The Ultimate Options Course How Options Are Priced

Transcription

1 The Ultimate Options Course How Options Are Priced Kerry W. Given, Ph.D. (Dr. Duke) Parkwood Capital, LLC 2011 Parkwood Capital, LLC. All Rights Reserved.

2 Disclosures and Disclaimers Buying and selling stocks and opaons involves risks and may not be suitable for all investors. Prior to buying or selling an opaon, the investor must receive a copy of the booklet, CharacterisAcs and Risks of Standardized OpAons, from your broker or from The OpAons Clearing CorporaAon, 1 North Wacker Drive, Suite 500, Chicago, IL The informaaon in this presentaaon is presented for educaaonal purposes only. It should not be construed as a recommendaaon or solicitaaon to buy or sell opaons. Many examples of opaons trades are presented in this presentaaon as illustraaons of the principles being taught in this course. These examples are not recommendaaons or solicitaaons to buy or sell any stock or opaon. To simplify the calculaaons, commission costs have not been included in the examples in this presentaaon. Commission costs will affect the outcome of any stock or opaons trade and must be considered prior to entering the transacaon. No representaaon is being made that any account will or is likely to achieve profits or losses similar to those discussed in this presentaaon. The past performance of any trading system or methodology is not necessarily indicaave of future results. 2

3 Introduction Is it a bargain? Can I predict the direcaon correctly and sall lose money? Where is my risk? 3

4 Is This Option a Bargain? In stock trading: P/E raaos, book value, growth in earnings, debt/equity raaos, relaave strength, etc. The Black Scholes equaaon (1973): Inputs: stock price, strike price, historical stock volaality, Ame to expiraaon, and interest rate Output: the theoreacal value of the opaon Compared to the market price? 4

5 The Black Scholes Model ϕ is the probability distribuaon funcaon we discussed in our first class. The Black Scholes model computes the theoretical price of an option. Thus, we can determine whether an option is overvalued or undervalued. where: s = the price of the underlying stock or index x = the strike price of the option r = the risk free interest rate t = time in years until option expiration σ = the historical volatility of the underlying stock or index ϕ = the normal probability distribution function This is similar to using a Price/Earnings (P/E) ratio to determine if a stock is overvalued or undervalued. The objective is to understand the variables and their interdependencies, not to be able to use this equation. All of these calculations have been done for us but we need to understand where the Greeks come from and how the variables interact with each other. 5

6 What is Implied Volatility? The Black Scholes equaaon calculates the theoreacal price of an opaon based upon: Stock price Strike price Stock s historical volaality Time to expiraaon Interest rate At the close on March 11, 2011, AAPL s Apr $350 call was quoted at $13.10 bid, $13.25 ask. We enter the stock price ($352), strike price ($350), 33 days to expiraaon, the historical volaality (20%) and the interest rate (1.00%) into Black Scholes, and we compute $9.88 as the theoreacal price for the Apr $350 call. Therefore, the market is pricing this opaon about 33% over the theoreacal value. Why? If we enter the market price of $13.18 into Black Scholes and solve for the volaality, we get 27.65% the volaality that is implied by the market price for this opaon, thus, the implied vola+lity. The market expects AAPL s volaality in the next 33 days to be greater than its historic 20% but this is not a direcaonal indicator! 6

7 OptionsXpress Option Pricer Bring up an opaons chain and click OpAon Pricer We can vary these parameters to test what if scenarios Today s market price for the May $345 call TheoreAcal price from the model calculaaon 7

8 Implied Volatility Historical volaality is the actual measure of the stock s past price movement. Implied volaality (IV) is the market s consensus assessment of the expected or future volaality. High values of IV tell us the market is anacipaang larger price moves for the underlying stock, up or down. In general, increased IV is associated with increased risk. When IV is low, the opaons are inexpensive and when IV is high, opaons are expensive. In general, I want to buy low IV and sell high IV. OpAon spreads allow us to somewhat cancel out the effects of high IV because we are both buying and selling high IV. OpAons strategies have widely differing sensiaviaes to changes in IV. 8

9 The Cyclic Movement of IV NFLX Note NFLX s earnings announcements in October, January, April, and July. IV peaks and then drops aker the announcement. You can think of high IV as: 1) reflecang high market demand for the opaons, driving up the price, or 2) the market s general consensus that a large price move is more probable, and the higher opaon prices compensate for that risk. 9

