# 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. – Magic is in the chain Jun 23 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. – Alex C Jun 23 at 21:04
• Period 2, Up/Up state: result should be 127, no? – amdopt Jun 24 at 15:23