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Flashcards in Option strategies and synthetic positions Deck (22):
1

What are the basic synthetic positions?

There are six basic synthetic positions:

1. Synthetic Long Stock = Long Call + Short Put

2. Synthetic Short Stock = Short Call + Long Put

3. Synthetic Long Call = Long Stock + Long Put

4. Synthetic Short Call = Short Stock + Short Put

5. Synthetic Short Put = Short Call + Long Stock

6. Synthetic Long Put = Long Call + Short Stock

They can be thought of as a 'synthetic triangle' of CALL, PUT, and STOCK. A combination of two elements in the synthetic triangle creates a synthetic position of the third element.

This synthetic triangular relationship is governed by the principle of Put Call Parity (requires the extrinsic values (aka time value) of call and put options to be in equilibrium so as to prevent arbitrage).

In order for the synthetic triangle relationship to work, all options used together must be of the same expiration, strike and represent the same amount of shares used in combination.

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

If you want to find out the synthetic equivalent to a long put, just isolate that +P position:

S + P – C = 0

If that long put is paired with other assets so that it has no risk, then the other assets must be equal to a short put. This immediately shows that long stock (+S) plus a (-C) short call must be equal to a short put (-P).

S - C = - P

It turns out that no matter which asset you pick, the other two are the synthetic opposite and fully hedge the risk. It should make sense, then, that we could also pick any two assets and know that the third will fully hedge those two.

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Put Call Parity is a concept identified by Stoll in 1969, that defines the relationship that must exist in European call and put options. Put options, call options and their underlying stock forms an interrelated securities complex in which the combination of any 2 components yields the same profit/loss profile as the 3rd instrument. Under this kind of complex relationship, no combination of 2 components should yield a position with an asymmetric profit/loss profile as the 3rd instrument so that balance is maintained in the system. This balance is known as the Put Call Parity in option trading. The concept of Put Call Parity is especially important when trading synthetic positions ('synthetic triangle'). When there is a mispricing between an instrument and its synthetic position, an options arbitrage opportunity exists.

2

How to make a Synthetic Long Stock?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

1. Synthetic Long Stock = Long Call + Short Put

S = C - P

When you buy a stock, you are exposed to unlimited profits and unlimited losses while losing nothing when the stock remains stagnant. A synthetic long stock completely duplicates those characteristics. The premium gained from the short put covers the premium on the long call (thus losing nothing if the stock remains stagnant), the call option grants unlimited profits and the short put options introduced the unlimited loss (down to 0 on the stock value).

The principal differences are the smaller capital outlay, the time limitation imposed by the term of the options, and the absence of a stock owner's rights: voting and dividends.

Investor would be looking for an appreciation in the stock's price during the life of the options; the sharper, the better. Since the term of the strategy is limited, the stock's longer-term outlook isn't as critical. However, if the investor is bearish on the stock's longer-term future, it would require a careful pinpointing of the trends; when the stock will head up, and when it will go down. The difficulty of making such a precise forecast suggests that this would not be an optimal strategy for a bearish investor.

3

How to make a Synthetic Short Stock?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

2. Synthetic Short Stock = Short Call + Long Put

-S = P - C

When you short a stock, you are exposed to unlimited loss and unlimited profit while losing nothing when the stock remains stagnant. A synthetic short stock completely duplicates those characteristics. The premium gained from the short call covers the premium on the long put (thus losing nothing if the stock remains stagnant), the long put option grants unlimited profits and the short call options introduced the unlimited loss.

The principal differences are the time limitation imposed by the term of the options, the absence of the large initial cash inflow that a short sale would produce, but also the absence of the practical difficulties and obligations associated with short sales.

Investor would be looking for a decline in the stock's price during the term of the options.

Since the strategy's term is limited, the longer-term outlook for the stock isn't as critical as for, say, an outright short stock position.

4

How to make a Synthetic Long Call?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

3. Synthetic Long Call = Long Stock + Long Put

C = S + P

If you are an experienced option trader, you would be able to immediately tell that the above equation is saying that Fiduciary Calls = Protective Puts! That's right! That's what this synthetic position is trying to say.

A fiduciary call is just a long call option. A protective put is a long stock and long put.

Ergo, fiduciary call = protective put.

Provides the benefits of stock ownership (potential price appreciation), with some downside protection.

5

How to make a Synthetic Short Call?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

4. Synthetic Short Call = Short Stock + Short Put

-C = - S - P

When you short a call option, you are exposed to limited profits, unlimited losses and the premium on the call options decay to your advantage. The short stock contributes the limited downside profits (all the way to $0 so technically unlimited profits to downside) and the short put options limit that profit to the premium decay of the put options while offsetting part of the loss to upside.

