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Please provide detailed steps including how you got each number.Include the formulas.
practice q: A futures price is currently $78 and its volatility is 20%. The continuously compounded risk-free interest rate is 4% per annum. Answer the following questions:
a) Construct a three-period binomial tree for the evolution of the futures price over the next six months.
b) Calculate the risk-neutral probability of an up movement over a single time step.
c) Use the binomial tree in part (i) and risk-neutral valuation to evaluate a six-month European put futures option with exercise price of $80.
d) Use the binomial tree in part (i) and risk-neutral valuation to evaluate a six-month American call futures option with exercise price of $80.
e) By using the Black's option pricing model, price the European put futures option with exercise price of $80 and maturity of six months
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