# Value of portfolio with fixed discrete dividends

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.

• 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. Jun 23 '19 at 18:48
• 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. Jun 23 '19 at 21:04
• Period 2, Up/Up state: result should be 127, no? Jun 24 '19 at 15:23