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OPTIONS STRATEGIES |
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Basic Option Theory
In, at and out-of-the-money
A call option is in-the-money when the underlying price is higher than the option's exercise price, and is out-of-the-money when the underlying price is lower than the option's exercise price. A put option is in-the-money when the underlying price is lower than the option's exercise price, and is out-of-the-money when the underlying price is higher than the option's exercise price. An option is at-the-money when the underlying price is equal to tKe option's exercise price. In practice the option with the exercise price nearest to the prevailing underlying price is called the at-the-money option.
Intrinsic and time value
The option price, or premium, can be considered as the sum of two specific elements: intrinsic value and time value.
Intrinsic value
The intrinsic value of an option is the amount an option holder can realise by exercising the option immediately. Intrinsic value is always positive or zero. An out-of-the-money option has zero intrinsic value.
Intrinsic value of in-the-money call option = underlying product price - strike price
Intrinsic value of in-the-money put option = strike price - underlying product price
Time value
The time value of an option is the value over and above intrinsic value that the market places on the option. It can be considered as the value of the continuing exposure to the movement in the underlying product price that the option provides. The price that the market puts on this time value depends on a number of factors: time to expiry, volatility of the underlying product price, risk free interest rates and expected dividends.
Time to expiry
Time has value, since the longer the option has to go until expiry, the more opportunity there is for the underlying price to move to a level such that the option becomes in-the-money. Generally, the longer the time to expiry, the higher the option's time value. As expiry approaches, the value of an option tends to zero, and the rate of time decay accelerates.
Volatility
The volatility of an option is a measure of the spread of the price movements of the underlying instrument. The more volatile the underlying instrument, the greater the time value of the option will be. This will mean greater uncertainty for the option seller who, will charge a high premium to compensate. Option prices increase as volatility rises and decrease as volatility falls.
Option sensitivities
Throughout this section, the strategy examples refer to market sensitivities of the options involved. These sensitivities are commonly referred to as the 'Greeks' and these are defined below.
Delta: measures the change in the option price for a given change in the price of the underlying and thus enables exposure to the underlying to be determined. The delta is between 0 and + 1 for calls and between 0 and -1 for puts (thus a call option with a delta of 0.5 will increase in price by 1 tick for every 2 tick increase in the underlying).
Gamma: measures the change in delta for a given change in the underlying. (e.g. if a call option has a delta of 0.5 and a gamma of 0.05. this indicates that the new delta will be 0.55 if the underlying price moves up by one full point and 0.45 if the underlying price moves down by one full point).
Theta: measures the effect of time decay on an option. As time passes, options will lose time value and the theta indicates the extent of this decay. Both call and put options are wasting assets and therefore have a negative theta. Note that the decay of options is nonlinear in that the rate of decay will accelerate as the option approaches expiry. As the table below illustrates, the theta will reach its highest value immediately before expiry.
Vega: measures the effect that a change in implied volatility has on an option's price. Both calls and puts will tend to increase in value as volatility increases. as this raises the probability that the option will move in-the-money. Both calls and puts will thus possess a positive vega.
Long Call
The trade: Buy a call with an exercise price of (A).
Market expectation: Market bullish volatility bullish. The more bullish the expectation, the further out-of-the-money (higher strike) the purchased call should be. A Long Call combines limited downside exposure with high gearing in a rising market.
Profit and loss characteristics at expiry:
Profit: Unlimited in a rising market.
Loss: Unlimited to the initial premium.
Break-even: Reached when the underlying rises above the strike price A, by the same amount as the premium paid to establish the position.
Delta: Increases towards + 1 as the underlying rises and the call moves in-the-money.
Gamma: Highest around the at-the-money level, particularly when the option is approaching expiry
Theta: Value of position will decrease as option loses time value.
Vega: Value of position will tend to rise if expected volatility increases. Vega will be highest the closer the underlying is to the strike. and the longer the time to maturity.
Short Call
The trade: Sell a call (A).
Market expectation: Market bearish/volatility bearish. Holder expects a gradual fall in the market and lower volatility. The optimal strike is dependent on time decay and vega level; although, in general, the more bearish the expectation, the greater the sold option should be in-the-money (lower strike) in order to maximise premium income. Profit is limited to the premium received and thus if the market view is more than moderately bearish, a Long Put may yield higher profits.
Profit & loss characteristics at expiry:
Profit: Unlimited to the premium received from selling the call.
Loss: Unlimited in a rising market.
Break-even: reached when the underlying rises above the strike price A, by the same amount as the premium received from selling call.
Delta: Decreases towards -1 as the underlying rises and the sold option moves in-the-money.
Gamma: Highest around the at-the-money level, particularly when the option is approaching expiry.
Theta: Value of position will increase as sold option loses time value.
