
# Bear Call Spread

## Strategy name and alternative names

**Bear Call Spread**. An alternative name is **Credit Call Spread**.

## Main characteristics

Bearish position.
It is a vertical spread involving an equal number of long and short calls on the same underlying asset and with the same expiration date.
It is a credit spread, which means you receive money to put on the position.
The strategy profits as long as the price of the underlying security remains below the breakeven point.

## Options used in the combination

Sell to open one at-the-money (ATM) call and **simultaneously** buy to open one out-of-the money (OTM) call.
The strike price of the short call is below that of the long call.
The advantage of this spread is that it benefits from time decay and provides an immediate inflow of cash.
The maximum gain and loss on the spread are very limited and well defined.

:::cut:::

## Risk profile

![](vbcs_exp-pnl-1024x576.png){.thumb}
Figure: Fig. 1, P&L Chart: The X axis is price and Y axis is profit/loss. The range of the Y axis is plus or minus the distance between the two strikes. The domain of the X axis is centered on the strike price of the short call.

**Maximum profit**
: The net credit received when you put on the spread.

**Maximum loss**
: The maximum loss occurs when the price of the underlying security hits
or rises above the strike price of the long call.
It is equal to the difference between the long and short strikes minus the net credit received.

**Breakeven point**
: At expiration, the breakeven point is the strike price of the short call plus the net credit.

**Key points**
: On a profit/loss chart (see above) where the X axis is price and the Y axis is profit/loss,
the value of the spread is a minimum at or above the long call’s strike price.
The spread is composed of three connected line segments.
The leftmost segment is horizontal from zero to the strike price of the short call.
The middle segment is a negatively sloped diagonal line starting at the strike price of the short call
and continuing until the strike price of the long call.
The rightmost segment is a horizontal line beginning at the strike price of the long call
and continuing to the right.
The breakeven point is the X-intercept.

## Preconditions to open this spread

You would put on a Bear Call Spread if you feel that the underlying asset’s price will remain stagnant
or decline through expiration, and wanted to profit if your prediction is correct.
The spread is more conservative than a naked short call, because the long call limits the maximum loss.
However, the long call reduces the net credit received compared to simply shorting the call.

## Greeks

![](greeks-1024x576.png){.thumb}
Figure: Fig. 2, Greeks

### Delta

An option’s probable price movement in relation to the price movement of the underlying stock.
The value ranges from `0` to `1` for a long call and `-1` to `0` for a short call where 0 means the option price is not affected by the stock price,
and 1 means the option prices moves penny for penny in lockstep with the underlying’s price.
Delta of whole spread thus ranges from a negative value to `0`.
While the overall spread is considered neutral, it is negative when the underlying price rises toward the short strike
and reaches a minimum at the average strike price.
As the underlying’s price continues to rise above the average strike, delta increases until it final returns to its maximum value of `0`.
In other words, the delta curve is symmetrical around the average strike price.

### Vega

Vega is the effect of the underlying stock’s volatility on the option’s price.
For example, a vega of `0.3` means that an option’s price will rise by 30 cents for each point increase
in the underlying stock’s implied volatility. For a Bear Call Spread, you want vega to drop after putting on the spread,
because you’d like the price of the underlying asset to remain stable. Vega is zero when the underlying’s price
is well below the short strike, and becomes increasingly negative until the underlying’s price approaches the short strike price.
Vega reverses and increases as the underlying’s price continues to rise, crossing the X axis (`vega = 0`)
at the average strike and continuing to rise until hitting a maximum somewhat beyond the long call’s strike price.
It then reverses direction again and approaches zero as the underlying’s price continues to rise.

### Theta

The time decay of an option’s price as the expiration date approaches.
At the close of expiration day, an option’s theta is `0`. Theta is lower for long expiration periods,
which means the option loses time value more slowly than it would for short expiration periods.
A longer expiration period increases the chance that the spread will expire in the money.
Theta for a Bear Call Spread is positive (which means the short spread doesn’t lose value over time)
until the underlying’s price rises to a point between the two strike prices.
At that point, theta becomes negative, because there is less chance that underlying’s price will return to the short strike price.

