Option Volatility and Pricing - Natenberg

Ch1

• Options futures are settled like stock, so they are unrealized gains / losses until position closes.  This is in contrast to futures, which are settled at the eod where all gains / losses are realized and deposited into each person's acct.
• Modelling 
• Time to expiration
• For volatility purposes we're only interested in trading days
• For interest rate purposes we must include every day
• Price of Underlying
• Use the price which will establish a hedge in the underlying. 
• Sell calls / buy puts use the ask
• Buy calls / sell puts use the bid (long delta offset against short delta)
• Interest Rates
• With stock type settlement - higher interest rate lowers value of option
• Higher interest raises stock price, but also increase carrying cost, which lowers value of option
• If you have 60 days until expiration, use 60 day t bill, find the appropriate t-bill that matches the option expiration
• Dividends
• If dividend is delayed, call options increase in value, puts decrease
• Volatility
• Daily STD - 256 trading days / year, so divide annual volatility by 16 to get the 1std of daily returns.  Ie: if 20% volatility, one would expect < 1.25% or less daily price change 2 / 3 days, and < 2.5% 19/20 days (2 std)
• Weekly STD - 52 weeks / year, so divide by 7.2.  20%/7.2  = < 2.75% for every 2/3 weeks
• Option Characteristics
• Delta is also approximately the % that option will finish in the money.  It's also the hedge ratio against the underlying
• For contracts w/ longer expiration the ATM 50 delta option will not always be the one closest to the current price, but the price * interest rate
• Gamma is directional risk
• ATM have highest gamma
• Theta is time decay
• gamma and theta have opposite signs and are negatively correlated.  the market will either move (gamma) or stay still (theta)
• Vega of all options decline as expiration approaches, so long term options are always more sensitive to vega than short term
• These greeks help you identify risks to make good decisions, not remove risk.  A trader that over analyzes these greeks will suffer analysis through paralysis and will be unable to make money.  The point is to find out which risks are acceptable and which are not.
• Spreads
• Volatility spreads should be constructed so that they are almost delta neutral
• these are concerned primarily with the magnitude of movement in the underlying, not the direction
• volatility consideration should always be more important than delta consideration, if not, the trade is not a volatility spread
• Spreads which are helped by movement in the underlying have positive gamma, and hurt by movement have negative gamma
• positive gamma is said to be long premium and hoping for a volatile market with large moves in the underlying
• negative gamma  is short premium
• any positive gamma trade will have a negative theta, and vice versa
• Spreads helped by rise in volatility have positive vega
• Every volatility spread can be placed in 4 categories

Category	Gamma	Vega
Backspread	Positive	Positive
Ratio Vertical Spread	Negative	Negative
Long Time Spread	Negative	Positive
Short Time Spread	Positive	Negative

• if IV is high, look for spreads with negative vega, if IV is low look for spreads with positive vega
• long time spreads are likely to be profitable when IV is low but expected to rise, short time spreads is opposite
• Adjustments
• adjust at regular intervals - adjust based on your volatility estimate, ie: daily volatility estimate, require daily adjustments
• adjust at predetermined delta - if you're willing to take directional risk, allow for delta up to a certain point
• adjust by feel - if the position's gamma will put you at a certain level of delta at a particular price level(positive delta at support), and you're correct, you will have saved yourself an unprofitable adjustment
• Risk Adjustments - which risks are you comfortable with?
• Theoretical Edge is what you determine to be the correct value for the option greeks.
• Delta Risk - risk that underlying will move in one direction over the other
• neutral position doesn't eliminate all risk, but it is immune to directional risk in a limited range
• Gamma Risk - risk of a large move in the underlying.  
• negative gamma position can quickly lose its theoretical edge with a large move in the underlying contract.  the consequence of this move must always be evaluated when analyzing each position
• Theta Risk -risk that time passes w/ no movment. 
• if you have positive gamma, how long can you wait before the theoretical edge disappears.  If the movement fails to appear in 1 day, 1 week, ect...does that negate the edge?
• Vega Risk - risk that volatility entered into model is incorrect
• vega is a risk present in every position, how much can volatility move before the potential profit from a position disappears
• Rho risk - risk that interest rate changes over the life of the option

Options For beginners and Beyond
Ch4 Greeks

• Delta - amount options moves from $1 move in underlying
• Gamma - amount delta changes for $1 move in underlying
• Theta - time decay of options in $
• Vega - amount option price moves for a 1 unit (ie: 1%) change in implied volatility
• Rho - amount option changes based on 1 unit(ie: 1%) change interest rate

Ch 9

• Trade with the trend.  Make sure stock has resumed its trend before entering again

