Consider a stock with initial price $$50\mathrm{.}00$ and volatility of returns of $30\%.$ Suppose the risk$-$free rate is $4\mathrm{.}5\%.$ For options with one year to maturity, obtain $3($a$)$ the premiums for call options with strike prices of $$48\mathrm{.}00$ and $$46\mathrm{.}003($b$)$ the premiums for put options with strike prices of $$54\mathrm{.}00$ and $$52\mathrm{.}00.$ Comment on the option prices you obtain.