A 'covered put' is a type of synthetic short call. Entering a covered put entails selling puts against a stock you are short. It has the same risk profile as a short call, so it's considered a type of synthetic short call. In a covered put you're short a stock, but in the near term you believe a bounce is coming. Instead of covering your short with intentions of re-shorting at a higher level (may have negative tax consequences), you sell puts to make a few bucks on the bounce. If the stock closes above the strike, you keep the premium - mission accomplished. You'll also make money with time decay if the stock moves sideways. If the stock drops you won't participate in the decline because your profit from being short the stock will be countered by the loss from the naked puts. Also, if the stock closes below the strike at expiration and you do not buy your puts back, the stock will be "put" to you (you'll be forced to buy it; you'll then be long and short the stock), so you'll no longer have a position.

6

How to make a Synthetic Short Put?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

5. Synthetic Short Put = Short Call + Long Stock

-P = S - C

In a Short Put option position, you are exposed to limited profit to upside and unlimited loss potential while gaining the extrinsic value no matter what happens. Long Stocks contributes the unlimited loss potential to the synthetic position while the short call limits the potential upside profit.

Entering a synthetic short put entails selling calls on a stock you own. It has the same risk profile as a naked put (short put) (hence why it's considered a synthetic short put), but it's actually just a 'covered call'.

Entering a covered call entails selling calls against a long stock position. There are two main purposes of this strategy. 1) You're long a stock and want to generate monthly or quarterly cash flow while maintaining ownership of the stock. You sell out-of-the-money calls against your position. As long as the stock closes below the strike price at expiration, you keep the stock and can sell calls again. Collecting a couple % each month or quarter adds up; it's like collecting a monthly or quarterly dividend. 2) You buy a stock specifically for the purpose of selling calls, and while it may be nice for the stock to close just below the strike at expiration so you can sell calls again, you're perfectly ok with the stock rallying and getting called from you. This is typically done with a volatile stock which fetches a high premium.

In both cases, if you the stock rallies a lot, you don't participate in the rally because your short call position will offset your stock gains. And if the stock drops a bunch, you get to keep the premium, but you're still the owner of a stock which has declined in value.

7

How to make a Synthetic Long Put?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

6. Synthetic Long Put = Long Call + Short Stock

P = -S + C

Entering a synthetic long put entails buying calls against a stock you are short. Protective call is a type of synthetic long put. Entering a protective call entails buying calls against a stock you are short. It has the same risk profile as a long put, so it's considered a type of synthetic long put.

Motivation: The only motive is to profit from a fall in stock's price.

Max Loss: The maximum loss is limited. The worst that can happen is for the stock price to be above the strike price at expiration, in which case the short stock position can be closed out by exercising the call option. The loss would be the selling price of the stock (where it was sold short), less the purchase price of the stock (the strike price), less the premium paid for the call option.

Max Gain: The maximum gain is limited but potentially substantial. The best that can happen is for the stock to become worthless. In that case, the investor could buy the stock for zero to close out the short stock position. The total profit, however, would be reduced by the premium paid for the call option, which expired worthless.

8

What does it mean to be 'short'?

Short (to be short) - To Short means to Sell To Open. That means to write or sell an options contract to a buyer. This gives you the obligation to fulfill the exercise of the option should the buyer decides to do so.

The terms "Long" and "Short" aren't unique to options trading. They are terms used in the financial markets across every single asset class. "Long" and "Short" in the financial markets refer to whether you are the "Buyer/Owner" or "Seller/Borrower" of a financial instrument. So when you are long a stock, you are actually the buyer and owner of the stock. When you are short a stock, you are actually the seller or borrower of a stock (borrowing in order to sell when you don't own the stock yet). This same logic applies to options trading.

To be "Short" an options contract means to be the "Seller/Producer" of an options contract. When you go "Short" an options contract, you are actually producing an options contract, or writing up a whole new options contract (this is why being short an option is also known as "Writing" an option), for sale to an options buyer in the options market. If buying options is a directional bet on the direction of the underlying stock, then being "Short" or "Writing" an option makes you the bookmaker to that bet, selling a "lottery ticket" for a small price and keeping the win if the bet didn't work out at the buyer expected. In order to be short an options contract, all you have to do is to use the "Sell To Open" order, which means to open a new options position by selling rather than buying.

9

What is extrinsic value?

The part of a stock option's price above the option's intrinsic value arising from other factors such as implied volatility and length of contract.

