A call option sells for $3$ and a put option sells for $5.$ Both options expire in one year and the underlying are shares of firm X$.$ The exercise price of the call option is $45$ and the exercise price of the put option is $47.$ The $1-$year risk$-$free interest rate is $5\%.$ It can be said that:

a$.$ The spot price of the underlying asset is $40\mathrm{.}85.$

b$.$ The put$-$call parity holds.

c$.$ The put$-$call parity does not hold.

d$.$ None of the above is correct.