Please assume that you are looking price a six-month call option on natural gas futures contract using a two period binomial pricing model. The futures price is $2.23 and the strike price is $2.00. You have estimated the parameters for u and d to be 1.233 and 0.811, respectively. The risk free rate is 1.0% per year. Please draw the binomial tree and provide prices for the futures contract and the option at each node in the tree. You may do this by hand and scan or take a picture of your work to upload, or you may do this in MS Excel.
What are the values of delta at the first and second steps in the tree (one delta for the first step (fu) and two deltas for the second step (fuu and fud))?
If I tell you that the implied volatility on a futures options contract is 25% and there are three months to expiration, please tell me what figures you would use for u and d in a binomial options pricing model.
You are currently long four futures contracts on natural gas. You want to temporarily (and just partially) hedge your exposure for one month so you purchase four futures put options contracts that each have a delta of -0.33. What is your new exposure to the futures price movement? (in terms of futures contracts).
Please go to the Cmegroup website and find the September 2017 futures options on crude oil (CL). Using the Derivagem spreadsheet (DG201 below), please find the implied volatilities of the September 45 strike put option and the September 55 call option. You may assume 1.00% for the risk free rate and five months until expiration.
How do these figures compare to the chart of the oil VIX provided earlier in this Lesson?
Are the implied volatilities the same for the call and the put options? Why or why not?