Extrinsic Value, also not-so-accurately known as "Time Value" or "Time Premium", is the real cost of owning a stock options contract. It is the part of the price of an option which the writer of the option gets to keep as profit should the stock remain stagnant all the way to expiration. As such, extrinsic value is actually compensation to the writer of an option for undertaking the risk of writing an option. Extrinsic value is also the part of the price of an option that decreases as time goes by through a phenomena known as "Time Decay" in options trading.

Extrinsic value answers the question of "How much money justifies the risk the writer of the option is undertaking". This risk is defined in options trading using 4 different criteria and factored into a mathematical options pricing models such as the Black-Scholes Model. Indeed, when someone writes an option, that person's risk is not only limited to how long the person is exposed to the risk of being assigned but also a variety of other risks. The 4 factors that come together to determine extrinsic value are:

1. Time left to expiration (Theta)

2. Changes in interest rate (Rho)

3. Volatility of the underlying stock (Vega)

4. Dividends of the underlying stock

10

What is put-call parity?

c + X / (1 + RFR)^T = S + p

(Call premium + PV of Exercise price) = (Stock [underlying] price + Put premium)

Demonstrates that the payoffs of a portfolio of European fiduciary call and portfolio of protective put must be equal

Put Call Parity is an option pricing concept that requires the extrinsic values of call and put options to be in equilibrium so as to prevent arbitrage. Put Call Parity is also known as the Law Of One Price.

Put Call Parity is a concept identified by Stoll in 1969, that defines the relationship that must exist in European call and put options. Put options, call options and their underlying stock forms an interrelated securities complex in which the combination of any 2 components yields the same profit/loss profile as the 3rd instrument. Under this kind of complex relationship, no combination of 2 components should yield a position with an asymmetric profit/loss profile as the 3rd instrument so that balance is maintained in the system. This balance is known as the Put Call Parity in option trading. The concept of Put Call Parity is especially important when trading synthetic positions ('synthetic triangle'). When there is a mispricing between an instrument and its synthetic position, an options arbitrage opportunity exists.

Put Call Parity requires, mathematically, that option trading positions with similar payoff or risk profiles (i.e Synthetic Positions) must end up with the same profit or loss upon expiration such that no arbitrage opportunities exist. An example of Put Call Parity is in terms of Fiduciary Calls (long call only) and Protective Puts (long stock and long put). Fiduciary Calls and Protective Puts have the same profit/loss profile that you see below. If the underlying stock remains completely stagnant by expiration of both positions, both positions would decline in value equal to the extrinsic value (premium) paid on the options. Neither option trading positions would have any advantage over the other during expiration.

11

What is the equation of the 'synthetic triangle'?

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

1. Synthetic Long Stock = Long Call + Short Put

S = C - P

2. Synthetic Short Stock = Short Call + Long Put

-S = P - C

3. Synthetic Long Call = Long Stock + Long Put

C = S + P

4. Synthetic Short Call = Short Stock + Short Put

-C = - S - P

5. Synthetic Short Put = Short Call + Long Stock

-P = S - C

6. Synthetic Long Put = Long Call + Short Stock

P = -S + C

12

What's a protective put?

3. Synthetic Long Call = Long Stock + Long Put

Protective put = Long stock + Long put

A fiduciary call is just a long call option. A protective put is a long stock and long put (a synthetic long call).

Ergo, fiduciary call = protective put.

The protective put establishes a 'floor' price under which investor's stock value cannot fall.

If the stock keeps rising, the investor benefits from the upside gains. Yet no matter how low the stock might fall, the investor can exercise the put to liquidate the stock at the strike price.

Some examples of when investors consider protective puts:
- Before an imminent news announcement that could send a favorite stock into a slump.
- When it's vital to insure the value of a specific stock for a certain period; for instance, to cover a house down payment or tuition outlays five months from now.
- When one stock represents a large percentage of the investor's portfolio.
- When an investor is restricted from selling a particular stock for some time period.
- When a stockowner wants to protect substantial unrealized gains.

The choice of strike prices determines where the downside protection 'kicks in’. If the stock stays strong, the investor still gets the benefit of upside gains. (In fact, if the short-term forecast brightens before the put expires, it could be sold back to recoup some of its cost.) However, if the stock falls below the strike, as originally feared, the investor has the benefit of several choices.

One option is to exercise the put, which triggers the sale of the stock. The strike price sets the minimum exit price. If the long-term outlook has turned bearish, this could be the most prudent move.