10 Volatility Skews IV may vary within the stock s opaon chain. A posiave skew: IV of the front month is higher than the IV for next month. A posiave IV skew suggests a big move is expected in the current month. NegaAve volaality skews may occur when an earnings announcement is scheduled for next month. Some authors measure skews in percentage difference, others in points of percentage difference, e.g., for the IVs of 23% in July and 21% in Aug, this is either a 2 point or a 9.5% posiave skew. On 1/18/11, GOOG closed at $640. The Jan $640 call = $15.35 with an IV of 67% with only three days lek to expiraaon, but the Feb $640 call = $22.20 with an IV of 30%, a posiave IV skew due to the earnings announcement scheduled 1/20/11. If the Jan call had a normal IV of 30%, the price would have been $

11 Sources of IV Data CBOE Web Site: Home Tools VolaAlity OpAmizer IV Index (Free). Larry McMillan s web site the Strategy Zone service provides detailed IV data such as current IV and the percenale of this IV within the past year of IV data; also has many volaality screens of opaons to find good calendar spreads, covered calls, volaality skews, and under/over valued opaons; updated daily. Your opaons brokerage site. Most of the IV data is one day old, i.e., it is the IV as of the close of trading yesterday. For most purposes, that is more than adequate. The web site, (the source of the free IV data at CBOE) sells a subscripaon service for real Ame IV data for stocks and indexes. 11

12 VIX The Market Volatility Index The VIX is a measure of overall market volaality; developed in 1993 by the CBOE and Duke University. The VIX calculaaon uses front month and next month SPX opaons to create a theoreacal ATM opaon with 30 days to expiraaon. The IV of this theoreacal opaon is the VIX. The calculaaons are updated throughout the day. VIX gives us a quanataave measure of the implied volaality of the market as a whole. As the underlying SPX opaons used to create the VIX increase in price, the VIX increases. Look at the VIX as a measure of future market volaality, not future direcaon. The all Ame high for the VIX was 89.53% on 10/24/08; the all Ame low was 9.31% on 12/22/93. 12

13 VIX The Market Volatility Index VIX S&P 500 (SPX) 13

14 Building the Price of an Option The market price of an opaon is the sum of three elements: 1) Intrinsic value what is the value if I exercised the opaon? If 3M is trading at $96.24, then the May $95 call has intrinsic value of $1.24. The opaon will be priced > $1.24 due to Ame and IV (priced at $2.20). 2) Time value how much Ame is lek? The 3M June $95 call is priced at $2.83; the $0.63 difference is due to the addiaonal Ame (assuming IV is idenacal). 3) Implied VolaElity (IV) how does the market price compare to the theoreacal price? The 3M May $95 call is priced at $2.20, but the theoreacal value is $2.39; the $0.19 difference is due to implied volaality (14.9%) being lower than historical volaality (17%). 14

15 Option Pricing Examples IBM = $93.96 and the Oct $85 call (3 days) = $9.35, Nov $85 call (38 days) = $12.20, and the Jan09 $85 call (94 days) = $ The intrinsic value is $9 for each of these opaons. The primary difference is Ame in this case. IV can vary from month to month if a significant event is expected. GE = $20.92 and the Oct $17.50 call = $3.52. Therefore, intrinsic value = $3.42, so the price includes only $0.10 of Ame and volaality (3 days). But GOOG = $ and the Oct $360 call = $ Intrinsic value = $5.46, so Ame and volaality = $19.29, but the Ame is the same (3 days); so IV is the difference GOOG reports earnings in 2 days! OpAons are more expensive as: The opaon goes ITM, As IV increases, and With more Ame to expiraaon. 15

16 What Are The Greeks? Any opaon posiaon is exposed to risk from three areas: 1) a change in the price of the underlying stock or index, 2) a change in volaality, 3) the passage of Ame. The Greeks quanafy the posiaon s risk sensiavity Delta (Δ) measures the change in our opaon price with a change in the stock/index price. Gamma (γ) measures the change in our delta value with a change in the stock/index price. Vega (V) measures the change in our opaon price with a change in IV. Theta (θ) measures the change in our opaon price with the passage of one day of Ame. 16

17 A Closer Look At the Greeks Delta (Δ) measures the change in our opaon price with a change in the stock/index price. Delta of 53 means our opaon will gain $0.53 in value with a $1.00 increase in stock/index price Ranges from 0 to 100 (someames listed as a percentage, e.g., 45% or 0.45) Delta is about 50 ATM Larger as we go ITM (trends to 100) and smaller as we go OTM (trends to zero) Larger as Ame to expiraaon goes up Gamma (γ) measures the change in our delta value with a change in the stock/index price. Gamma of means our opaon s delta will gain in value for a $1.00 increase in stock/index price (Δ = 53, first +$1 in stock will increase the opaon price by $0.53, while Δ increases to 60. So the next one dollar increase in the stock/index price will increase the opaon price by $0.60) Gamma is largest ATM; smaller as we move ITM or OTM Gamma is largest as we near expiraaon 17