Vega: Value of position will tend to fall if expected volatility increases. Vega will be highest the closer the underlying is to the strike and the longer the time to maturity.
Long Put
The trade: Buy a put (A).
Market expectation: Market bearish/volatility bullish. The more bearish the expectation, the further out-of-the-money (lower strike) the purchased put should be. A Long Put combines limited upside exposure with high gearing in a falling market.
Profit and loss characteristics at expiry:
Profit: Effectively unlimited in a falling market.
Loss: Limited to the initial premium paid.
Break-even: Reached when the underlying falls below the strike price A by the same amount as the premium paid to establish the position.
Delta: Decreases towards -1 as the underlying falls and the option moves in-the-money.
Gamma: Highest around the at-the-money level, particularly when the option is approaching expiry.
Theta: Value of position will decrease as option loses time value.
Vega: Value of position will tend to increase if expected volatility increases. Vega will be highest the closer the underlying is to the strike. and the longer the time to maturity.
Short Put
The trade: Sell a put (A).
Market expectation: Market bullish/volatility bearish. Holder expects a gradual rise in the market with lower volatility. The optimal strike to be sold will be dependent on time decay and the vega level, although in general, the more bullish the view, the greater the sold option should be in-the-money (higher strike) in order to maximise premium income. Profit is limited to the premium received and thus if the market view is more than moderately bullish, a long call may yield higher profits.
Profit & loss characteristics at expiry:
Profit: Unlimited to the premium received from selling the put.
Loss: Unlimited in a falling market.
Break-even: Reached when the underlying falls below the strike price A by the same amount as the premium received from selling the put.
Delta: Increases towards + 1 as the underlying falls and the sold option moves in-the-money.
Gamma: Highest around at-the-money and approaching expiry.
Theta: Value of position will increase as sold option loses time value.
Vega: Value of position will decrease as expected volatility increases. Vega will be highest the closer the underlying is to the strike, and the longer the time to maturity.
Long Call Spread
The trade: Buy a call (A), sell call at higher strike (B).
Market expectation: Market bullish/volatility neutral. The spread has the advantage of being cheaper to establish than the purchase of a single call, as the premium received from the sold call reduces the overall cost. The spread offers a limited profit potential if the underlying rises and a limited loss if the underlying falls.
Profit and loss characteristics at expiry:
Profit: Limited to the difference between the two strikes minus net premium cost. Maximum profit occurs where the underlying rises to 1he level of the higher strike B or above.
Loss: Limited to any initial premium paid in establishing the position. Maximum loss occurs where the underlying falls to the level of the lower strike A or below.
Break-even: Reached when the underlying is .above strike A by the same amount as the net cost of establishing the position.
Delta: The highest level will be between the strikes AB. Below strike A or above strike B, the delta will tend to fall towards zero.
Gamma: Positive if underlying closer to strike A, negative if underlying closer to strike B, neutral if around midpoint A-B.
Theta: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around midpoint A-B.
Vega: Positive if underlying closer to strike A, negative if underlying closer to strike B. neutral if around midpoint of A-B. NB The long call spread and the short put spread create near identical positions.
Short Put Spread
The trade: Sell a put (B), buy put at a lower strike (A).
Market expectation: Market bullish/volatility neutral. The Short Put at B aims to take advantage of a bullish market and the premium gained affords some downside protection with a Long Put at A. The spread offers a limited profit potential if the underlying rises and a limited loss if the underlying falls.
Profit and loss characteristics at expiry:
Profit: Limited to the net premium credit. Maximum profit occurs where underlying rises to the level of the higher strike B or above.
Loss: Maximum loss occurs where the underlying falls to the level of the lower strike A or below.
Break-even: Reached when the underlying is below strike B by the same amount as the net credit of establishing the position.
Delta: The highest level will be between the strikes A-B. Below strike A or above strike B, the delta will tend to fall towards zero.
Gamma: Positive if underlying closer to strike A, negative if underlying closer to strike B, neutral if around midpoint of A-B.
Theta: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around midpoint of A-B.
Vega: Positive if underlying closer to strike A. negative if underlying closer to strike B. neutral if around midpoint of A-B.
Short Call Spread
The trade: Sell a call (A), buy caIl at higher strike (B).
Market expectation: Market bearish/volatility neutral. The Short Call at A aims to take advantage of a bearish market and the premium gained affords some upside protection with a Long Call at B. The spread offers a limited profit if the underlying falls and a limited loss exposure if the underlying rises.
Profit & loss characteristics at expiry:
Profit: Unlimited to the net premium credit. Maximum profit occurs where underlying falls to the level of the lower strike A or below.
Loss: Unlimited to the difference between the two strikes minus the net credit received in establishing the position. Maximum loss occurs where the underlying rises to the level of the higher strike B or above.