If the worst seems to be over, an alternative for still-bullish investors is to keep the stock and sell the put. The sale should recoup some of the original premium paid, and may even result in a profit. If so, it in effect lowers the stock's cost basis.

If the investor remains nervous, the put could be held into expiration to extend the protection for as long as possible. Then it either expires worthless or, if it is sufficiently in-the-money, is exercised and the stock would be sold.

The put can provide excellent protection against a downturn during the term of the option. The major drawback of the strategy is its cost, which raises the bar on netting upside profits. Investors who aren't very bullish might have better strategy alternatives.

VARIATIONS: The 'married put' and protective put strategies are identical, except for the time when the stock is acquired. The protective put involves buying a put to hedge a stock already in the portfolio. If the put is bought at the same time as the stock, the strategy is called a married put. Synthetic call is simply a generic term for this combination.

If you add a protective put to a covered call (short call + long stock) then you get a 'collar'.

13

What's a covered call?

5. Synthetic Short Put = Short Call + Long Stock

Covered call = Short Call + Long Stock

In a Short Put option position, you are exposed to limited profit to upside and unlimited loss potential while gaining the extrinsic value no matter what happens. Long Stocks contributes the unlimited loss potential to the synthetic position while the short call limits the potential upside profit.

Entering a synthetic short put entails selling calls on a stock you own. It has the same risk profile as a naked put (short put) (hence why it's considered a synthetic short put), but it's actually just a 'covered call'. Covered call writing is less dangerous than selling naked call options because you have the stock.

An investor who buys or owns stock and writes call options in the equivalent amount can earn premium income without taking on additional risk. The premium received adds to the investor's bottom line regardless of outcome. It offers a small downside 'cushion' in the event the stock slides downward and can boost returns on the upside.

Predictably, this benefit comes at a cost. For as long as the short call position is open, the investor forfeits much of the stock's profit potential. If the stock price rallies above the call's strike price, the stock is increasingly likely to be called away. Since the possibility of assignment is central to this strategy, it makes more sense for investors who view assignment as a positive outcome.

Because covered call writers can select their own exit price (i.e., strike plus premium received), assignment can be seen as success; after all, the target price was realized. This strategy becomes a convenient tool in equity allocation management.

The investor doesn't have to sell an at-the-money call. Choosing between strike prices simply involves a tradeoff between priorities.

The covered call writer could select a higher, out-of-the-money strike price and preserve more of the stock's upside potential for the duration of the strategy. However, the further out-of-the-money call would generate less premium income, which means there would be a smaller downside cushion in case of a stock decline. But whatever the choice, the strike price (plus the premium) should represent an acceptable liquidation price.

A stockowner who would regret losing the stock during a nice rally should think carefully before writing a covered call. The only sure way to avoid assignment is to close out the position. It requires vigilance, quick action, and might cost extra to buy the call back especially if the stock is climbing fast.

If you add a protective put (long put + long stock) to a covered call then you get a 'collar'.

14

What's a collar?

Entering a collar entails buying a lower strike put and selling a higher strike call on a stock already owned. Essentially, a collar is a covered call with a protective put.

Usually, the investor will select a call strike above and a long put strike below the starting stock price. There is latitude, but the strike choices will affect the cost of the hedge as well as the protection it provides. These strikes are referred to as the 'floor' and the 'ceiling' of the position, and the stock is 'collared' between the two strikes.

The investor adds a collar to an existing long stock position as a temporary, slightly less-than-complete hedge against the effects of a possible near-term decline. The long put strike provides a minimum selling price for the stock, and the short call strike sets a maximum profit price. To protect or collar a short stock position, an investor could combine a long call with a short put.

This strategy establishes a fixed amount of price exposure for the term of the strategy. The long put provides an acceptable exit price at which the investor can liquidate if the stock suffers losses. The premium income from the short call helps pay for the put, but simultaneously sets a limit to the upside profit potential.

Both the potential profit and loss are very limited, depending on the difference between the strikes. Profit potential is not paramount here. This is, after all, a hedging strategy. The issues for the protective collar investor concern mainly how to balance the level of protection against the cost of protection for a worrisome period.

15

What are the Greeks?

The Greeks are a collection of statistical values that give the investor a better overall view of option premiums change given changes in pricing model inputs.

BETA is a measure of how closely the movement of an individual stock tracks the movement of the entire stock market.

DELTA is a measure of the relationship between an option premium and the underlying stock price. For a call option, a Delta of .50 means a half-point rise in premium for every dollar that the stock goes up. For a put option contract, the premium rises as stock prices fall. As options near expiration, in-the-money contracts approach a Delta of 1.00.

