What is the black-scholes equation to govern this situation, Financial Management

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What is the black-scholes equation to govern this situation

A futures price is currently 50. At the end of 6 months it will be either 55 or 45. The risk free interest rate is 6% per annum. We want to value a 6-month European call option with a strike price of 50.

a) What is the Black-Scholes equation to govern this situation?

b) What is the value of the option? (Consider using a one-step binomial tree)

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