Overview of Options – An Introduction October 2004 Return to Risk Limited website:

Options Definition The right, but not the obligation, to enter into a transaction [buy or sell] at a pre-agreed price, quantity, time [by a specified date in the future], and terms. The option buyer typically pays the seller an upfront free (the premium) for the option rights.

Options Markets Over-The-Counter (OTC) –And Physicals Market, Tailored Exchange Traded –Standardized Terms –Style –Expiry Dates –Strike Levels

Basic Options Structures Calls – Options acquired by a buyer (holder) and granted by a seller (writer) to buy at a fixed price Puts – Options acquired by a buyer and granted by a seller to sell at a fixed price

Basic Options Structures All option products & strategies are some combination of buying or selling of calls or puts

Basic Options Provisions Buy or Sell (Write) –Long or Short Call or Put Underlying Asset –Product, Security / Instrument Strike (Exercise) Price Premium Exercise Date and Style

Basic Options Provisions - Strike Strike Price – Fixed price to be paid if option exercised, as specified in the options agreement Set in intervals on exchange traded options At any preferred level OTC How would you set the strike?

Basic Options Provisions - Premium Premium – Price of the option that buyer pays and seller receives at the time of option transaction. Consideration paid for rights Non-Refundable

Option Exercise Provisions or “Style” American - Style European - Style Asian - Style Bermudan - Style What is the impact on option value?

American-style Exercise Provision Buyer (Holder) may exercise at any time prior to expiry Value factor related to dividends on equity options

European-style Exercise Provision Buyer (Holder) may exercise only on expiry date Valuation difference

Asian-style Exercise Provision Class of options which have payouts dependent on the history of the price (some averaging basis) of the underlying asset during a pre-defined time period. –Average Price Options (APO’s) –Path Dependency, Barriers, Look-Backs, KO’s Potentially more complex price modeling

Early Exercise Of Options Exercising an option prior to expiration date Would that be economically attractive? Provisions for automatic exercise of “In-the-Money Options”

Option Concepts Insurance Policy Analogy Commonly Cited Fee For Providing Financial Protection Transfer Of (Price) Risk Intuitive Pricing Real Estate Options To Buy, Extended By Property Owners

Volatility Factor Measure Of The Degree Of Change In The Value Of The Underlying Asset Historical Volatility “Implied” Volatility

Very common jargon in financial trading Delta Vega Gamma Theta The “Greeks”  V  

The “Greeks” - Delta  The Most Commonly Watched Factor Since Used In Delta Hedging The Degree Of Change In Option Value In Relation To A Change In The Value Of The Underlying Asset

The “Greeks” - Vega Measures Effect On Premium Of A Change In Perceptions Of Future Volatility –Vega Also Referred To As Kappa The Degree Of Change In Option Value Relative To A Change In The Price Volatility Of The Underlying Asset

The “Greeks” - Vega Vega Is Closely Followed By Traders Since Trading Options Is Viewed As Trading Volatility

The “Greeks” - Gamma  The Rate Of Change Of Delta An Indicator Of How Stable Delta Is If A Position Or Portfolio Has A High Gamma, What Might That Suggest?

The “Greeks” – Theta  Measures Effect On Premium Of A Change In Time To Expiry The Degree Of Change In Option Value In Relation To A Change In The Time To Expiry Becomes More Important Closer To Expiry

The “Greeks” – Theta  Time Value Decreases At A Faster Rate As Option Expiry Date Is Approached

The “Greeks” – Rho  The Degree Of Change In Option Value In Relation To A Change In Interest Rates Of More Importance In Very Long-Term Options

Delta Measurement Example If The Price Of Natural Gas Changes By 1 Unit And The Option Value (Current Premium) Changes By 0.4 Then What Is The Option Delta Currently? So, What Does That Suggest?

Delta Concepts Delta Of An Option Approaches “0” As Option Moves Deep Out-Of-The-Money Delta Of An Option Approaches “1” As Option Moves Deep In-The-Money –Option Begins To Behave Like The Underlying Why Is That?

