Options - Binomial Trees

1. A stock price is currently $\$60$. It is known that at the end of three months it will be either $\$63$ or $\$58$. The risk-free rate is $10 \%$ per annum with continuous compounding.
   What is the value of three month European call option with a strik price of $\$59$?


2. A stock price is currently $\$60$. Over each of the next two 4-months periods it is expected to go up by $7\%$ or down by $6 \%$per annum with
   continuous compounding. What is the value of a 8-month European call option with a stick price of $\$61$.


3. A stok price is currently $\$70$.It expected that at the end of 3 months it will be either $\$65$ or $\$75$. The risk-free
   interest rate is $6\%$ per annum with continuous compounding. What is the value of a 3-months European put option with a strike price of $\$70$.


4. A stock price is currently 30. It expected that at the end of 3-months it will be either $\$27$ or $\$33$.
   The risk-free interest rate is 10 per annum with continuous compounding. Suppose $S_{T}$ is the stock price at the end of 3-months. What the value of
   a derivative that pays off $(S_{T})^{3}-3(S_{T})^{2}$