Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC

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1 Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC 2 The Options Industry Council Options involve risks and are not suitable for everyone. Prior to buying or selling options, an investor must receive a copy of Characteristics and Risks of Standardized Options. Individuals should not enter into options transactions until they have read and understood the risk disclosure document, Characteristics and Risks of Standardized Options, available by calling OPTIONS or by visiting OptionsEducation.org. Copies may be obtained by contacting your broker or The Options Industry Council at One North Wacker Drive, Chicago, IL In order to simplify the computations, commissions, fees, margin interest and taxes have not been included in the examples used in these materials. These costs will impact the outcome of all stock and options transactions and must be considered prior to entering into any transactions. Investors should consult their tax advisor about any potential tax consequences. Any strategies discussed, including examples using actual securities and price data, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. Past performance is not a guarantee of future results.

2 3 OIC s Participant Exchanges 4 Annual Options Volume, Cleared Contracts

3 5 Presentation Outline Quick Overview on Pricing The Greeks Theta Vega Rho Capturing Theta Capturing Vega 6 Pricing Models Option pricing models mathematical formulas remove subjective decisions from pricing process assume stock prices in marketplace are random Input quantifiable factors that create an option s price Output theoretical values for call and put options Greeks - price sensitivities to changing factors Delta Gamma Theta Vega Rho

4 7 Option Pricing Factors Quantifiable underlying stock price strike price volatility time until expiration risk free interest rate (e.g., T-bill) dividends Input for any option pricing model 8 Options in the Marketplace Who makes options prices? all market participants (buyers and sellers) individual and institutional investors professional market-makers best bid/ask is consensus of all bids and offers What is an option ultimately worth? what the market is willing to pay pricing models used as guideline supply/demand and market dynamics override theoretical values

5 The Greeks 10 The Five Greeks Delta Expected change in option value with changing underlying stock price Gamma Expected change in option delta with changing underlying stock price Theta Vega Rho Expected change in option value with passage of time (time decay) Expected change in option value with changing implied volatility Expected change in option value with changing risk free interest rate

6 11 Nature of the Greeks Meaningful only during option s lifetime at expiration they are moot Impact of any Greek is on option s time value an expiring option is worth only intrinsic value (if any) Greeks may affect each other e.g., change in an options theta (time decay) may affect its delta Impact of Greeks differ for each option contract in-the-money vs. at-the-money vs. out-of-the-money near-term vs. far-term 12 Individual Investors Greek calculations often not a focus grasp of underlying mathematics by no means required Most important concerns for individuals are eternal stock selection broad market direction outlook for industry sectors risk all of these create a personal comfort zone in order to pursue individual investment goals

7 13 Individual Investors With respect to each of the Greeks more important to understand nature of sensitivities being measured closer look at each will help Value of Greeks understanding where your risk can come from balancing risk vs. reward before positions established setting your expectations reducing surprises in option price behavior 14 Where to Find Theoretical Values and the Greeks Option pricing calculators various financial Web sites Some option chains brokerage firm Web sites quote provider Portion of option chain from IVolatility.com Accessible via For illustrative purposes only

8 Theta 16 Theta Theta: Option value s sensitivity to time Expected time decay in option value with the passage of 1 day expressed in decimal form (-.080) represents cash amount per share all other pricing factors constant Calls and puts both have negative theta amounts

9 17 More on Theta Theta may be measured for periods longer than 1 day e.g., 2-day theta or 10-day theta Decay is per calendar day, not per trading day Theta represents rent buyers pay and writers receive buyers want time for favorable move in stock price writers sell that time Buyers hope delta gains will offset theta loss Only time value decays at expiration option worth only intrinsic value (if any) 18 Theta Calculation An option is trading today at $3.50 theta of -$.030 (-$.03) contract is worth $3.50 x 100 shares = $ Option s expected value tomorrow = $ $.03 = $3.47 contract is worth $3.47 x 100 shares = $ theta -$.03 $3.00 loss per contract Assuming other pricing factors constant

