Consider a stock currently priced at $$150.$ In the next period, the stock can either increase by $33$ percent or decrease by $15$ percent. Assume a European put option

with an exercise price of $$150$ and the risk$-$free rate of $4\mathrm{.}5$ percent. Suppose the put option is currently trading at $$11.$ Assume that you can long and short US Treasury

securities $($equivalently$,$ you can lend and borrow money at the risk$-$free interest rate$).$ Also, the stock does not pay any dividend over the life of the option.

Use a one period binomial model to calculate the price of the put option $(x=150).$ You may solve this problem by completing the cells in gray. Or you could solve in the

most comfortable way.