Pricing crude oil futures options

In this part we would like you to build the three-step binomial tree for American futures options for crude oil and price those options using the equivalent binomial model. Use the hedge portfolio approach to price the American call futures option and risk neutral valuation to price the equivalent American put futures option.

For the purpose of the above task consider a hypothetical option that expires in one year and has a strike price 10% greater then the current futures price. Consider also the case when the futures contract expires two days after the option expiration date and this interval can be perceived as negligible for the purpose of a quantitative analysis in this exercise. Assume that the annualised volatility of one-year crude oil futures price is 45%.

You also need to source online the other inputs for the binomial model, that is:

• The current futures crude oil price of the underlying contract

• The one year risk free interest rate

For the selected values of the above parameters, you need to report the source of the data, the date of collection and provide a screenshot of the online source.

Prepare the binomial model for both options and conduct the relevant quantitative analysis in an Excel spreadsheet.

Describe also the process for obtaining the value of the option at a particular node for each of the two options. For the call option, clearly explain the replication strategy, the assets involved in the strategy and which positions are taken in the relevant assets. You should demonstrate here your practical ability to apply the binomial model in futures option valuation.

Once you obtain the prices for American call and put futures options from the binomial model, we would like you to use Black’s model to compute the prices of European call and put futures options. Can you use Black’s model to price American futures options? Explain how are the prices of the European and American futures options are related to each other.