In this example, the Delta for stock XYZ is 0.50. As the price of the stock changes by $2.00, the price of the options changes by $.50 for every $1.00. Therefore the price of the options changes by (.50 x 2) = $1.00. The call options increase by $1.00 and the put options decrease by $1.00. The Delta is not a fixed percentage. Changes in price of stock and time to expiration affect the Delta value.

GAMMA is the sensitivity of Delta to a one-unit change in the underlying. Gamma indicates an absolute change in Delta. For example, a Gamma of 0.150 indicates the Delta increases or decreases by 0.150 if the underlying price increases or decreases by $1.00. Results will usually not be exact.

LAMDA is a measure of leverage, the expected percent change in an option premium for a 1% change in the value of the underlying product.

RHO is the sensitivity of option value to change in interest rate. Rho indicates the absolute change in option value for a 1% change in the interest rate. For example, a Rho of .060 indicates the option's theoretical value increases by .060 if the interest rate decreases by 1.0. Results may not be exact due to rounding.

THETA is the sensitivity of an option’s premium to change in time. Theta indicates an absolute change in the option value for a one-unit reduction in time until expiration. Theta may be displayed as a 1-day or 7-day measure. For example, a Theta of -.250 indicates the option's theoretical value changes by -.250 if the days to expiration reduce by seven. Results may not be exact due to rounding. NOTE: seven day Theta will change to one day Theta if days to expiration are seven or less (see Time decay).

VEGA (or KAPPA) is the sensitivity of option value to changes in implied volatility. Vega indicates an absolute change in option value for a 1% change in volatility. For example, a Vega of .090 indicates the option's theoretical value increases by .090 if the implied volatility increases by 1.0%. Alternately, the option’s theoretical value decreases by .090 if the implied volatility decreases by 1.0%. Results may not be exact due to rounding.

16

What is delta?

The first and most commonly used greek is "delta". For the record, and contrary to what is frequently written and said about it, delta is NOT the probability that the option will expire ITM. Simply, delta is a number that measures how much the theoretical value of an option will change if the underlying stock moves up or down $1.00. Positive delta means that the option position will rise in value if the stock price rises, and drop in value if the stock price falls. Negative delta means that the option position will theoretically rise in value if the stock price falls, and theoretically drop in value if the stock price rises.

The delta of a call can range from 0.00 to 1.00; the delta of a put can range from 0.00 to –1.00. Long calls have positive delta; short calls have negative delta. Long puts have negative delta; short puts have positive delta. Long stock has positive delta; short stock has negative delta. The closer an option's delta is to 1.00 or –1.00, the more the price of the option responds like actual long or short stock when the stock price moves.

So, if the XYZ Aug 50 call has a value of $2.00 and a delta of +.45 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 call will theoretically rise to $2.45. If XYZ falls to $47, the value of the XYZ Aug 50 call will theoretically drop to $1.55.

If the XYZ Aug 50 put has a value of $3.75 and a delta of -.55 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 put will drop to $3.20. If XYZ falls to $47, the value of the XYZ Aug 50 put will rise to $4.30.

Now, these numbers assume that nothing else changes, such as a rise or fall in volatility or interest rates, or time passing. Changes in any one of these can change delta, even if the price of the stock doesn't change.

Note that the delta of the XYZ Aug 50 call is .45 and the delta of the Aug 50 put is -.55. The sum of their absolute values is 1.00 (|.45| + |-.55| = 1.00). This is true for every call and put at every strike. The intuition behind this is that long stock has a delta of +1.00. Synthetic long stock is long a call and short a put at the same strike in the same month. Therefore, the delta of a long call plus the delta of a short put must equal the delta of long stock. In the case of the XYZ Aug call and put, .45 + .55 = 1.00. Remember, a short put has a positive delta. (Note: delta can be calculated with different formulas, which won't be discussed here. Using the Black-Scholes model for European-style options, the sum of the absolute values of the call and put is 1.00. But using other models for American-style options and under certain circumstances, the sum of the absolute values of the call and put can be slightly less or slightly more than 1.00.)

You can add, subtract, and multiply deltas to calculate the delta of a position of options and stock. The position delta is a way to see the risk/reward characteristics of your position in terms of shares of stock, and it's how thinkorswim presents it to you on the Position Statement on the Monitor page. The calculation is very straightforward. Position delta = option theoretical delta * quantity of option contracts * number of shares of stock per option contract. (The number of shares of stock per option contract in the U.S. is usually 100 shares. But it can be more or less, due to stock splits or mergers.) thinkorswim performs this calculation for each option in your position, then adds them together for each stock.

