The current price of a non$-$dividend$-$paying stock is $$451\mathrm{.}92$ and the annual standard deviation of the stock's return is $50\%.$ The risk$-$free rate is $3\mathrm{.}2\%($continuously compounded$).$

A European put option on the stock has a strike price of $$470$ and expires in $0\mathrm{.}5$ years.

A B

$1$ Inputs

$2$ Stock price $451\mathrm{.}92$

$3$ Exercise price $470$

$4$ Expiration $($years$)0\mathrm{.}5$

$5$ St$.$Dev. of returns $0\mathrm{.}5$

$6$ Dividend yield $0$

$7$ Risk$-$free rate $0\mathrm{.}032$

Attempt $1/50$ for $10$ pts$.$

Part $1$

What should be the price $($premium$)$ of the put option?