onsider two European call options on the stock of XYZ$.$ Both options mature one year from now. The first option $($Option #$1)$ has a strike price of $$30\mathrm{.}0$ and trades at $$18\mathrm{.}4$ today; the second option $($Option #$2)$ has a strike price of $$45\mathrm{.}0.$ Currently, the stock price is equal to $$45\mathrm{.}7,$ and the one$-$year continuously$-$compounded risk$-$free rate is $3\%.$ The stock does not pay dividends.

What is the lowest price of the second option $($Option #$2)$ consistent with absence of arbitrage?cc