Ch14 Volatility

• No matter how much the underlying moves, volatility always fluctuated from 5% to 20% for deutschemarks over a 10 year period, w/ an equilibrium of 11%
• Volatility Cone plots volatility over an X day period showing graphing the high and low as std during those periods
• Volatility of consecutive periods (ie: 15% 4weeks) tends to be correlated with the next 4 week period (next 4 weeks will be close to 15%)
• How to forecast
• What is long term volatility of underlying?
• What is the recent historical volatility in relation to mean volatility?
• What is the recent trend in historical volatility?
• Where is IV and what is it's trend?
• Are we dealing w/ short or long term options?
• How stable does the volatility tend to be?
• ie: 10 weeks to expiration => look at 50d (10w) historical volatility (20.6%), it is higher than long term mean (18.6%).  IV is declining and at (22.1%) => short volatility position makes sense
• if volatility cone shows that 10% HV is common range, a less risk strategy should be chosen
• Short term contracts are more likely to have larger swings in their IV compared to longer term contracts.  When IV contracts or expands, it is more noticeable in the short term contracts
• 
  

Option Strategies

• Debit spreads 
• are medium to long term trades
• you want to use options with expiration months that allow enough time for this move to occur
• Credit Spreads
• typically short term where you want to capture the credit as soon as reasonable possibly
• Conditions of a good credit spread
• Extra premium has been pumped into the side being sold
• Underlying stock needs little or no movement to achieve maximum profit
• both of the above achieved with front month options
• Look for 1 time events but wait until dust settles and premium still higher than before,  then initiate spread with short leg near the price extreme => look for roughly equal reward to max risk
• early Feb, RMBS, royalty fees, big drop, price stabilized at support, sell mar 22.5 / buy mar 25, for 1.25 credit and 1.25 risk
• early Feb DIS, hostile takeover by comcast for $27, price shot up to $28, then stabilized at $27 2 days later, it would be rejected unless comcast raised offer.  Sell Mar 27.5 / buy 30, 1.3 credit  / 1.20 max loss
• Mid apr, fell after good eps on high volume to $34 before stabilizing.  May Sell 35 / buy 32.50, credit 1.2 / 1.2 max loss
• avoid situations where it will be a continuing saga, as in accounting irregularities or possible restatement of earnings
• Put IV is higher lower in the chain, so makes bull put spreads less lucrative
• Calendar Spreads
• good for stable stocks that will move less than 15% over a month
• primary feature of calendars is to roll a new option every month for the front month short leg
• at least 1 month expiration difference so you can roll once
• use calls for expected upward drift, puts for expected downward drift
• exit the trade if you're taking a 50% loss, roll or close if you've achieved 50% of the gain
• IV is the most important characteristic of calendar spreads
• volatility skew - short option IV is larger than long option IV
• % increase in IV of short option compared to that of the long option
• 10% - 25% is ideal range, avoid IV skews > 30% esp when both have high IV
• early may XYZ is $17.  $17.50 Jun IV is 49, Jan IV is 41 = (49/41)  = 19.5% skew.  Buy Jan 17.5 for $2.10, sell Jun 17.5 for $1.15,$125 max gain /  max risk is $95
• Deep ITM Put Calendars - Expect stock to rise over time
• Buy 1 Leap (21 - 24months) w/ strike well above current price and sell nearer term Leap(9 to 12months) with same strike
• Both will be nearly the same price, thus making the cost low and offer substantial leverage.  As near month expires worthless, you can close immediately for max profit
• if all time values disappears and open interest is low, you might get assigned.
• sell the stock assigned to you and resell the same put option simultaneously, as 1 transaction.  
• Diagonal Spreads
• works best when the 2 strikes are no more than $2.50 apart because it keeps the maximum risk on the trade at a reasonable level, which restricts this trade to low / medium priced stocks, or indices
• Covered Call
• Focus on the stock price, and to a much lesser extent the option price.  Decide on an appropriate stop loss for the stock, and protect if it goes below by closing the option and stock
• Decide on the strike price at  a level where you are actually willing to sell the stock
• Choose 1 or 2 months out, do not go too far
• If you're going to get assigned, just accept the loss, don't buy back the call for a loss
• Straddles/Strangle - long call / long put
• Price between $20 - $50, if cheaper than $20, might not be enough room to fall, if above $50 options may be too expensive to create a straddle with good profit potential
• Identify an event.  EPS, court decision, FDA rulings
• Event is 30 to 60 days away.  Options do not expire until at least 30 days after the event.  So you're looking at least 60 to 90 days until expiration
• Upcoming event should not have already generated interest, open interest / trading volume should be normal.  IV vs HV should also be normal
• Look for a stock within a narrow trading range.  When it does breakout the option price will gain extra time value
• Exiting:
• Sometimes better to exit 1 side before the event.
• Don't stay in the straddle much longer after the event, sell the profitable option before time value decreases
• Never hold both sides of straddle until expiration.  Exit with 3 to 4 weeks before expiration
• Stock Repair
• buy 1 ATM call for each 100 shares, then sell 2 OTM calls
• only works if stock price rebounds
• example: stock declines from $35 to $23 by March
• L Jun 25 C for $3.30 / S 2 Jun 30 C for 1.75 => credit of $.20
• this creates a covered call w/ a bull call spread
• if stock closes at $30 by expiration you will have made $35
• to open for a credit, you need about 2 months until expiration
• Stock enhancement
• buy 100 shares at $58, holding for $75 target, starting in Mar
• L Jan 70 C for $3.70, S 2 Jan 75 C for $2.50 => credit of $1.30
• if stock is above $75, you will have generated equivalent of $81
• you can do also replace stock above w/ 1 Jan 40 call, for $19.70
• Collar
• stocks you intend to hold minimum 10 months
• example: nov 2004, you buy XYZ at $19 and plan to hold at least 1 year
• Buy 1 Jan 20 put for $2.90, Sell 1 Jan 25 call for $1
• max loss is $90(-4.3%), max gain is 17%
• enhanced if stock pays dividend
• if at a loss, it is possible to close early, however max gain you must wait until expiration
• used on conservative, non-volatile stocks
• Synthetic
• Long Stock - L 1 ATM Call, and S 1 ATM Put
• S Deep ITM Put will have delta close to +1, and substitute as L stock
• slightly higher probability of early assignment than call, because less time value
• S Deep ITM Call will have delta close to -1, and substitute as S stock
• BackSpreads
• only used when stock will move big, a small move generates a maximum loss
• example: in Feb XYZ is at $19, and you think it can go to $35 in the next year
• L 2 Jan 22.5 C $1.70, sell 1 Jan 20 call at $2.80.  Cost $60, max risk $310
• Butterfly
• focuses on a narrow range of profitability, but used when price is trending towards a target
• Ex: July, XYZ trading for $30, setup butterfly at $35 w/ 1 L Nov 30 P .80 / 2 S Nov 35 P $4.60, max profit at $35
• Adjustments can be made to take off the profitable S middle leg and leave on the L outer legs for a subsequent move in the opposite direction
• if price went up to $38 by late sept, you could sell the Nov 35 puts for $1, and collect $3.60 then hold the puts for a move down
• Iron Condor
• Use options that expire in 1 - 2 months
• No need to let trade get to worst case scenario
• Ex: Late December stock trading for $56, open 60 / 65, 40 / 45 iron condor, for $185, max loss $500
• if stock falls below 48 or above 62, close the trade for $100 loss.
• Double Diagonal
• You can roll the short legs once in this set to create additional profit
• No need to let trade get to worst case scenario
• Ex:Late December stock trading for $56, open Feb 60 / March 65, 40March  / 45 Feb double diagonal, for $150 profit, max loss $400
• if stock is below $48 or above $63 close for a $100 loss
• if price moves up to $60 or down to $50, the short feb options can be rolled to march options
• or feb 60 calls can be rolled up to 65, or feb 50 puts can be rolled down to feb 45 puts to create calendar spreads
• Vertical Spreads - used mainly for directional trades
• A vertical spread will always maintain its delta position, any time you buy the lower strike and sell the higher strike, you create a bullish (positive delta position). 
• The greater the distance, the greater the delta
• If IV is too low, vertical spreads should focus on purchasing the at the money option
• if IV is too high, vertical spreads should focus on selling the at the money option
• The focus is mainly on the at the money option to buy / sell when the volatility is mispriced.  You can trade the OTM or ITM first, and then leg into the ATM portion (closest to 50 delta)
• Conversions / Reversals
• create syntheic long or short, and then go short or long the underlying
• Boxes
• Synthetic L lower and Synthetic S higher, at expiration it will be worth the difference of strike prices.  This entire box will be discounted according to the interest rate
• 
  