Complex Options Structures Path Dependent Options –Asians Combinations Of Options –Or Combos Of Options & Other Instruments Such As Swaps –Embedded Options –Building Blocks

Examples Of Options Structures Extendables –Expandables –Double-Ups, Double-Downs –Simplicity of structure for buyer –A bit more complex for seller to price and trade Participation swaps

Decomposing A Participation Swap To Understand From A Pricing Standpoint And From A Trading / Hedging / Managing Standpoint A Swap With Option Embedded At Ratio To Produce Desired Participation & Pricing Components Hedged Separately By Trading Desk

When To Consider Using Options For Hedging …rather than fixed price, fixed volume commitments When Underlying Exposure Is Uncertain Or Contingent When Option Pricing Is Viewed As Attractive When Weak Credit Standing Precludes Use Of Fixed Price Swaps, Or Other Instruments

When To Consider Using Options For Hedging When Competitive Business Position Dictates Avoiding Locking-in Costs –And Yet Price Protection Against Catastrophic Price Change Is Sought When Seeking To Monetize Embedded Optionality Of Existing Position [Physicals]

When To Consider Using Options For Hedging When Seeking A Tool To Reduce Or Transfer Risk When Selling Puts To Generate Income, At A Strike At Which Writer Is Happy To Own The Underlying Asset Ultimately, When Exposures Dictate Using Options

When Do Traders Typically Use Options In Their Portfolios When Pricing Is Viewed As Attractive When Seeking To Enhance Portfolio Income –To Play The Market With Limited Risk (No More Than Premium Paid) When Attempting To Use Leverage To Increase Yield

When Do Traders Typically Use Options In Their Portfolios When Systems And Trading Expertise Provide Capability To Manage Complexity When Seeking To Generate Income On Holding Of Underlying Asset –Covered Calls Ultimately, When Exposures, Market View, And Trading Strategy Dictate Using Options

Secondary Trading In Options –Rights Sold And Re-Sold Typically Not Just “Buy And Hold” –Frequently Traders Will Exit Or Roll Positions Before Nearing Expiry IPE Sample Pricing –Web ExampleWeb Example Options Trading Strategies

Options Pricing Sample Brent Crude Oil Options Calls: With $28.99 Exercise Price Current Settlement Price Implied Volatility Open Interest $ ¢32.52%440 $ ¢31.93%993 $ ¢32.49%201

Options Trading Strategies Straddles, Strangles Butterfly Spreads, Bull Spreads, Bear Spreads, Box Spreads, Calendar Spreads Typically Used In Taking Speculative Views On Future Market Price Moves –Not Usually Employed In Hedging Techniques –Configures Payoff Profile Consistent With Trader’s Market View

Options Trading Strategies Straddles – Simultaneous Purchase And/Or Sale Of The Same Number Of Calls And Puts With Identical Strike Prices And Expiration Dates [Long or Short] Strangles – Simultaneous Purchase And/Or Sale Of Calls And Puts At Different Strike Prices

Options Trading Strategies Bull Spread – Simultaneous Purchase & Sale Of Calls Or Puts That Will Produce Maximum Profits When Value Of Underlying Asset Rises Bear Spreads – Purchase & Sale Of Calls Or Puts For Maximum Profits When Value Of Underlying Asset Falls

Options Trading Strategies Box Spread – Combination Of Bull & Bear Spreads Transacted Simultaneously Calendar Spreads – [Time Spreads] Purchase & Sale Of Calls Or Puts With Different Expiration Dates

Options Pricing Theoretically The Net Present Value Of All Potential Outcomes For The Option Various Methodologies For Determining Issues In Energy Options –Price Distribution –Price History –Illiquidity

Options Pricing Theory Black-Scholes Formula Numerical Computational Techniques –Monte Carlo –Lattice Probability Tree Methods –Bi-Nominal, Tri-Nominal Methods –Assumes Price Follows Stochastic Process Options Can Be Considered “Wasting Assets” That [Generally] Decline In Value Over Time. After Expiration Date, Becomes Worthless.

