Question $2$ Binomial Model $(20)$: A call option is written on a stock whose current price is $$50.$ The option has maturity of three years $($date $0$ to date $3),$ and during this time the annual stock price is expected to increase by $25\%$ or to decrease by $10\%.$ The annual interest rate is constant at $6\%.$ The option is exercisable at price of $$62.$ What is its value today?

Question $3$ Binomial Model $(50)$: The above option $($question$2)$ is now exercisable at date $1$ at a price of $$52,$ at date $2$ for a price of $$60,$ and at date $3$ for a price of $62.$ What is its value today? Will you ever exercise the option early? Do you observe any differences in prices with the option on question$2?$ Explain why.

What if the option has exercise prices at date $1$ at a price of $$50,$ at date $2$ for a price of $$57,$ and at date $3$ for a price of $$62?$ Do you observe any difference now with the price of the option on question $2$ or the option above $($question$3)?$ Explain why.