10 19 Time Decay Not Constant Time Value $$$ In-the-Money Option At-the-Money Option Theta Amounts Time Overall rate of time decay is exponential ATM rate = of decay decay exponential increases as = volatility expiration is nears key decay factor Theta ITM = amounts decay linear reflect = cost-to-carry this is key decay factor 20 Time Decay Option premium erodes with the passage of time Only time value affected not intrinsic value Erosion accelerates as expiration approaches Call Value Time to Expiration (Months)

11 21 Theta Calls INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Quarterly Dividend Dividend Amount Volatility 25.00% 7 day Theta Interest Rate 1.50% Vega Days until Expiration 90 Rho We can expect the call option price to decrease by $0.05 after 7 days have passed. 22 Theta Puts INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Quarterly Dividend Dividend Amount Volatility 25.00% 7 day Theta Interest Rate 1.50% Vega Days until Expiration 90 Rho We can expect the put option price to decrease by $0.04 after 7 days have passed.

12 23 Theta vs. Volatility Theta Theta vs. Volatility Strike Price Call 40% vol. Put 40% vol. Call 20% vol. Put 20% vol. Implied volatility impacts theta amounts with rising volatility theta increases with decreasing volatility theta decreases Higher volatility more time value more to decay by expiration XYZ $ days 2% int. 24 Theta vs. Time Theta Theta vs. Time With At-the-money Theta more greatest time options with until at-themoney rate time options of value decay close is slower to expiration have most expiration theta amounts is greatest decrease As expiration option goes approaches in-the-money or out-of-the-money rate of decay increases theta time value amounts decreases increase theta decreases Strike Price 1 Week 1 Month 3 Month 6 Month 18 Month

13 25 Price Comparison Compare at-the-money call prices 50 call on $50.00 stock Stock unchanged Now Three-month option Two-year LEAPS $3.33 $10.97 One month later: 20% $2.67 3% $10.64 Two months later: 31% $1.84 3% $10.32 Three months later: 100% $0.00 3% $ Theta Rules of Thumb Time decay (theta) is at its greatest near the end of the life of an option Short-term option decay is greater than long-term option decay Time decay hurts option holders Time decay helps option writers Time decay is greatest for A-T-M options; less for both deep I-T-M and far O-T-M options

14 Vega 28 Vega Vega: Option value s sensitivity to volatility Expected change in option value with a 1%-point change in implied volatility up or down expressed in decimal form (.080) represents cash amount per share all other pricing factors constant Calls and puts both have positive vega amounts implied option value by vega amount implied option value by vega amount

15 29 Vega Characteristics Also known as kappa (Greek letter) thus symbol K Volatility considered most influential price factor great impact in dollars on option values possible changes often occur intra-day changes may be abrupt and significant Increase in implied or vega does not require change in stock price Two Types of Volatility

16 31 Historical Volatility A stock s volatility is in the past Can be observed and quantified A statistic, or a fact, not a prediction Today Stock Price Time 32 Implied Volatility Represents the Future Today Stock Price Historical Volatility Implied Volatility Option implied volatility reflects current expectations of future stock volatility Only options have implied volatility

17 33 Implied Volatililty Can be at great variance with a stock s historical volatility Its prediction of future stock volatility is not necessarily right or wrong Changes to Implied Volalities May occur intra-day or over time May occur abruptly and significantly Does not require change in stock price Does not require change in stock s historical volatility 34 Implied vs. Historical Volatility From Table and graph from IVolatility.com Accessible via For illustrative purposes only

18 35 Investigating Implied Volatility You will not always find implied volatility level to be the same across strike prices Sample below for illustrative purposes only XYZ XYZ XYZ XYZ XYZ Implied volatility is decreasing XYZ XYZ XYZ Portion of option chain from IVolatility.com Accessible via For illustrative purposes only 36 Investigating Implied Volatility You will not always find implied volatility levels to be the same across expiration months Samples below for illustrative purposes only XYZ XYZ XYZ XYZ XYZ XYZ XYZ July XYZDecember Portion of option chains from IVolatility.com Accessible via For illustrative purposes only Compare implied volatility levels between the two months

