Derivative-Based Risk ManagementCrude Oil Deliverable

Oil King Management Team:Xiao Meng

Sayam IbrahimTanya Patwa

The Situation

We are an oil drilling company called Oil King operating in Texas.  We will have a delivery of 100,000 barrels (100 futures

contracts) of WTI crude oil to a cruise line company deliverable on January 1 2008.  We have not locked in a price yet. (We

are Long)

Market Outlook

As of December 7th the January futures contracts are at $88.28.There have been talks

of OPEC increasing the supply of crude oil, which would cause the price of the January

contract to sell off. However, if OPEC decides not to increase world supply of oil, the price may increase. The odds of each situation

occurring are equal. As a result, we expect the volatility of crude oil to remain at historical

levels and we have a neutral view in regards to price direction.

Update!!!

Given the recent news that has just been released, it is difficult to predict the direction of crude oil futures prices. However, due to the fact that these

headlines will have major impacts on crude prices, our view is now that volatility will be extremely high without a directional bias.

Our Purpose

We want to hedge our long crude oil position based on our view that volatility between today and the contract maturity date will be greater

than the implied volatility, with a direction neutral view. After a thorough analysis done by our

quantitative analyst, Dr. Bodurtha, he came to the conclusion that the volatility (judgmental) will

be 50%, which is greater than the implied volatility of 37.79%. This implies a likely range of

$71.14 – $109.55 for 25 days.

Volatility Going Up

F8 (Jan08) Futures Most Liquid

Futures Market SituationUnderlying - SS = Crude oil - CL Jan Mar

Current date 12/07/2007 Settle (Close) Price 88.28 87.94

Actual Maturity date 1/1/2008 3/1/2008

Symbol CLF8 CLH8

• Units of underlying each contract represent:  1,000 Barrels (42,000 gallons)

Risk Management

We seek to manage the risk of Light Sweet crude oil (CL)

Total exposure value: 100,000 barrels = $8.828 million.

Percentage loss limit decided upon for our exposure based on our risk tolerance: 5%, which is equivalent to a dollar value of $441,400.

Critical probability level

We want only a 5% chance of losing more than $441,400.

For the CL underlying January 1 maturity date and 25 (remaining) day futures contract: = $88.28 with R = 4.8 and RP = 0% (*next slide)

Our 5% loss limit critical price level is calculated relative to a measure of the consensus market expectation:

Expected Futures Price = $88.28

Risk Premium Calculation

Vol monthly Annual σ(WTI) / σ(S&P)

S&P 6.572465 22.76769 1.208070336

WTI 7.94 27.50497  

       

Correlation S&P-WTI   -0.08261  

       

Beta -0.0998    

       

Market Return   5.00%  

       

Risk Free Rate   4.17%  

       

Crude Oil Risk Premium     -0.000828319

Our risk premium calculation is a small negative number

(-0.000828319), which we attribute to recent market

trends in which commodity prices have been increasing while equity markets have

been selling off. Consequently, we will use 0% as our risk

premium.

Critical Prices for One Year

Annualized standard deviation estimate (risk metrics): 26.154%

For a long exposure, the lower critical price level equals = 88.28*e-.26154* 1.65 = $57.34

For a short exposure, the upper critical price level equals = 88.28*e.26154 * 1.65 = $135.92

Likely range for one year: $57.34 – $135.92

Critical Prices for 25 days

Annualized standard deviation estimate (risk metrics): 26.154%

For a long exposure, the lower critical price level equals = 88.28*e-.26154 * 1.65 = $78.79

For a short exposure, the upper critical price level equals = 88.28*e.26154 * 1.65 = $98.92

Likely range for 25 days: $78.79 - $98.92

Hedging with FuturesFrom the calculation above, there is a 5 % chance that the underlying

price will be at or below $78.79 in 25 days. The associated loss relative to selling the underlying at the current futures price of $88.28 equals the "loss at the lower critical price level" = -10.75%

Long exposure that may be retained: = -5%/-10.75% = 46.51%

Roughly, we must decrease our exposure by one minus the amount of loss that may be retained: 1 - (.4651) = .5349

For the underlying position of $8.828 million, we must sell 53.49% or$4,722,097

How many futures contracts equal our underlying exposure? = 100

How many futures must we sell to meet our risk targets? 54

Value @ Risk

Initial Position

Hedge with Futures

Hedging with Options

• Direction view: neutral

• Volatility view: volatile

Calls Puts

In-at-out of money Strike Price Price Quote Strike Price Price Quote

More OTM 92 0.48 85 0.54

OTM 90 1 87 1.13

ATM 88.5 1.6 88.5 1.82

ITM 87 2.41 90 2.72

More ITM 85 3.82 92 4.2

Views and Positions

Vol up Vol stable Vol down

Up *(synthetic call) Not Likely

 Not Likely

Stable Xlong straddle(even more

volatile: long strangle)

*(butterfly

spread)

 

Not Likely

Down *(synthetic put) Not Likely  Not Likely

Recommended Strategy: Synthetic Long Straddle

Purpose: Trade Volatility, Insurance

More Aggressive Long Straddle

Purpose: Trade Volatility, Insurance

Alternative Way to Create Long Straddle cost is the same

Purpose: Trade Volatility, Insurance

More Aggressive Long Straddle(alternative strategy)

Purpose: Trade Volatility, Insurance

Even more volatility: Long Strangle

Purpose: Trade Volatility, Insurance

More Aggressive Long Strangle

Purpose: Trade Volatility, Insurance

Volatility Neutral: Butterfly Spread

Purpose: Trade Volatility, Insurance, Income

More Aggressive Butterfly Spread

Purpose: Trade Volatility, Insurance, Income

Price up: Synthetic Long Call

Purpose: Trade, Insurance

Breakeven Analysis for Call

Price Down: Synthetic Long Put

Purpose: Trade, Insurance

Breakeven Analysis for Put

Recommendation Given that our view is long volatility and price direction neutral,

our options are long straddle and long strangle. More specifically, we have the choice of levering our volatility position with options while still meeting our 5% risk limit. We have decided that as an oil drilling company, our purpose is to hedge our exposure with as little risk as possible. While we have set our risk limits to 5%, given the nature of our business, it is not in our best interest to approach our risk limits to speculate with a levered position, the more aggressive straddle and strangle. After evaluating the different alternatives available to us, we believe that the best strategy given our risk tolerance, nature of business, and purpose is to put on a synthetic long straddle trade (3.62%). Although, it would be cheaper to implement a strangle (2.41%), given the fact that only 25 days remain to maturity, a long straddle position seems to be the more sensible approach. This is because the options are at the money and thus delta is 50, while the delta of the strangle is less than 50 because it involves out of the money options, implying a lower likelihood of ending in the money in before expiration.