Black-Scholes Options Pricing Model Developed by Fischer Black and Myron Scholes In 1973 First Theoretical Options Pricing Model Quantified Value Of Key Variables (Primarily Underlying Asset Value & Price Volatility) –Basis Of The Model Is To Estimate Probability That Option Will Finish In The Money

Black-Scholes Options Pricing Model Derived From Observation Of Mathematics From Physical Phenomena (Heat-Exchange Equation) Widely Used, Extensively Studied

Black-Scholes Options Pricing Model Assumes Price Of Option Related To Square Root Of Time Assumes Price Volatility Is At A Constant Level And Can Be Measured Through Standard Deviation Of Historical Prices Concentrated On European-style Options, Or No Dividends

Black-Scholes Options Pricing Model Critical Assumption For Model –Stochastic Price (Random Walk Theory) –Underlying Asset Price Follows Lognormal Distribution Assumptions May Not Be Valid For Energy Markets

Adjusted Black-Scholes Options Pricing Model Often Used Term, Also Referred To As Modified Black Model Or Extended Model Adjustment In Pricing Formula To Accommodate Alternative Assumptions –Black Model For Options On Futures, Rather Than Stock –Assumes Lognormal Distribution For Futures

Adjusted Black-Scholes Options Pricing Model Adjustment In Pricing Formula To Accommodate Alternative Assumptions –For Energy Presume Deterministic & Random Price Components –Deterministic Component Follows Mean Reversion To Reflect Seasonality Feature –Random Price Component As Lognormal

Monte Carlo Methodology Simulation Of Possible Outcomes Probability Assessment Various Methodologies Computer Resource Intensive Options Price Simulation Based On Assumptions & Probabilities, Not A Clarivoyant Prediction…

Monte Carlo Methodology Sp r2d2Spr2d2Sp r2u2Spr2u2Sp r 2 duS p Probability Of Outcomes… rdS p ruS p

Cox-Ross-Rubenstein Option Pricing Model Introduced Shortly After Black-Scholes A Binominal Model Constructs A Probability Tree Volatility Cones As Projections Of Volatility Into The Future Considered Much The Same As Black-Scholes Model, Just A Different Methodology

Likely Factors Influencing Pricing Of Options Price Volatility Of Underlying Asset Duration Of The Option – Time To Expiration Strike Price Of The Option Value Of The Underlying Commodity [Or Financial Instrument] Risk Free Interest Rate

Likely Factors Influencing Pricing Of Options Terms And Conditions How Could One Impact The Price Of An Option Through Contract Provisions?

Physical Assets As Options In Terms Of Economic Valuation… A Way To View The Value Of A Production Facility –Such As A Power Plant A Call On Capacity –A Call Option Product Storage Facility –Such As Natural Gas Or Fuel Storage

Writing Covered Calls Covered In Terms Of Owning The Underlying Asset To “Cover” Option Position If Call Is Exercised Obviously Less Risky Strategy –But Commits Asset A Call On Production Capacity A Call On Product Stored Or Owned –Such As Natural Gas Or Fuel Storage

Optimizing Options Value Realized For Generation Retail Sales Are The Sale Of The Plant’s [Or Portfolio’s] Option Value “Struck” At The O&M Cost Fuel As The Variable Cost Spark Spread

Price Distribution Lognormal [Bell Shaped Curve] Skew Event Risk –Fat Tails –Probability –Degree Of Certainty

Returns On Basic Options

Option Pricing Various Theoretical Pricing Basis For Options –Black-Scholes –Merton Model –Adjusted Black-Scholes –Cox, Ross & Rubenstein –Bi-Nominal, Tri-Nominal But Presumably Ultimate Market Price Determined By Supply & Demand

