Consider a call$$option on the S&P$500$ index maturing in one year, the strike price of$$which is $4200.$ The current level of the S&P$500$ index is $4000.$ Assuming that in one year, the$$S&P$500$ index has equal probabilities of being either $4500($up$)$ or $3600($down$).$ What are the cash flows of this call option at the maturity date $($market up$,$ market down$)?$

Continuing the question above, what is the no$-$arbitrage price of a one$-$year$$put option on the S&P$500$ index with the same strike price?