.

The reason we strip out the dividends is that the value of the a share is determined by the discounted sum of its payoffs ie its dividends - since the person who has entered into the derivative will not receive this future dividends which has been declared we need to minus it from the shares value.

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