Suppose a stock is currently worth $50.$ Next month it will be worth either $60$ or$40$ with equal

probabilities. A unit risk$-$free investment results in $\backslash$alpha $=1\mathrm{.}05$ units in one month$$s time.

a$.$ Consider a European put option on the stock with maturity one month and strike price K $=$

$55.$ Using the principle of risk neutrality find the price of the put option.