Strategies by type

• Neutral w/ Bearish Volatility
• Covered call
• Butterfly
• Condor
• Double Diagonal
• Collar
• Neutral w/ Bullish Volatility
• Straddle / Strangle
• Calendar
• Bearish
• Bear Call Spread (credit)
• Put Backspread
• Bullish
• Bull Put Spread(credit)
• Call Backspread

Risk To Reward

• Come up with graphs using a computer 
• Use the risk of greatest concern
• if volatility is the greatest concern choose vega
• position vega / theoretical price (price i believe options are worth) and compare the different strategies
• large move? look at delta
• if gamma is positive, don't need to include

Adjustments

• new traders should avoid adjustments which increase the size of their position
• if you want to remain risk neutral, buy or sell the underlying contract to adjust the delta of the position
• if you use options, the remaining greeks will all also be adjusted, use them to get risk back to where you believe it should be while increasing your theoretical edge

Graphing

• x is price axis, y is profit axis
• Theoretical edge - After you input what you believe to be the correct volatility, the current price should have a positive PNL 
• Delta - at the current price, a positive delta will cross the current price w/ an upward slope
• the magnitude of the slope is the magnitude of the delta.  a delta neutral position will be flat across the current price
• Gamma - positive gamma will begin to bend upward as the price moves away from the current price in either direction, it will look convex like a smile
• Extreme moves - if the angle up or down at the edges of an extreme move are infinite, it acts like a naked position.  If it flattens out there are equal numbers
• Theta - as time passes positive theta will shift the graph up, while negative theta shifts down
• Positive Vega - as time passes positive vega shifts graph up while, negative shifts graph down