A futures price is currently 40 cents. It is expected to move up to 45 cents or

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A futures price is currently 40 cents. It is expected to move up to 45 cents or down to 35 cents in the next six months. The risk-free interest rate is 5%. What is the probability of an up movement in a risk-neutral world? What is the value of a six month European put option on the futures struck at 39 cents. How would you hedge a long position in this option?
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