18 A Closer Look At the Greeks Vega (V) measures the change in our opaon price with a change in IV. Vega of means our opaon will gain $0.124 in value for a 1 percentage point increase in IV Vega is largest ATM; smaller as we move ITM or OTM Larger with more Ame to expiraaon Theta (θ) measures the change in our opaon price with the passage of one day of Ame. Theta of means our opaon will lose $0.057 in value over the next 24 hours For a long opaon, theta is negaave, i.e., our opaon is losing value with elapsed Ame Theta is largest as we near expiraaon (Ame decay speeds up) Largest ATM; smaller as we move ITM or OTM 18

19 Examples of the Greeks Delta (Δ): GOOG = $364. The delta of the ITM $350 call = 0.63 and the OTM $380 call = If I buy one $350 call for $32.60 and the price of GOOG increases by $5, my opaon will be selling for $35.75, a 9.7% increase. If I buy one $380 call for $16.50 and the price of GOOG increases by $5, my opaon will be selling for $18.65, a 13% increase. Buying opaons with higher Δ gives you closer to a dollar for dollar move in your opaon price with the stock price, but they cost more because they have more intrinsic value. Gamma (γ): GOOG = $364. The gamma of the Nov $360 call = and the Jan $360 call = If GOOG increases in price by $1, the delta for the Nov $360 call will increase from to and the delta for the Jan $360 call will increase from to Larger values of γ warn you of increasing price sensiavity. γ is largest ATM and close to expiraaon. 19

20 Examples of the Greeks Vega (V): GOOG = $364. The Nov $360 call = $25.30 and V = and the Jan $360 call = $40.20 and V = IV increases by 10 percentage points. My Nov $360 call is now worth $29.41, up 16%, and the Jan $360 call is worth $47.10, up 17%. Vega is largest ATM and vega increases with Ame. If I buy opaons and IV increases, my opaons will be worth more, and my longer term opaons will increase the most. Theta (θ): GOOG =$364. The Nov $360 call = $25.30 and theta = If everything else stays constant, this call will be worth $24.89 tomorrow. Tomorrow s theta will be larger. Theta for an individual opaon is always negaave and it becomes larger as we near expiraaon. Each day I own an opaon and the price doesn t move, I lose money due to Ame decay, and the loss increases each day. 20

21 How Do We Use the Greeks? 1. Compare two candidates for a trade: Delta = 100 means our posiaon is equivalent to owning 100 shares; larger posiave values indicate the trade is more bullish (larger negaave delta = more bearish). Vega: large values indicate our trade is vulnerable to IV changes. Theta: negaave values indicate we are losing money while waiang for the expected price move, while posiave values indicate the posiaon is gaining in value as Ame passes. 2. Manage the trade use the Greeks to know when and how much to adjust or close the posiaon: Delta measures how bullish or bearish our posiaon is becoming; large posiave or negaave delta = higher price risk. Gamma tells you how quickly the posiaon can move against you. Vega measures our exposure to a move of IV in either direcaon. Theta: watch as you make adjustments to an income generaaon trade to be sure theta remains reasonably large and posiave. 21

22 Position Greeks IBM closed at $ on August 22, The Greeks: Sept $125 call: Δ = 0.507, V = 0.138, θ = Sept $130 call: Δ = , V = 0.102, θ = Oct $125 call: Δ = , V = 0.194, θ = The Greeks for a 5 contract Sept 125/130 bull call spread at a debit of $1025: Δ = 5 x 100 x ( ) = $145; bullish posiaon; a move of $1 up for IBM adds $145 in value to our posiaon, but the converse is also true! V = 5 x 100 x ( ) = $18; small IV dependence θ = 5 x 100 x ( ( )) = $8; negaave θ = Ame is our enemy; we will lose $8 overnight, but this number will become larger each day. By contrast, a 5 contract Sept Oct $125 call calendar at a debit of $1125: Δ = 5 x 100 x ( ) = $5; close to price neutral (delta neutral) V = 5 x 100 x ( ) = + $28; moderate IV dependence θ = 5 x 100 x ( ( )) = + $3; posiave θ = Ame is our friend. 22

23 Position Greeks in OptionsXpress From the PosiAons screen, click the Greeks link to get to the Greeks screen with both individual opaon Greeks and the overall posiaon Greeks 23

24 Using the Greeks To Manage a Position Screenshots provided courtesy of OpAoneAcs PlaAnum, 2011 all rights reserved RUT Aug 590/ /770 iron condor IniAated 7/2/08 for $3600 credit with RUT = $687 Δ = +$8 and θ = +$96; my rule: track posiaon delta for adjustments; and keep Δ <