So, if you are long 5 of the XYZ Aug 50 calls, each with a delta of +.45, and short 100 shares of XYZ stock, you will have a position delta of +125. (Short 100 shares of stock = -100 deltas, long 5 calls with delta +.45, with 100 shares of stock per contract = +225. –100 + 225 = +125)

A way to interpret this delta is that if the price of XYZ rises $1, you will theoretically make $125. If XYZ falls $1, you will theoretically lose $125. IMPORTANT: These numbers are theoretical. In reality, delta is accurate for only very small changes in the stock price. Nevertheless, it is still a very useful tool for a $1.00 change, and is a good way to evaluate your risk.

An ATM option has a delta close to .50. The more ITM an option is, the closer its delta is to 1.00 (for calls) or –1.00 (for puts). The more OTM and option is, the closer its delta is to 0.00.

Delta is sensitive to changes in volatility and time to expiration. The delta of ATM options is relatively immune to changes in time and volatility. This means an option with 120 days to expiration and an option with 20 days to expiration both have deltas close to .50. But the more ITM or OTM an option is, the more sensitive its delta is to changes in volatility or time to expiration. Fewer days to expiration or a decrease in volatility push the deltas of ITM calls closer to 1.00 (-1.00 for puts) and the deltas of OTM options closer to 0.00. So an ITM option with 120 days to expiration and a delta of .80 could see its delta grow to .99 with only a couple days to expiration without the stock moving at all.

The delta of an option depends largely on the price of the stock relative to the strike price. Therefore, when the stock price changes, the delta of the option changes. That's why gamma is important.

17

What is gamma?

Gamma is an estimate of how much the delta of an option changes when the price of the stock moves $1.00. As a tool, gamma can tell you how "stable" your delta is. A big gamma means that your delta can start changing dramatically for even a small move in the stock price.

Long calls and long puts both always have positive gamma. Short calls and short puts both always have negative gamma. Stock has zero gamma because its delta is always 1.00 – it never changes. Positive gamma means that the delta of long calls will become more positive and move toward +1.00 when the stock prices rises, and less positive and move toward 0.00 when the stock price falls. It means that the delta of long puts will become more negative and move toward –1.00 when the stock price falls, and less negative and move toward 0.00 when the stock price rises. The reverse is true for short gamma.

For example, the XYZ Aug 50 call has a delta of +.45, and the XYZ Aug 50 put has a delta of -.55, with the price of XYZ at $48.00. The gamma for both the XYZ Aug 50 call and put is .07. If XYZ moves up $1.00 to $49.00, the delta of the XYZ Aug 50 call becomes +.52 (+.45 + ($1 * .07), and the delta of the XYZ Aug 50 put becomes -.48 (-.55 + ($1 * .07). If XYZ drops $1.00 to $47.00, the delta of the XYZ Aug 50 call becomes +.38 (+.45 + (-$1 * .07), and the delta of the XYZ Aug 50 put becomes -.62 (-.55 + (-$1 * .07).

Position gamma measures how much the delta of a position changes when the stock price moves $1.00. Position gamma is calculated much in the same way as position delta. In the Position Statement on the Monitor page, thinkorswim takes the gamma of each option in your position, multiplies it by the number of contracts and the number of shares of stock per option contract, then adds them together.

Just as delta changes, so does gamma. If you were to look at a graph of gamma versus the strike prices of the options, it would look like a hill, the top of which is very near the ATM strike. Gamma is highest for ATM options, and is progressively lower as options are ITM and OTM. This means that the delta of ATM options changes the most when the stock price moves up or down. Let's look at a deep ITM call option (delta near 1.00), an ATM call option (delta near .50), and an OTM call option (delta near .10). If the stock rises, the value of the ITM call will increase the most because it acts most like stock. Even though the ITM call has positive gamma, its delta really doesn't get much closer to 1.00 than before the stock rose. The value of the OTM call will also increase, and its delta will probably increase as well, but it will still be a long way from 1.00. The value of the ATM option increases, and its delta changes the most. That is, its delta is moving closer to 1.00 much quicker than the delta of the OTM call. Practically speaking, the ATM call can provide a good balance of potential profit if the stock rises versus loss if the stock falls. The OTM call will not make as much money if the stock rises, and the ITM will lose more money if the stock falls.

Judging how gamma changes as time passes and volatility changes depends on whether the option is ITM, ATM or OTM. Time passing or a decrease in volatility acts as if it's "pulling up" the top of the hill on the graph of gamma, and making the slope away from the top steeper. What happens is that the ATM gamma increases, but the ITM and OTM gamma decreases. The gamma of ATM options is higher when either volatility is lower or there are fewer days to expiration. But if an option is sufficiently OTM or ITM, the gamma is also lower when volatility is lower or there are fewer days to expiration.