19 37 Vega Calls INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Quarterly Dividend Dividend Amount Volatility 25.00% Interest Rate 1.50% Vega Days until Expiration 90 Rho We can expect the call option price to increase by $0.04 if the volatility increases by 1% and to decrease by $0.04 if volatility decreases by 1%. 38 Vega Puts INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Quarterly Dividend Dividend Amount Volatility 25.00% Interest Rate 1.50% Vega Days until Expiration 90 Rho We can expect the put option price to increase by $0.04 if the volatility increases by 1% and to decrease by $0.04 if volatility decreases by 1%.

20 39 Vega INPUTS RESULTS Underlying Price $27.00 Calls Puts Strike Price $25.00 Theo. Value Quarterly Dividend Delta Dividend Amount Gamma Volatility 25.00% 7 day Theta Interest Rate 1.50% Vega Days until Expiration 90 Rho Vega Volatility Increases INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Theo. Value Quarterly Dividend Dividend Amount Volatility 30.00% Interest Rate 1.50% Days until Expiration 90 When volatility increased from 25% to 30% call prices rose from to and put prices rose from to

21 41 Vega Volatility Decreases INPUTS RESULTS Calls Puts Underlying Price $27.00 Strike Price $25.00 Theo. Value Quarterly Dividend Dividend Amount Volatility 20.00% Interest Rate 1.50% Days until Expiration 90 When volatility decreased from 25% to 20% calls prices dropped from to and put prices dropped from to Implied Volatility INPUTS Underlying Price $27.00 Calls Puts Strike Price $25.00 Current Price $2.55 Quarterly Dividend Dividend Amount Volatility 23.95% Interest Rate 1.50% Days until Expiration 90 A call price of $2.55 will yield an implied volatility of 23.95% for the $25.00 strike expiring in 90 days.

22 43 Implied Volatility INPUTS Underlying Price $27.00 Calls Puts Strike Price $25.00 Current Price $5.00 Quarterly Dividend Dividend Amount Volatility 75.63% Interest Rate 1.50% Days until Expiration 90 A call price of $5.00 will yield an implied volatility of 75.63% for the $25.00 strike expiring in 90 days. 44 Vega Examples Vega impact greatest in dollar amounts on at-the-money contracts in percentage terms on out-of-the-money contracts Option today valued at $4.50 with vega (.03) volatility 1 pt. option price $ = $4.53 volatility 1 pt. option price $ = $4.47 Option today valued at $2.75 with vega (.02) volatility 1 pt. option price $ = $2.77 volatility 1 pt. option price $ = $2.73

23 45 Vega vs. Time Vega Vega vs. Time Strike Price 18 month 6 month 3 month 1 month More time until expiration greater the vega Vega size related to amount of time value more time value greater the vega LEAPS vega may be significantly higher XYZ $ % vol. 2% int. 46 Where to Find Vega Option chains Brokerage firm Web sites and quote services Vega Portion of option chain from IVolatility.com Accessible via For illustrative purposes only

24 47 Volatility Rules of Thumb Volatility measures price movements, it does not indicate direction Implied Volatility is usually greatest before news announcements The higher the implied volatility the higher the option s price The lower the implied volatility the lower the option s price Increasing volatility helps long option positions and hurts short option positions Decreasing volatility helps short option positions and hurts long option positions Rho

25 49 Rho Rho: Option value s sensitivity to interest Expected change in option value with a 1%-point change in risk-free interest rate up or down expressed in decimal form (.080) represents cash amount per share all other pricing factors constant Considered the least significant of all pricing factors component of cost of carry small portion of any option s total premium 50 Rho vs. Time Examples 3-month call valued at $3.70 today rho =.07 interest rate 1% call = $ = $3.77 increase in call value = 1.9% 18-month call (same strike) valued at $9.45 today rho =.40 interest rate 1% call = $ = $9.85 increase in call value = 4.2%