Break-even: Reached when the underlying is above strike price A by the same amount as the net credit of establishing the position.
Delta: The highest level will be between the strikes A-B. Below strike A or above strike B, the delta will tend to fall towards zero.
Gamma: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around midpoint of A-B.
Theta: Positive if underlying closer to strike A, negative if underlying closer to strike B, neutral if around midpoint of A-B.
Vega: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around midpoint of A-B.
NB: The Short call spread and the long put spread create near identical positions.
Long Put Spread
The trade: Buy a put (B), sell put at lower strike (A).
Market expectation: Market bearish/volatility neutral. The spread has the advantage of being cheaper to establish than the purchase of a single put, as the premium received from the sold put reduces the overall cost. The spread offers a limited loss exposure if the underlying rises, and a limited profit if the underlying falls.
Profit & loss characteristics at expiry:
Profit: Unlimited to the difference between the two strikes minus net premium cost. Maximum profit occurs where underlying falls to the level of the lower strike A or below.
Loss: Unlimited to the initial premium paid in establishing the position. Maximum loss occurs where the underlying rises to the level of the higher strike B or above.
Break-even: Reached when the underlying is below strike price B by the same amount as the net cost of establishing the position.
Delta: The highest level will be between the strikes A-B. Below strike A or above strike B, the delta will tend to fall towards zero.
Gamma: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around midpoint of A-B.
Theta: Positive if underlying closer to strike A, negative if underlying closer to strike B, neutral if around midpoint of A-B.
Vega: Negative if underlying closer to strike A, positive if underlying closer to strike B, neutral if around. midpoint of A-B.
Long Combo
The trade: Sell a call. (B), buy put at tower strike (A). Has same profile as synthetic split strike short future.
Market expectation: Market bearish/volatility neutral. The risk/reward profile is similar to that of a short future except that there is a plateau (A-B) over which there will be no change in profit/loss. The plateau makes this a more suitable trade than a short future if volatility expectations are uncertain.
Profit & loss characteristics at expiry:
Profit: Unlimited in a falling market.
Loss: Unlimited in a rising market.
Break-even: Depending on the strikes chosen, the position may yield a small premium cost or credit. If the position is established at a net cost, break-even will occur where the market falls below point A by the same amount. If the position is established at a credit, break even will occur where the market rises above point B by the same amount.
Delta: The further the position from A or S, B the nearer me delta will be towards-1.
Gamma: Positive at A, negative at B. neutral around midpoint of A-B.
Theta: Slightly negative at A, slightly positive at B. neutral around midpoint of A-B.
Vega: Slightly positive at A, slightly negative at B, neutral around midpoint of A-B.
Short Combo
The trade: Buy a call (B), sell put at lower strike (A). Same profile as synthetic split strike long future.
Market expectation: Market bullish/volatility neutral. The risk/reward profile is similar to that of a long future except that there is a plateau (A-B) in which there is no change in profit/loss. The plateau makes this a more suitable trade than a long future if volatility expectations are uncertain.
Profit & loss characteristics at expiry:
Profit: Unlimited in a rising market.
Loss: Unlimited in a falling market.
Break-even: Depending on the strikes chosen, establishing the position may yield a small premium cost or credit. If the position is created at a cost, break-even will occur where the market rises above point B by this amount. If the position is established at a credit. the break-even point will occur if the market falls below point A by the same amount.
Delta: The further the position is from A or B. the nearer the delta will move towards + 1.
Gamma: Negative at A, positive at B. neutral around midpoint of A-B.
Theta: Slightly positive at A, slightly negative at B, neutral around the mid point A-B.
Vega: Slightly negative at A, slightly positive at B, neutral around midpoint of A-B.
Long Straddle
The trade: Buy a put (A), buy call at same strike.
Market expectation: Market neutral volatility bullish. With the underlying at A and an unknown directional move or increase in volatility is anticipated.
Profit & loss characteristics at expiry:
Profit: Unlimited for an increase or decrease in the underlying.
Loss: Unlimited to the premium paid in establishing the position. Will be greatest if the underlying is at strike A at expiry.
Break-even: Reached if the underlying rises or falls from strike A by the same amount as the premium cost of establishing the position.
Delta: Neutral (assumed at-the-money position), becomes highly positive (negative) for large increases (decreases) in underlying. As a volatility trade, the position would be kept delta neutral with dynamic hedging until it is closed out or is altered to take account of a clear change of market direction.
Gamma: Highest when at-the-money and approaching expiry.
Theta: Value of position will decrease as the options lose time value. Theta may be positive if the position is far in-the-money and/or close to expiry.
Vega: Value of position will increase as expected volatility increases.
Short Straddle
The trade: Sell a put (A), sell call at same strike.