What this all means to the option trader is that a position with positive gamma is relatively safe, that is, it will generate the deltas that benefit from an up or down move in the stock. But a position with negative gamma can be dangerous. It will generate deltas that will hurt you in an up or down move in the stock. But all positions that have negative gamma are not all dangerous. For example, a short straddle and a long ATM butterfly both have negative gamma. But the short straddle presents unlimited risk if the stock price moves up or down. The long ATM butterfly will lose money if the stock price moves up or down, but the losses are limited to the total cost of the butterfly.

Gamma is a good reason to look at a profit/loss graph of your position over a wide range of possible stock prices. The thinkorswim Analysis page will help you see how risky a negative gamma position might be.

18

What is theta?

T is for time!

Theta, a.k.a. time decay, is an estimate of how much the theoretical value of an option decreases when 1 day passes and there is no move in either the stock price or volatility. Theta is used to estimate how much an option's extrinsic value is whittled away by the always-constant passage of time. The theta for a call and put at the same strike price and the same expiration month are not equal. Without going into detail, the difference in theta between calls and puts depends on the cost of carry for the underlying stock. When the cost of carry for the stock is positive (i.e. dividend yield is less than the interest rate) theta for the call is higher than the put. When the cost of carry for the stock is negative (i.e. dividend yield is greater than the interest rate) theta for the call is lower than the put.

Long calls and long puts always have negative theta. Short calls and short puts always have positive theta. Stock has zero theta – its value is not eroded by time. All other things being equal, an option with more days to expiration will have more extrinsic value than an option with fewer days to expiration. The difference between the extrinsic value of the option with more days to expiration and the option with fewer days to expiration is due to theta. Therefore, it makes sense that long options have negative theta and short options have positive theta. If options are continuously losing their extrinsic value, a long option position will lose money because of theta, while a short option position will make money because of theta.

But theta doesn't reduce an option's value in an even rate. Theta has much more impact on an option with fewer days to expiration than an option with more days to expiration. For example, the XYZ Oct 75 put is worth $3.00, has 20 days until expiration and has a theta of -.15. The XYZ Dec 75 put is worth $4.75, has 80 days until expiration and has a theta of -.03. If one day passes, and the price of XYZ stock doesn't change, and there is no change in the implied volatility of either option, the value of the XYZ Oct 75 put will drop by $0.15 to $2.85, and the value of the XYZ Dec 75 put will drop by $0.03 to $4.72.

Theta is highest for ATM options, and is progressively lower as options are ITM and OTM. This makes sense because ATM options have the highest extrinsic value, so they have more extrinsic value to lose over time than an ITM or OTM option. The theta of options is higher when either volatility is lower or there are fewer days to expiration. If you think about gamma in relation to theta, a position of long options that has the highest positive gamma also has the highest negative theta. There is a trade-off between gamma and theta. Think of long gamma as the stuff that provides the power to a position to make money if the stock price starts to move big (think of a long straddle). But theta is the price you pay for all that power. The longer the stock price does not move big, the more theta will hurt your position.

Position theta measures how much the value of a position changes when one day passes. Position theta is calculated much in the same way as position delta, but instead of using the number of shares of stock per option contract, theta uses the dollar value of 1 point for the option contract. (The dollar value of 1 point in an option contract for U.S. equities is usually $100, but can be different due to stock splits.) thinkorswim takes the theta of each option in your position, multiplies it by the number of contracts and the value of 1 point for the option contract, then adds them together.

19

What is vega (or kappa)?

V is for volatility!

Vega (the only greek that isn't represented by a real Greek letter) is an estimate of how much the theoretical value of an option changes when volatility changes 1.00%. Higher volatility means higher option prices. The reason for this is that higher volatility means a greater price swings in the stock price, which translates into a greater likelihood for an option to make money by expiration.

Long calls and long puts both always have positive vega. Short calls and short puts both always have negative vega. Stock has zero vega – it's value is not affected by volatility. Positive vega means that the value of an option position increases when volatility increases, and decreases when volatility decreases. Negative vega means that the value of an option position decreases when volatility increases, and increases when volatility decreases.

Let's look at the XYZ Aug 50 call again. It has a value of $2.00 and a vega of +.20 with the volatility of XYZ stock at 30.00%. If the volatility of XYZ rises to 31.00%, the value of the XYZ Aug 50 call will rise to $2.20. If the volatility of XYZ falls to 29.00%, the value of the XYZ Aug 50 call will drop to $1.80.