### Gamma

This is the rate of change of delta – the responsiveness of the position to the underlying’s price movement.
In a Bear Call Spread, gamma is negative below the average strike price, which means delta will decrease in the direction of the stock move.
Gamma is positive above the average strike, and a further upmove by the underlying asset increases delta.
If the underlying moves far above the average strike, gamma re-approaches zero.

## Dynamic illustrations

![](vbcs_time.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 3, Time decay animation: Describing physics of the spread’s price as time expires.

![](vbcs_vola.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}

Fig. 4, Volatility dependency animation: Describing physics of the spread’s price when implied volatility rises or falls.

## Position example on current market conditions

Assume the share price of XYZ stock is `$100.00`.
Sell to open one XYZ 100-strike call with 60 days until expiration and simultaneously buy to open one XYZ 105-strike call
with the same expiration for a net credit of `$1.27`. Neglect commissions.

**Net Credit**
: `$1.27`. You receive `$127`, which is escrowed in your margin account.

**Maximum profit**
: `$127`

**Maximum loss**
: `100 x ($100 – $105 + $1.27) = -$373`

**Breakeven point**
: `$100 + $1.27 = $101.27`

## How to manage position

You are bearish on the underlying asset and would like the underlying’s price to remain stable or decline.
Here are a few things to do if the underlying’s price moves.

### Weak upward move

If the underlying security weakly moves above the short call’s strike price but you remain bearish,
you could close out the spread and replace it with a long put or long straddle to take advantage of a drop in the underlying’s price.

### Strong upward move in underlying stock price

If the underlying security moves above the breakeven point and you are afraid it will continue to rise,
you can convert the Bear Call Spread into a Short Call Ladder Spread by buying one or more OTM calls at increasingly higher strike prices.

### Strong downward move in underlying stock price that you expect to continue

You could sell to close the long call and recoup a little of the premium.
This would transform the position to a naked short call with unlimited risk.

## Variation

The Bear Call Spread has a negative risk/reward ratio, meaning you can lose more money than you can gain.
If you are long-term bearish on the underlying asset and want a better risk/reward ratio, you could put on a Deep ITM Bear Call Spread,
in which both the short and long calls are deeply in the money. Because the value of deep ITM options are due mostly to intrinsic
rather than time value, a surprise upward move in the underlying’s price would have very little effect
on the price difference between the short and long calls. Thus, upside risk is minimal.
Conversely, the net credit on a Deep ITM Bear Call Spread should be close to the difference
between the two strikes, since time value is relatively small.
You can structure a Deep ITM Bear Call Spread such that the risk/reward ratio approaches `1:9`.

## Summary

A Bear Call Spread limits your gains and losses in well-defined ways.
The standard Bear Call Spread has an unattractive risk/reward ratio, but you can improve the ratio by using deep ITM calls.
A further risk with a Bear Call Spread is that you are in danger of being assigned whenever the underlying’s price is above the short strike price.
If you are assigned, you must deliver the underlying asset at the strike price, which will cut into your profit or cause you a loss.
Even though you’ve covered the short call with a long call, you still must establish a long position for at least one day so that you can deliver it.
If that occurs, the long call won’t help you unless the underlying’s price rises above the long strike,
since the long call’s strike price is the maximum price you’ll have to pay for the underlying asset.



# Straddle

## Strategy name and alternative names

**Straddle**. An alternative name is **Long Straddle**.

## Main characteristics

Neutral position. It is a combination involving an equal number of long puts and long calls at the same strike price and the same expiration date.
It is a debit combination, which means you must pay to put on the position.
The strategy profits when the price of the underlying security moves up or down beyond the breakeven points.

