Understanding Options: A Comprehensive Guide to Financial Derivatives

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

2. 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.

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

4. 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

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

6. 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

7. 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?

8. 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

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

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

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

12. 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

13. 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”

14. 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

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

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

17. 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

18. 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

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

20. 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?

21. 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

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

23. 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

24. 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?

25. 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?

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

27. 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

28. 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

29. 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

30. 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]

31. 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

32. 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

33. 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

34. 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

35. Options Pricing Sample

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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.

42. 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

43. Black-ScholesOptions Pricing Model • Derived From Observation Of Mathematics From Physical Phenomena (Heat-Exchange Equation) • Widely Used, Extensively Studied

44. 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

45. 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

46. 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

47. 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

48. 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…

49. Monte Carlo Methodology Probability Of Outcomes… r2u2Sp ruSp Sp r2duSp rdSp r2d2Sp

50. 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