Explain the difference between a call option and a put option. Explain the difference between an American option and European option. Find the value of a call option using the binomial option pricing formula for single period when given the following information: you have an option with 6 months until expiration, the payoff in the up scenario is $12, and the payoff in the down scenario is $0, the risk-free rate is 5%, the weight for the up scenario is 1.1, and the weight for the down scenario is 0.7.