A US pension fund $($called Twilight Years$)$ has $$50$m in stocks which it will have to sell in $3$ months time $($to pay out to new pensioners$).$ It wants to benefit from any rise in stock prices over the next $3$ months but does not want to lose $($very much$)$ if stock prices fall. The maximum $($gross$)$ amount it is willing to lose is $10\%$ of the value of its portfolio. All options have $3$ months to maturity. The pension fund should:

a$.$ buy a put option with a strike price equal to $$45$m

b$.$ buy a call option with a strike price equal to $$45$m

c$.$ sell a call option with a strike price equal to $$45$m

d$.$ sell a put option with a strike price equal to the current stock price

e$.$ buy a put option with a strike price equal to $$40$m