# Binomial model option

An American call option with exercise price $$K = 90$$ written on an asset where the asset prices in dollars are given below, the interest rate per period is zero, and a dividend of $$5$$ is paid between time $$0$$ and time $$1$$. $$\begin{array}{|c|c|c|} \hline \omega& S(0) & S(1) & S(2) \\ \hline \omega_1&100 & 115&145 \\ \hline \omega_2&100 &115 & 105\\ \hline \omega_3&100 &85 & 105\\ \hline \omega_4&100 &85 & 65\\ \hline \end{array}$$

My question is, when calculating risk neutral probabilities, does one add back the dividend to both $$S(1)$$ and $$S(2)$$ or just to $$S(1)$$ ?

$$\begin{matrix} & & & \\&& S_2=(145+5) & \\&S_1=(115+5)&& \\S_0=100 & & S_2=(105+5) & \\&S_1=(85+5)&& \\&& S_2=(65+5) & \end{matrix}$$ or

$$\begin{matrix} & & & \\&& S_2=(145) & \\&S_1=(115+5)&& \\S_0=100 & & S_2=(105) & \\&S_1=(85+5)&& \\&& S_2=(65) & \end{matrix}$$

• Both. Otherwise it looks like the 5 dollars disappeared between t=1 and t=2. – dm63 Apr 22 at 13:36