Market expectation: Market neutral volatility bearish. With the underlying at A and a period of low or decreasing volatility is anticipated, and the underlying is not expected to move dramatically.
Profit & loss characteristics at expiry:
Profit: Unlimited to the credit received from establishing the position. Highest if the market settles at A.
Loss: Unlimited for both an increase or decrease in the underlying.
Break-even: Reached if the underlying rises or falls from strike A by the same amount as the premium received from establishing the position.
Delta: Neutral (presumed at-the-money position), becomes highly negative (positive) for large increases (decreases) in the underlying. As a volatility trade, the position would be kept delta neutral with dynamic hedging until it is closed out or is altered to take account of a clear change of market direction.
Gamma: Highest when at-the-money and approaching expiry.
Theta: Value of position will increase as the options lose time value. Theta may be negative if the position is far out-of-the-money and or close to expiry.
Vega: Value of position will decrease as expected volatility increases.
Long Strangle
The trade: Buy a put (A), buy a call at higher strike (B).
Market expectation: Market neutral volatility bullish. The holder expects a major movement in the market but is unsure as to its direction. A larger directional move is needed than a straddle in order to yield a profit but if the market stagnates, losses will be less.
Profit & loss characteristics at expiry:
Profit: The profit potential is unlimited although a substantial directional movement is necessary to yield a profit for both a rise or fall in the underlying.
Loss: Occurs if the market is static; limited to the premium paid in establishing the position.
Break-even: Occurs if the market rises above the higher strike price at B by an amount equal to the cost of establishing the position, or if the market falls below the lower strike price at A by the amount equal to the cost of establishing the position.
Delta: Neutral: (presumed at-the-money position), becomes highly positive (negative) for large increases (decreases) in underlying.
Gamma: Will be highest at strikes A and B but will tend to decrease as the underlying falls or rises significantly.
Theta: Time decay will act against the holder of the position.
Vega: The position will increase in value as volatility rises.
NB: Whilst the expiry profile is similar to that of the Long Guts, the difference relates to premium outlay. With the Long Strangle strategy you are buying two out of-the-money options (with a Long Guts both options are in the-money).
Short Strangle
The trade: Sell a put (A), sell call at higher strike (B).
Market expectation: Direction neutral volatility bearish. The holder expects low volatility and no major directional move. More cautious than a straddle as profit potential divs a larger range although maximum potential profits will be lower.
Profit & loss characteristics at expiry:
Profit: Unlimited to the premium received. Will be highest if the underlying remains within the market level A-B.
Loss: Unlimited for a sharp move in the underlying in either direction. Break-even: reached if the underlying falls below strike A or rises above strike B by the same amount as the premium received in establishing the position.
Delta: Neutral (presumed at-the-money position), becomes highly negative (positive) for large increases (decreases) in the underlying.
Gamma: Highest at strikes A and B but will tend to decrease as the underlying falls or rises significantly.
Theta: Increase in value as options decay.
Vega: Value of position will decrease as volatility increases.
NB: Whilst the expiry profile is similar to that of the Long Guts, the difference relates to premium outlay. With the Long Strangle strategy you are selling two out of-the-money options (with a Long Guts both options are in the-money).
Long Butterfly
The trade: Buy put (or call) A, sell two puts (or calls) at higher strike B. buy put (or call) at an even higher strike C.
Market expectation: Direction neutral volatility bearish. In this case, the holder expects the underlying to remain around strike B, or it is felt that there will be a fall in implied volatility. Position is less risky than selling straddles or strangles as there is a limited downside exposure.
Profit & loss characteristics at expiry:
Profit: Maximum profit limited to the difference in strikes between A and B minus the net cost of establishing the position. Maximised at mid strike B (assuming A-B and B-C: are equal).
Loss: Maximum loss limited to the net cost of the position for either a rise or a fall in the underlying.
Break-even: Reached when the underlying is higher than A or lower than C by the cost of establishing the position.
Delta: Neutral (assuming an at-the-money position). Delta becomes more positive as underlying moves to A, negative as the underlying moves to C.
Gamma: Highest at or about strike B. Below strike A, or above strike C. the gamma will tend to decline. May become positive at greater distances from B.
Theta: Time decay will be negligible until the final month of the contract. Decay will benefit the holder between underlying levels A and C, being greatest at B. If the underlying moves outside this area, decay will act against holder.
Vega: Increased volatility will reduce the value of the position. Volatility may have a positive impact if the underlying is below A or above C by a sufficient margin.
Short Butterfly
The trade: Sell put (or call) A, buy lwo puts (or calls) B, sell put (or call) C.
Market expectation: Market neutral volatility bullish. In this case the holder expects a directional move in the underlying, or a rise in implied volatility.