Option Pricing Theory Aside, The Practical Pricing Issues Can Sometimes Be A Bit Difficult

Option Pricing Valuation Price Discovery –Timing –Expertise –Basis Risk Free Interest Rate

Option Pricing Factors Higher The Volatility, The More Expensive The Option Longer The Life Of The Option, The More Expensive The Option

Historical Volatility Historical Volatility Is Determined From Past Price Data –Selection Of Appropriate Time Period Historical Volatility Can Be Estimated By Calculating The Square Root Of Variance

Implied Volatility Implied Volatility Is Determined Mathematically From Option Pricing Formulas When Premium Is Known Implied Volatility Is Closely Watched By Traders Reflects Market Perceptions Of Future Volatility, Not Necessarily Historical Levels

Average Price Options Averaging The Underlying Asset Price Smoothes The Volatility –Highs & Lows Can Cancel Each Other Out –So APO’s Tend To Be Cheaper Than Standard Options May Be A Better Match For Exposure Based On Daily Consumption Of A Commodity (NG)

Average Price Options Since APO’s Are Path Dependent, Option Writers May Use Monte Carlo Simulations To Estimate Value –Computational Techniques May Improve The Accuracy Of These Simulations –Delta Hedging APO’s May Require Frequent Adjustments Early In Option’s Life

Delta Hedging Dynamic Hedging – Using Futures To Hedge An Option Position Involves Frequently Buying And Selling Futures Contracts To “Re-Balance” Options Portfolio –Widely Used Technique Transactions Costs Consideration

Delta Hedging Delta-Neutral – Maintaining A Risk Neutral Position (Hedging) Requires Continual Monitoring And Managing Trading Expertise

Option Value At-The-Money In-The-Money Out-Of-The-Money Option Price Can Be Viewed As Comprised Of Two Components –Intrinsic Value –Extrinsic Value, Time Value

Option Value - Intrinsic Intrinsic Value Of An Option Is Simply The Amount, If Any, By Which The Option Is In-The-Money Profit That Could Be Realized If Option Were Exercised Immediately Easy Valuation

Option Value - Extrinsic Extrinsic Value Reflects The Potential Future Value Of The Option, Influenced Primarily By The Time Remaining To Expiry And The Price Volatility Of The Underlying Asset The Hard Part To Value

Option Value Deep In-The-Money Deep Out-Of-The-Money

Selling Uncovered Calls Naked Option – Sold When The Option Seller Does Not Own The Underlying Asset Risk Factor

Selling Covered Calls Option Sold When The Seller Owns The Underlying Asset For Example, A Power Generator Selling Calls On Capacity Opportunity Cost

Options On Spreads Price Distribution Is Likely Not Lognormal Price Spread Can Be Negative Complex Pricing Issues Refinery “Crack Spreads” Power “Spark Spreads”

Financial Risk On Options For Buyers Of Options, Risk (Of Losses) Are Limited To Premium Paid For Option –& Profits Are Potentially Unlimited, But… –…Be Careful… –A Very Deceiving Perspective: PCA Example –Probability Assessment On Risk / Return Ratio

Financial Risk On Options As Writers Of Options, Financial Exposure Would Be Potentially Unlimited Profits Are Limited To Premium Received Is There a Situation Where One Would Write An Option?

Credit Risk On Options For Writer Of Options, Counter Party Credit Exposure Limited To Settlement Risk (On Premium Payment) –Generally Considered Minimal But Counter Party (Buyer) May Require Substantial Credit Support Such As Margin/Collateral, LC

Credit Risk On Options For Option Buyers, Credit Exposure Is Similar To Fixed Price Instruments, Such As Swaps –Level Of Counter Party Credit Risk Depends On Market Price Risk, Which Is Theoretically Unlimited –Know Your Customer / Counter Party

Using Options High Potential Opportunity In Energy Options …But Potentially Very Dangerous If A Blunder Made –Numerous Areas Of Possible Risk

Overview of Options An Introduction