Problem $2$

Intro

The current price of a non$-$dividend$-$paying stock is $$16\mathrm{.}16$ and you expect the stock price to either go up

by a factor of $1\mathrm{.}285$ or down by a factor of $0\mathrm{.}778$ over the next $0\mathrm{.}7$ years.

A European call option on the stock expires in $0\mathrm{.}7$ years. Its strike price is $$16.$ The risk$-$free rate is $8\%$

$($annual$,$ continuously compounded$).$

Part $1$

What is the value of the option?