25 Using the Greeks To Manage a Position Screenshots provided courtesy of OpAoneAcs PlaAnum, 2011 all rights reserved By 8/8/08 RUT has moved up strongly. Δ = $92 and θ = +$279 25

26 Using the Greeks To Manage a Position Screenshots provided courtesy of OpAoneAcs PlaAnum, 2011 all rights reserved 8/8/08 aker closing five call spreads to reduce risk. Δ = $67 and θ = +$226 26

27 Using the Greeks To Choose a Trade Screenshots provided courtesy of OpAoneAcs PlaAnum, 2011 all rights reserved On 9/12/08, we are considering two different trades. Which is be er? This risk graph is for the first trade under consideraaon, a RUT Oct/Nov $720 Call Calendar. 27

28 Using the Greeks To Choose a Trade Screenshots provided courtesy of OpAoneAcs PlaAnum, 2011 all rights reserved On 9/12/08, we are considering two different trades. Which is be er? This risk graph is for the second trade under consideraaon, a RUT Oct Iron Condor spread. At first blush, these trades have similar profit and loss potenaal, and broad BE ranges. 28

29 Using the Greeks To Choose a Trade Trade Max Profit Max Loss Δ γ V θ Calendar $5,000 $10, Condor $6,200 $13, The Risk/Reward raao is similar for each trade at about 2 to 1. Delta (Δ) is small for each posiaon; if the RUT index moves up by $1, our calendar will be worth $9 more and our condor will be worth $28 less. Gamma (γ) for both posiaons is small so we are not in a sensiave area where delta could change rapidly. Vega (V) is significant but opposite for each posiaon. The calendar will gain $369 in value with a one point increase in IV, or lose $369 with a one point decrease in IV. The condor also has a high sensiavity to IV, but opposite in nature. We check RUT s current IV and find it is 31.54% which is in the 99 th percenale of the past two years of IV data. Thus, it is far more likely IV will decrease than increase, favoring the condor trade. Theta (θ) is posiave and similar in magnitude for each trade, meaning we will make money with the passage of Ame (note that theta is a daily value, i.e., gaining $146 for the next day, but increasing for the following day). Therefore, I would favor the iron condor trade under these circumstances, primarily due to the much lower vega risk. 29

30 Using the Greeks To Manage a Trade We have two separate trades in this account, but it is difficult to see the two posiaons: 1) 5 contracts of a May/Jun $480 call and $450 put double calendar, and 2) 5 contracts of a May $360/$430 puts and $450/$520 calls iron bu erfly We could manage each trade separately, or we can use the Greeks to manage the enare account s posiaon. What is the risk described by each of the Greeks for this account? 30

31 Using the Greeks To Manage a Trade Price risk: if RUT moves up $10 tomorrow, our account balance will decrease by $1360 significant risk. VolaAlity risk: if IV decreases by one point tomorrow, our account balance will decrease by $84 very small risk. Time decay risk: all other things constant, our account will increase by $442 tomorrow very good. Conclusion: we need to adjust our posiaon to reduce the delta risk; more about adjustments in future classes. 31

32 Conclusions The price of an opaon is made up of: 1) intrinsic value, 2) Ame value, and 3) implied volaality. Implied volaality (IV) is a criacal foundaaonal concept in opaons trading; always know where IV is relaave to its history. Shiks in IV and volaality skews can be early warning signs of moves expected by the market. Increased IV suggests larger price moves are more likely, but it does not suggest a direcaon. IV is a criacal risk factor in some opaons strategies, but less so in others. For any opaon posiaon, we face risk from three areas: 1) a change in the price of the underlying stock or index 2) a change in volaality 3) the passage of Ame The Greeks allow us to separate and quanafy these three areas of risk. Use the posiaon Greeks of your trades to: 1) Evaluate the best candidate before placing the trade, and then 2) To manage the trade, e.g., monitor risk and trigger adjustments to the trade 32

33 Homework 1. What do we normally use the Black Scholes equaaon to calculate? 2. Explain the difference between historical volaality and implied volaality. 3. If the VIX is higher than it has been in the last 12 months, what does that tell me? 4. An opaon s price has three components. Name them and explain how they fluctuate in the market. 5. Define the Greeks: delta, gamma, vega, and theta. 6. What does it mean if my posiaon delta is +$105? 7. If IV is at historically high levels, would I want my posiaon vega to be posiave or negaave? Why? 8. When is theta posiave and when is it negaave? 9. If I own an ATM call opaon and the underlying stock price and IV remain unchanged, will my posiaon s value be increased, decreased, or unchanged? Why? 33