The price of a European call that expires in nine months and has a strike price of $$47$ is $$2.$

The underlying stock price is $$46,$ and a dividend of $$2$ is expected in three months and again in five months.

The term structure is flat, with all risk$-$tree interest rates being $5\%($continuous compounding$)$

What is the price of a European put option that expires in nine months and has a strike price of $$47?$

Explain carefully the arbitrage opportunities if the European put price is $$2.$

What are the upper and lower bounds of a $9$ months European NETFLIX Call option that involves a strike of $$78$ if today the price of one stock is $$77?$ Risk$-$free rate is $3\%$ continuous compounding.

Under what circumstances there will be arbitrageur opportunities?