As the Purchasing Manager of UPS Shipping, you are worried that with the continued war in Ukraine, the price of diesel fuel may rise. Given the information below, please answer questions a. to e. You may find the following downloadable spreadsheet software very useful: http://www.OptionTradingTips.com

Risk Free Rate	2%
Number of Vehicles	100
Killometers per Vehicle per Annum	250,000
Litres per 100 km	30
Total Kilometers for Fleet	25,000,000.0
Litres consumed for Fleet	7,500,000.0
Fuel Oil Contract Size Litres	200,000
Annual Required Contracts	37.50
Fuel Oil Volatility	30%
Current Spot Price per Litre	$ 0.40

Given the above specifications and market information, please answer the following questions:

(a) What would be the cost of making your exposure Delta Neutral using a one year at-the-money Call Option on a single Diesel Fuel Contract exercisable only at the end of one year? What would be the price of hedging the entire exposure for one year?

(b) Why, from a value perspective, might an Option exercisable any time over the year, be more valuable than one which can only be used at expiry?

(c) You are concerned that the at-the-money hedging strategy is quite expensive. Can you devise a Put Option Strategy to approximately fully offset the expense of the Call Option? Please do your calculations at total exposure level, i.e., to hedge the annual expenditure. In addition to your calculated results cut-and-pasted from Excel, please create a pay-off diagram showing your strategy. Are there alternatives to matching option per option?

Recalling that for a position to be Gamma Neutral position the Delta's rate of change must be close to zero even as the underlying rises or falls. For the Call Option, how out-of-the money must the Strike Price be in order for the position to be Gamma Neutral?

(e) As Purchasing Manager you are worried about market volatility, showing analytically, how would the price of the Call Hedging Strategy be affected if volatility increased by 10%? Showing analytically, how would your Long Call and Short Put Option strategy be affected by changes to volatility? [Hint: Use the computed Vega to support your answer].