Assume the following for a European put option that pays dividends.

Time to maturity $=6$ months.

Assume that every $3$ months, stock can go up by either $10\%$ or come down by $5\%.$

Risk$-$free rate for $3$ months: You can use either continuously compounded $=2\%$ or

discretely compounded $=2\mathrm{.}0201\%$

Current stock price is $$60.$

Exercise price is $$59$

Price will fall by $$2$ just prior to the end of the first $3-$ month period due to dividends.

Do the following:

a$.$ Draw the stock price tree

b$.$ Draw the option payoff tree

c$.$ Compute the option price

Use $2$ decimals everywhere including for proabilitties and stock price. For example, if you

compute probability as $0\mathrm{.}468,$ then use $0\mathrm{.}47$ everywhere