Assume a 2 step tree to value a European option that is due in 4 months when the futures price is 85, strike price is 80, risk-free rate is 1.5% and 𝜎 = 0.30.
Draw out the binomial tree to include the futures price at every node and the call/put option values at the ending node.
Compute the initial premiums for a call and a put option. (Show your work)
Repeat the binomial tree (as done in part (a-b)) for an American put and call option.Do any of the premium values change? If so, which one(s)?
Compute the initial premium for the American options.
Download historical futures data for crude oil from quandl using the following command Quandl(“CHRIS/CME_CL1”).
Compute the historical volatility for the month of January 2021.
Compute the monthly historical volatility for each month going back to 1985. Plothistorical volatility by month.
Does the monthly volatility associated with oil appear to be stationary? Conduct anynecessary tests and report your results.
A 1-year option is offered with current stock price of $100. The strike price of the option is $90 and the annual volatility rate is 40%. The risk-free rate of return on a 12-month bond is 2%. When the Black-Scholes model is used:
What is the value of 𝑑1?
What is the value of 𝑑2?
What is the price of a call option, c?
What is the price of a put option, p?
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