Profit & loss characteristics at expiry:
Profit: Maximum profit is the net credit received in establishing the position and will occur if there is a sufficient directional move of the underlying, in either direction.
Loss: Unlimited to the difference in strikes between A and B, minus the net credit in establishing the position.
Break-even: Reached when the underlying is higher than A or lower than C by the credit received from establishing the position.
Delta: Neutral (assumed at-the-money spread). Delta becomes more positive as undert-0ng moves to C, negative as the underlying moves to A.
Gamma: Highest at or about strike B and will tend to decline as the market moves in either direction from this point. May become negative at greater distances from B.
Theta: Time decay will be negligible until the final month of the contract. Decay will act against the holder between underlying levels A and C, being greatest at B. If the underlying moves outside this area, decay will benefic the holder.
Vega: Increased volatility will increase the theoretical value of the position. Volatility may: have a negative impact if the underlying is below A or above C by a sufficient margin.
Long Calendar Spread
This is a time value trade (involving the sale and purchase of options with different expiry months) and as such cannot be adequately plotted in terms of its risk/reward profile.
The trade: Sell near put (call), buy far put (call) at same strike.
Market expectation: Direction neutral volatility bullish. The near term option decays faster than the longer dated option, therefore the trade benefits from an increase in volatility.
Profit and loss characteristics at expiry (of near term option):
The potential profit in a time value trade is derived from the time decay characteristics of options (see the description of Theta in the introduction). The near, written put (call) will decay at a rate faster than that of the far, purchased put (call) as it approaches expiry and it is this differential in the rate of time decay which may yield a profit. Assuming the options are at-the-money and the market remains at this level, the sold option will expire worthless and the purchased option, although not possessing intrinsic value, will hold time value. As the initial position is established at a loss (because the far option will command a higher premium), to yield a profit, the time value of the long option after the expiry of the short dated option must be such that its value is greater than the initial cost of establishing the position.
Long Jelly Roll
This is a time value trade (involving the sale and purchase of options with different expiry months) and as such cannot be adequately plotted in terms of its risk/reward profile.
The trade: Buy put, sell call at same strike price in near expiry month, sell put, buy call at same strike in far expiry month (the strike price . in the far expiry need not be equal to the strike price in the near expiry). This trade is only valid for FTSE 100 Index option contracts.
Market expectation: Direction neutral volatility neutral. This trade consists of a short synthetic underlying in the near month and a long synthetic underlying in the far month. The holder will benefit if the differential between the futures price of the two expires (or the cost of carry differential in the case of premium up front options) widens.
Profit & loss characteristics at expiry (of near synthetic):
The potential profit of this trade is restricted as it arises from a widening of the futures price differential of the expiry months in question. After the expiry of the near term options, the holder is left with a long synthetic underlying position. The holder will therefore benefit from a rising market after the first expiry, and will be adversely affected by a falling market after the first expiry.
Long Box
The trade: Buy a call and sell a put, buy a put and sell a call and at a higher strike. All four options should have the same expiry date.
Market expectation: Direction neutral volatility neutral. This is a 'Locked trade', and hence its value is wholly independent of the price of the underlying. Where the synthetic long underlying price at one strike is trading at a lower price than the synthetic short underlying at me higher strike, such that the differential may be exploited.
Profit and loss characteristics at expiry:
If the pricing differential can be exploited, a profit will occur, the extent of the mis-pricing translating into the level of profit realised. The Box is regularly used by traders to close out positions near expiry. Generally traded at par (zero) for options on futures, and at the net cost of carry for index and equity options. Can be problematic if all positions are not closed out at exactly the same time.
Market sensitivities at 30 days to expiry:
As this is a form of arbitrage and profit is therefore independent of changes in the underlying, the value of the position will be independent of .the market.
Delta: Neutral
Gamma: Neutral
Theta: Neutral
Vega: Neutral: put call parity ensures that implied volatility will be exactly the same for both a call and a put with the same strike and expiry. NB: A Box is simply a conversion at one exercise price and a reversal at a different exercise price.
Long Two by One Ratio Call Spread
The trade: Sell a call (A), buy 2 calls at higher strike (B).
Market expectation: Market bullish/volatility bullish. Holder expects the market to settle above B. The position is usually established by selling an at-the-money or close to at-the-money call (A), and buying two out-of-the-money calls (B), such that it can be established at a small net credit. Depending on the strikes chosen, the position could also be established at break-even or at a small premium cost.
Profit & loss characteristics at expiry:
Profit: Unlimited if underlying rallies. At A or below, profit limited to net credit.
Loss: Greatest loss occurs at higher strike B, and is the difference between strikes B-A, minus (plus) net credit (debit).