26 51 Rho Rules of Thumb Rho measures the possible changes to the cost to carry a position should interest rates change Has a greater effect on higher priced securities Rho is smallest for far O-T-M options and largest for deep I-T-M options Rho is larger for long-term options and nearly 0 for very short term options Capturing Theta Time Spread (Horizontal Spread) (Calendar Spread)

27 53 Long Time Spread All calls or all puts on same underlying stock sell 1 near-term option same strike price buy 1 far-term option Selected strike generally at-the-money long costs more than short always debit spread Expectations neutral on underlying stock stock stabilizes at strike until near-term expiration profit from time decay of short call far-term implied volatility to maintain or increase 54 Long Time Spread Position Greeks - short theta (net positive) take advantage of difference in decay rates greater theta of short near-term contract smaller theta of long far-term contract Time Value $$$ Long Call Short Call Time

28 55 Long Time Spread Position Greeks - long vega (net positive) implied increase benefits long far-term option boosts profit at near-term expiration As near-term expiration approaches short option in-the-money assignment risk Assignment unacceptable consider closing spread 56 At Near-Term Expiration Maximum profit scenario short option at-the-money no assignment long option has maximum value (volatility dependent) Maximum profit value of long call less debit paid for spread Maximum profit calculation long-term option value at near-term expiration can only be predicted via pricing model

29 57 At Near-Term Expiration Maximum loss limited to debit paid for spread Maximum loss seen if underlying stock away from strike price both options out-of-the-money and worthless both options deep in-the-money with no time value spread between option values = 0 58 Call Time Spread Example Stock XYZ at $60.00 options 30% implied Time spread: Buy 1 XYZ 90-day call $3.70 Sell 1 XYZ 30-day call + $2.10 net paid: $1.60 debit Position Greeks Γ Θ Κ Long 90 day call Short 30 day call Net for position Not including commissions

30 59 At Near-Term Expiration Not including commissions Capturing Vega Long Straddle

31 61 Profit from Vega Increase Objective profit from increase in implied volatility Method establish delta neutral strategy get long vega Long straddle buy at-the-money call buy at-the-money put same strike and expiration 62 Long Straddle Long vega forecast is increase in implied volatility one straddle is two long options more long vega at-the-money contracts impact greatest in dollars Delta neutral success does not rely on change in stock price Long gamma unexpected significant move in stock price up or down could also result in profit

32 63 Long Straddle Theta primary risk is time decay one straddle is two long options more theta Expectation increase in implied to exceed time decay Appropriate when implied for option class is low compared to past implied levels Have timeframe for implied to increase before rate of decay begins to rapidly increase 64 Picking the Stock XYZ options currently have implied around 18% past year levels in 15% to 28% range most recent peak around 31% Timeframe for implied increase is next two weeks expiration selected is in 60 days XYZ Options 34% 30% 26% 22% 18% 14% Graph from IVolatility.com Accessible via For illustrative purposes only 10%

33 65 Position Stock XYZ at $50.00 Long straddle: Buy 1 XYZ 60-day call - $1.58 Buy 1 XYZ 60-day put - $1.35 net paid: - $2.93 debit Position Greeks Γ Θ Κ Long 60-day call Long 60-day put Net for position Today If implied increases from 18% to 26% today profit is $1.29 predicted by.160 net vega Not including commissions

34 67 Two Weeks Later After two weeks (timeframe for volatility increase) Implied still 18% = $.36 loss (time decay) Implied increased to 26% = $.76 profit investor exits position Profit/Loss Expiration 18% Volatility 26% Volatility Stock Price Not including commissions 68 Theoretical Value Rules of Thumb Theoretical value is a starting point Options will often be priced differently than theoretical value Other factors at work: Supply and demand Minimum price variation Bid ask spreads

35 69 Option Chain Option chains frequently include Theoretical values Implied volatility Greeks Theoretical Values Greeks Portion of option chain from IVolatility.com Accessible via For illustrative purposes only Implied Volatilities 70 Position Simulator Profit-Loss Graph Today

36 71 Position Simulator Profit-Loss Graph Today at Expiration 72 For More Information OPTIONS

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