Overview of Options – An Introduction

October 2004

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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 Example

Options Trading Strategies

Options Pricing SampleBrent Crude Oil OptionsCalls: With Underlying @ $28.99

Exercise

Price

Current Settlement

PriceImplied

VolatilityOpen

Interest

$28.50 85¢ 32.52% 440

$29.00 57¢ 31.93% 993

$29.50 37¢ 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-ScholesOptions 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-ScholesOptions Pricing Model

• Derived From Observation Of Mathematics From Physical Phenomena (Heat-Exchange Equation)

• Widely Used, Extensively Studied

Black-ScholesOptions 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-ScholesOptions 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-ScholesOptions 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-ScholesOptions 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

r2d2Sp

r2u2Sp

r2duSp

Probability Of Outcomes…

rdSp

ruSp

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 OptionsPayoff Diagram

-60

-40

-20

0

20

40

60

1 2 3 4 5 6 7 8 9 10 11

Spot Price

Pay

off

Long UnderlyingAsset

Short Put Option

Long Call Option

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