Break-even: Lower break-even point is reached when the underlying exceeds the lower strike option A by the same amount as the net credit received (if initial position established at a net cost, there is no lower break-even point). Higher break-even point reached when intrinsic value of option A, is equal to the combined intrinsic value of the two higher strike options B, plus (minus) the net credit (debit).
Market sensitivities at 30 days to expiry:
Delta: Increases towards + 1 as underlying rises. If, approaching expiry, the underlying is around strike A, the delta may become negative.
Gamma: Highest at B and declines as the underlying rises above B. If approaching expiry, the underlying is around strike A, the gamma may become negative.
Theta: Value of position will decrease as the bought options are affected by time decay. However, if the underlying remains below, or around strike A, the theta may become positive.
Vega: Value of position will increase as implied volatility increases. However, if approaching expiry, the underlying is around strike A, the vega may become negative.
Short Two by One Ratio Call Spread
The trade: Buy a call (A), sell 2 calls at higher strike (B).
Market expectation: Market neutral volatility bearish. Holder expects that the market will not rally but will settle around point B. Position usually established by buying an at or close to-the-money call, and selling two out-of-the-money calls such that although it is a net short position, it may be established at a small cost (as in the above example). Depending on the strikes chosen, the position could also be established at break-even or at a small credit.
Profit & loss characteristics at expiry:
Profit: Greatest profit occurs at higher strike B which is the difference between strikes B-A plus (minus) net credit (debit).
Loss: Unlimited if underlying rallies. At A or below, loss limited to net cost.
Break-even: Lower break-even reached when the underlying exceeds the lower strike option A, by the same amount as the net cost of the position (if initial position established at a net credit, there is no lower break-even point). Higher break-even point reached when intrinsic value of option A, plus (minus) the net credit (debit) from establishing the position, is equal to the combine;l intrinsic value of the two higher strike options B.
Market sensitivities at 30 days to expiry:
Delta: Approaches -1 as the underlying rises. If, approaching expiry, the underlying is around strike A, the delta may become positive.
Gamma: Highest at point B and declines as the underlying rises above B. If, approaching expiry, underlying is around strike A, it may become positive.
Theta: Value of position will increase as the short options are affected by time decay. If, the underlying remains below, or around strike A, the theta may become positive.
Vega: Value of position will decrease as implied volatility increases. If, approaching expiry, the underlying is around strike A and the vega may become positive.
Long Two by One Ratio Put Spread
The trade: Sell a put (B), buy two puts at lower strike (A).
Market expectation: Market bearish/volatility bullish. Holder expects market to fall below A. Position usually established by selling an at or close to the money put (B), and buying two out-of-the-money puts (A), such that although it is a net long position, it can be established at a small credit as in the above example. Depending on the strikes chosen, the position could also be established at breakeven or at a small premium cost.
Profit & loss characteristics at expiry:
Profit: Unlimited in a falling market. At B or above, profit limited to net credit.
Loss: Greatest loss which occurs at lower strike A, is the' difference between strikes B-A minus (plus) net credit (debit)
Break-even: Lower break-even reached when the combined intrinsic value of the two purchased puts at A, plus (minus) the initial credit (debit) from establishing the position, are equal to the value of the written put B. Higher break-even point reached when intrinsic value of option B is equal to initial credit. If initial position established at a net cost, there is no higher break-even point.
Market sensitivities at 30 days to expiry:
Delta: Approaches -1 as underlying falls. If approaching expiry, the underlying is around strike A and the delta may become positive.
Gamma: Highest at A and declines as the underlying falls below this point. If approaching expiry, the underlying is at B, the gamma may become negative.
Theta: Value of position will decrease as the long options are affected by time decay. If the underlying remains above, or around strike B, the theta may become positive.
Vega: Value of position will increase as implied volatility increases. If, approaching expiry, the underlying is around strike B and the vega may become negative.
Short Two by One Ratio Put Spread
The trade: Buy a put (B), sell two puts at lower strike (A).
Market expectation: Market neutral volatility bearish. Holder expects market to settle around strike A and feels that the market will not fall below A. Usually established by buying an at -the-money or close-to at-the-money put (B) and selling two out-of-the-money puts (A) such that it is established at a small cost. Depending on the strikes chosen, the position could also be established at break-even or at a small premium credit.
Profit & loss characteristics at expiry:
Profit: Greatest at A, it is the difference between strikes A-B plus (minus) net credit (debit).
Loss: Unlimited in a falling market. At B or above, loss limited to net cost.
Break-even: Lower break-even point is reached when the combined intrinsic value of the options at A equals the intrinsic value of option A, plus (minus) the net credit (debit) from establishing the position. Higher break-even point reached when intrinsic value of option A, is equal to the debit from establishing the position.
