Given the underlying stock price S $=20$ today, its price has a $90\%$ possibility to be S $=18$ and a $10\%$ possibility to be S $=22$ in three month. Thus, based on the the non$-$ arbitrage pricing principal, the fair price of a call option expiring in three month at strike price K $=21$ is $0\mathrm{.}633$ with the annual risk free interest rate r $=12\%($See details in the lecture notes$).$ If the current market price of the call falls to $0\mathrm{.}5,$ does there exist an arbitrage opportunity? If yes, construct a strategy to do the arbitrage and explain it$.$