Determine the premium for a $3-$month European put option on a $1-$year futures contract on the stock with strike price $45.$

b$.$ You are given:

$($i$)$ The $3-$month forward price of a stock is $90.$

$($ii$)$ The continuously compounded risk$-$free interest rate is $0\mathrm{.}08.$

$($iii$)$ The Black premium for a $3-$month put option on a $3-$month futures contract on the stock with strike price $90$ is $4\mathrm{.}75.$

Determine the volatility of the forward price of the stock.