Market sensitivities at 30 days to expiry:
Delta: Increases towards + 1 as market falls. If however, approaching expiry, the underlying is around strike A, and the delta may become negative.
Gamma: Highest at point A and declines as underlying falls below A, If approaching expiry, the underlying is at B and the gamma may become positive.
Theta: Value of position will increase, as short options are affected by time decay. If however, the underlying remains above or around strike B, the theta may become negative.
Vega: Value of position will decrease as implied volatility increases. If however, approaching expiry, the underlying is at B and the Vega may become positive.
Long Call Ladder
The trade: Buy a call (A), sell call at higher strike (B), sell call at an even higher strike (C).
Market expectation: Direction bearish/volatility bearish. In this case the holder expects the market to settle between Band C but feels mat volatility will not rise.
Profit & loss characteristics at expiry:
Profit: Limited to the difference between strikes A and B plus (minus) net credit (debit). Greatest profit occurs between strikes Band C.
Loss: Unlimited if underlying rallies. At A or below, loss limited to net cost.
Break-even: Lower break-even reached when the underlying exceeds the lower strike option A. by the same amount as the net cost of the position. Higher break-even point reached when the intrinsic value of option A, plus (minus) the net credit (debit) from establishing the position, is equal to the intrinsic value of the two higher strike options at Band C.
Market sensitivities at 30 days to expiry:
Delta: Approaches -1 as underlying rises. If, approaching expiry, the underlying is around strike A, the delta becomes positive.
Gamma: Usually negative. Highest between B and C. If, approaching expiry, the underlying is around strike A and the gamma becomes positive.
Theta: Value of position will increase as the short options are affected by time decay. If the underlying remains below or around strike A, theta becomes slightly negative.
Vega: Value of position will decrease as implied volatility increases. If approaching expiry, the underlying is around strike A and the vega may become positive.
Short Call Ladder
The trade: Sell a call (A), buy call at higher strike (B), buy call at an even higher strike (C).
Market expectation: Direction bullish/volatility bullish. Holder expects a substantial rise in the underlying market.
Profit & loss characteristics at expiry:
Profit: Unlimited if underlying rallies. At A or below, profit limited to net credit.
Loss: Limited to the difference between strikes A and B minus (plus) net credit (cost).
Break-even: Lower break-even reached when the underlying exceeds the lower strike option A by the same amount as the net credit received, (if initial position established at a net cost, there is no lower break-even point). Higher break-even point reached when intrinsic value of option A, is equal to the intrinsic value of the two higher strike options at Band C, plus (minus) the net credit (debit) in establishing the position.
Market sensitivities at 30 days to expiry:
Delta: Increases towards + 1 as underlying rises. If, approaching expiry, the underlying is around strike A, the delta becomes negative.
Gamma: Highest between strikes Band C. If, approaching expiry, the underlying is around strike A, the gamma becomes negative.
Theta: Value of position will decrease as the long options decay. If the underlying remains below or around strike A, theta becomes slightly positive.
Vega: Value of position will increase as implied volatility increases. If approaching expiry, the underlying is around strike A, the vega may becu1l1e slightly negative.
Long Put Ladder
The trade: Sell put (A), sell put at higher strike (B), buy put at an even higher strike (C).
Market expectation: Direction bullish/volatility bearish. Holder expects underlying to (continue to) be between strikes A and Band firmly believes that the market will not fall.
Profit & loss characteristics at expiry:
Profit: Limited to the difference B-C, plus (minus) net credit (debit). Maximised between strikes A and B.
Loss: Unlimited if underlying falls. At C or above, loss limited to net cost of position.
Break-even: Lower break-even reached when the intrinsic value of the purchased put C plus (minus) net credit (cost) is equal to the intrinsic value of the sold options A and B. Higher break-even reached when underlying falls below strike C by the same as the net cost of the position.
Market sensitivities at 30 days to expiry:
Delta: Positive. However, becomes negative if the underlying is around strike C approaching expiry.
Gamma: Highest between A and B. if however, approaching expiry, the underlying is at C. the gamma becomes positive.
Theta: Positive; value of position will increase as short options decay. If however, approaching expiry, the underlying is above or around C, theta may become slightly negative.
Vega: Negative; value of position will decrease as implied volatility increases. If however, approaching expiry, the underlying is at C, the vega may become slightly positive.
Short Put Ladder
The trade: Buy put (A), buy put at higher strike (B), sell put at equally higher strike (C).
Market expectation: Direction bearish/volatility bullish. Buyer expects a volatile market and additional profits can be made in a bearish market
Profit & loss characteristics at expiry:
Profit: Unlimited if underlying falls. At C or above, profit limited to the net credit
Loss: Limited to the difference between Band C minus (plus) net credit (debit).
