I know that this is a very simple question, but i want to make sure to grasp the concept of ex dividend and value of portfolio.

Suppose that we have a two period binomial tree of a stock with initial value of $S_0= 100$ and $u=1.2$ and $d=1/u$. The stock pays fixed discrete dividends: $d_1=10$ in the first period and $d_2= 5$ in the next period.

What is the Value of this portfolio at times $1$ and $2$?

$1)$ If the stock goes up then: $V_1= 100*(1.2)-10=110$

if the stock goes down then $V_1=100*(1/1.2)-10=73.33$

$2)$ if the stock goes up up then: $V_2= 110*(1.2)-5=115$

if the stock goes up and down then $V_2= 110(1/1.2)-5=86.66$

if the stock goes down and up then $V_2= 73.33(1.2)-5= 83$

if the stock goes down and down then $V_2= 73.33(1/1.2)-5= 56.11$

I would really appreciate if you can tell me if this is the correct value of the portfolio, or if I´m doing something wrong.

  • 1
    $\begingroup$ Looks fine but what happens to the dividend? Long position in the stock will earn this dividend, but someone who has bought an option won’t get the dividend. $\endgroup$ Jun 23 '19 at 18:48
  • 1
    $\begingroup$ Everything looks correct. Note that $86.66 \ne 83$, i.e the tree is not recombining, there are 4 states in period 2 (instead of 3 in the usual tree when there are no dividends). Up Down state is not the same as Down Up. This is as expected in a fixed dividend model. $\endgroup$
    – Alex C
    Jun 23 '19 at 21:04
  • 1
    $\begingroup$ Period 2, Up/Up state: result should be 127, no? $\endgroup$
    – amdopt
    Jun 24 '19 at 15:23

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