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Return to Risk Limited website: www.RiskLimited.com. Overview of Options – An Introduction. October 2004. Options Definition.

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options definition
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
Options Markets
  • Over-The-Counter (OTC)
    • And Physicals Market, Tailored
  • Exchange Traded
    • Standardized Terms
    • Style
    • Expiry Dates
    • Strike Levels
basic options structures
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 structures5
Basic Options Structures
  • All option products & strategies are some combination of buying or selling of calls or puts
basic options provisions
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
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
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
Option Exercise Provisions or “Style”
  • American - Style
  • European - Style
  • Asian - Style
  • Bermudan - Style
  • What is the impact on option value?
american style exercise provision
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
European-style Exercise Provision
  • Buyer (Holder) may exercise only on expiry date
  • Valuation difference
asian style exercise provision
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
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
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
Volatility Factor
  • Measure Of The Degree Of Change In The Value Of The Underlying Asset
  • Historical Volatility
  • “Implied” Volatility
the greeks
The “Greeks”
  • Very common jargon in financial trading
  • Delta
  • Vega
  • Gamma
  • Theta


the greeks delta
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
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 vega19
The “Greeks” - Vega
  • Vega Is Closely Followed By Traders Since Trading Options Is Viewed As Trading Volatility
the greeks gamma
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
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
  • BecomesMore Important

Closer To Expiry

the greeks theta22
The “Greeks” – Theta 
  • Time Value Decreases At A Faster Rate As Option Expiry Date Is Approached
the greeks rho r
The “Greeks” – Rho r
  • 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
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 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
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
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
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
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 hedging30
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 hedging31
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 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 portfolios33
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
options trading strategies
Options Trading Strategies
  • 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 strategies36
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 strategies37
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 strategies38
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 strategies39
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
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
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
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 scholes options pricing model43
Black-ScholesOptions Pricing Model
  • Derived From Observation Of Mathematics From Physical Phenomena (Heat-Exchange Equation)
  • Widely Used, Extensively Studied
black scholes options pricing model44
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 scholes options pricing model45
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 scholes options pricing model
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 scholes options pricing model47
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
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 methodology49
Monte Carlo Methodology

Probability Of Outcomes…







cox ross rubenstein option pricing model
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
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 options52
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
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
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
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
Price Distribution
  • Lognormal [Bell Shaped Curve]
  • Skew
  • Event Risk
    • Fat Tails
    • Probability
    • Degree Of Certainty
option pricing
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 pricing59
Option Pricing
  • Theory Aside, The Practical Pricing Issues Can Sometimes Be A Bit Difficult
option pricing60
Option Pricing
  • Valuation
  • Price Discovery
    • Timing
    • Expertise
    • Basis
  • Risk Free Interest Rate
option pricing factors
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
  • 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
  • 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
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 options65
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
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 hedging67
Delta Hedging
  • Delta-Neutral – Maintaining A Risk Neutral Position (Hedging)
  • Requires Continual Monitoring And Managing
  • Trading Expertise
option value
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
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
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 value71
Option Value
  • Deep In-The-Money
  • Deep Out-Of-The-Money
selling uncovered calls
Selling Uncovered Calls
  • Naked Option – Sold When The Option Seller Does Not Own The Underlying Asset
  • Risk Factor
selling covered calls
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
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
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 options76
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
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 options78
Credit Risk On Options
  • For Option Buyers, Credit Exposure Is Similar To Fixed Price Instruments, Such As Swaps
    • Level Of Counter PartyCredit Risk Depends On Market Price Risk, Which Is Theoretically Unlimited
    • Know Your Customer / Counter Party
using options
Using Options
  • High Potential Opportunity In Energy Options
  • …But Potentially Very Dangerous If A Blunder Made
    • Numerous Areas Of Possible Risk