Break-even: Higher break-even reached when the market falls below C by the value of the net credit Lower break-even reached when the intrinsic value of options A and B plus (minus) the net credit (debit) is equal to the intrinsic value of C.
Market sensitivities at 30 days to 'expiry:
Delta: Approaches -1 as underlying falls. If however, approaching expiry, the underlying is around strike B or C, the delta may become positive.
Gamma: Maximum between points A and B. However, if approaching expiry, the underlying is at C, the gamma may become negative.
Theta: Value of position will decrease as long options are affected by time decay. If however, the underlying is above, or about C, the theta may become positive.
Vega: Value of position will increase as implied volatility increases. If however, approaching expiry, the underlying is around C. the vega may become negative.
Long Volatility Trade
The trade: Buy puts and buy underlying or buy calls and sell underlying to give zero net delta. The position is dynamic in that as the underlying moves and the delta changes, additional futures must be bought or sold to maintain delta neutrality. For stock contingent trades, the "underlying" leg will comprise the underlying shares rather than the futures contract.
Market expectation: Market neutral volatility bullish. This position is a pure trade on volatility such that an increase in implied volatility will benefit the holder.
Profit & loss characteristics at expiry:
Profit: Dependent on an increase in implied volatility as well as any profits from the future hedge and hedge rebalancing.
Loss: Limited to the costs of establishing the position plus any loss in rebalancing the hedge.
Break-even:
(i) For a long put, long futures position, if the price of the underlying increases, break-even is obtained where the gain in the value of the futures position (less the initial premium and less the rebalancing cost) is equal to zero. If price falls, break-even is obtained where the loss on the futures position (less the intrinsic value of the put. plus/minus the rebalancing cost) is equal to zero.
(ii) For a long call, short futures position, if the underlying price increases, break-even is obtained where the gain in the call (less the loss in the future, plus/minus the rebalancing cost) is equal to zero. If price falls break-even is obtained where the gain on the futures (minus the loss on the call. plus/minus the re-balancing cost) is equal to zero.
Delta: Neutral.
Gamma: Positive the delta neutral position is highly sensitive to movement in the underlying, consequently the position requires dynamic hedging.
Theta: Value of position will decrease as options decay.
Vega: Value of position will increase as expected volatility increases.
Short Volatility Trade
The trade: Sell puts and sell underlying or sell calls and buy underlying to give zero net delta. The position is dynamic in that as the underlying moves and the delta changes, additional futures must be bought or sold to maintain delta neutrality. For stock contingent trades, the "underlying" leg will comprise the underlying shares rather than the futures contract.
Market expectation: Market neutral volatility bearish. The position is a trade on volatility such that a decrease in implied volatility will benefit the holder.
Profit & loss characteristics at expiry:
Profit: Limited to the credit received from the sold options and any profit on rebalancing the hedge.
Loss: The more implied volatility rises, the greater will be the potential losses.
Break-even:
(i) For a short put, short futures position, if the underlying price increases, break-even is obtained where the initial premium on the put, minus the loss on the futures, plus/minus the rebalancing cost, is equal to zero. If price falls, the gain on the futures position, minus the loss on the put, plus/minus the rebalancing cost is equal to zero.
(ii) For a short call, long futures position, if the underlying price rises, beak-even is obtained where the gain on the futures minus the loss on the call, plus/minus the rebalancing cost, is equal to zero. If price falls, break-even is obtained where the call premium, minus the loss on the futures, plus/minus the rebalancing cost, is equal to zero.
Delta: Neutral.
Gamma: Negative the delta neutral position is highly sensitive to movements in the underlying, consequently the position requires dynamic hedging.
Theta: Value of position will increase as the options decay.
Vega: Value of position will decrease as expected volatility increases.
Conversion/Reversal
The trade: Conversion: Sell call, buy put at same strike, buy underlying- Reversal: Buy call, sell put at same strike, sell underlying.
Market expectation: Direction neutral volatility neutral. A Conversion or Reversal is a 'locked trade' and hence its value is wholly independent of the price of the underlying. The options position in a Conversion will create a synthetic short underlying and potential profit/loss will result from any pricing differential between this and the long underlying position. The options position within a Reversal will create a synthetic long underlying and so profit/loss realised will be fixed to the difference between the price of the short underlying and the long synthetic underlying
Profit and loss characteristics at expiry: If the pricing differential can be exploited, a profit will occur. The extent of the mis-pricing between the underlying and synthetic underlying positions will translate into the level of profit realised.
As this 15 a form of arbitrage and profit is therefore independent of changes in the underlying, the positions value will be independent of the market, hence:
Delta: Neutral
Gamma: Neutral
Theta: Neutral
Vega: Neutral; put/call parity ensures that implied volatility must be the same for both a call and a put with the same strike and expiry.
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