Vega is highest for ATM options, and is progressively lower as options are ITM and OTM. This means that the value of ATM options changes the most when the volatility changes. The vega of ATM options is higher when either volatility is higher or there are more days to expiration.

Position vega measures how much the value of a position changes when volatility changes 1.00%. Position vega is calculated much in the same way as position theta. thinkorswim takes the vega of each option in your position, multiplies it by the number of contracts and the dollar value of 1 point for the option contract, then adds them together.

20

What is rho?

R is for (interest) rates!

Rho is an estimate of how much the theoretical value of an option changes when interest rates move 1.00%. The rho for a call and put at the same strike price and the same expiration month are not equal. Rho is one of the least used greeks. When interest rates in an economy are relatively stable, the chance that the value of an option position will change dramatically because of a drop or rise in interest rates is pretty low. Nevertheless, we'll describe it here for your edification.

Long calls and short puts have positive rho. Short calls and long puts have negative rho. How does this happen? The cost to hold a stock position is built into the value of an option. It all has to do with the idea of an option being a substitute of sorts for a stock position. For example, if you think the stock of XYZ is going to rise, you could buy 100 shares of XYZ for $4800, or you could buy 2 of the XYZ Aug 50 calls for $400. (2 XYZ Aug 50 calls would give me a position delta of +90 — pretty close to the XYZ stock position delta of +100.) As you can see, you would have to spend about 12X the amount spent on the options that you would spend on the stock. That means that you would have to borrow money or take cash out of an interest-bearing account to buy the stock. That interest cost is built into the call option's value.

The more expensive it is to hold a stock position, the more expensive the call option. An increase in interest rates increases the value of calls and decreases the value of puts. A decrease in interest rates decreases the value of calls and increases the value of puts.

Back to the XYZ Aug 50 calls. They have a value of $2.00 and a rho of +.02 with XYZ at $48.00 and interest rates at 5.00%. If interest rates increase to 6.00%, the value of the XYZ Aug 50 calls would increase to $2.02. If interest rates decrease to 4.00%, the value of the XYZ Aug 50 calls would decrease to $1.98.

21

What does delta neutral mean?

The "delta" of an option is the measure of how much the option changes in price for a one-point move in the underlying stock.

A delta-neutral strategy aims to make a profit regardless of the price moves of the underlying asset. For example, a trading strategy that uses gold derivatives (gold futures, gold options, gold variance swaps etc.) would be a delta-neutral strategy if its success or failure was independent of the actual price of gold. A delta neutral position is one in which the sum of the projected price changes of the long options in the spread is essentially offset by the projected price changes of the short options in the same spread.

As the value of the underlying assets changes, the position of the Greeks will shift between being positive, negative and neutral. Investors who want to maintain delta neutrality must adjust their holdings accordingly. Puts always have a negative delta (ranging from -1 to 0), while long calls always have a positive delta (ranging from 0 to 1), so the two can be used together to create a delta-neutral position. Options traders can use a neutral position delta strategy to make money when implied volatility declines.

The basic concept of delta neutral hedging is that you create a delta neutral position by buying twice as many at the money puts as stocks you own. This way, you are effectively insured against any losses should the price of the stock fall, but it can still profit if it continues to rise.

Let’s say you owned 100 shares in Company X stock, which is trading at $50. You think the price will increase in the long term, but you are worried it may drop in the short term. The overall delta value of your 100 shares is 100, so to turn it into a delta neutral position you need a corresponding position with a value of -100.

This could be achieved by buying 200 at the money puts options, each with a delta value of -0.5. If the stock should fall in price, then the returns from the puts will cover those losses. If the stock should rise in price, the puts will move out of the money and you will continue to profit from that rise. There is, of course, a cost associated with this hedging strategy, and that is the cost of buying the puts. This is a relatively small cost, though, for the protection offered.

A delta neutral hedging for stocks actually creates a Synthetic Straddle options trading position.

22

What can be combined to form a CCIRS?

A CCIRS involves exchanging cash flows in one currency for cash flows in another currency (ie exchanges interest flows in different currencies). The principal is normally physically exchanged at the spot FX rate at outset and re-exchanged at the same rate on final payment date.

KPMG: a

(1) floating-for-floating CCIRS: pay variable EUR, receive variable USD swap; and a
(2) IRS: pay variable USD, receive fixed USD swap

is equivalent to a CCIRS to pay variable EUR and receive fixed USD