## Options used in the combination

Buy to open one at-the-money (ATM) call and simultaneously buy to open one ATM put.
Both options derive from the same underlying stock and have the same strike price and expiration date.
The advantage of this combination is that it benefits from volatility, independent of the direction of stock price movement.
Both the put and the call have (potentially) unlimited upsides but limited loss exposure.

:::cut:::

## Risk profile

![](straddle_exp-pnl-1024x576.png){.thumb}
Figure: Fig. 1, P&L chart: The X axis is price and Y axis is profit/loss. The range of the Y axis is maximum loss to potential gain. The domain of the X axis is centered on the strike price.

**Maximum profit**
: If the stock price rises, the profit on the call leg is unlimited, and is equal to the difference between
the underlying’s price and the call strike price, minus the premium on the straddle (we’ll ignore commissions).
Upside potential on the call leg is unlimited.
If the stock price falls, the profit on the put leg is virtually unlimited, and is equal to the difference
between the put strike price and the underlying’s price, minus the premium on the straddle.
(Technically, upside potential on the put leg is limited to the strike price of the straddle minus the premium,
because a stock price can drop to no lower than zero.)

**Maximum loss**
: Premium paid, which equals the premium on the call plus the premium on the put.
Occurs when the underlying’s price at the expiration exactly equals the strike price.

**Breakeven point**
: There are two breakeven points on a straddle.
The upper breakeven point equals the strike price plus the premium paid.
The lower breakeven point equals the strike price minus the premium paid.

**Key points**
: On a profit/loss chart (see below) where the X axis is price and the Y axis is profit/loss,
the value of the combination is a minimum at the straddle’s strike price.
The strike price forms the base of a V-shaped curve, that is, two diagonal lines with opposite slopes
that rise from a point with (X,Y) coordinates of (strike price, stock price minus premium).
The maximum loss, at the strike price, is the premium. The left (put) leg of the V rises as the stock price falls
and is bounded by the y-axis. The right (call) leg of the V rises without limit as the stock price rises.
The left and right legs of the V cross the X axis at the breakeven points.

## Preconditions to open this combination

You would put on a straddle in the hope that the underlying stock will quickly break out or break down from the strike price.
You would choose an underlying stock that is relatively volatile, as this increases the chances that the stock price will move away
from the strike price (see the vega chart).
You don’t need an opinion on price direction to profit from a straddle, if the stock price moves a sufficient amount.
Some traders put on straddles just ahead of a corporate announcement, jury verdict or earnings announcement,
in the hope the news will move the stock price.
Your biggest fear is that the price of the underlying stock will not move far enough away from the strike to recoup all your premium.

## Greeks

![Fig. 2, Greeks](greeks-1024x576.png){.thumb}

### Delta

An option’s probable price movement in relation to the price movement of the underlying stock.
The value ranges from `0` to `1` for a long call and `-1` to `0` for a long put
where `0` means the option price is not affected by the stock price,
and `1` means the option prices moves penny for penny in lockstep with the underlying’s price.
Delta of whole spread thus ranges from `-1` to `1`.
At the strike price of a straddle, the deltas of the put and the call cancel each other out,
which is why the straddle is delta neutral.

There is a wrinkle when the stock price does not exactly match the strike price.
If the call is slightly in-the-money (`ITM`), it will have a slightly higher delta value than will the put,
giving you a positive delta position that, in the short term, gains on the upside and loses to the downside.
The reverse is true if the put is slightly ITM.
This is only a concern if you sell to close the straddle before expiration;
If you hold till expiration, the effect of a slightly non-neutral delta evaporates.

### Vega

The effect of the underlying stock’s volatility on the option’s price.
For a straddle, higher vega translates into higher option prices, all things being equal.
For example, a vega of `0.3` means that an option’s price will rise by `30` cents for each point increase
in the underlying stock’s implied volatility.
Buying a straddle during periods of high implied volatility can be disadvantageous,
because a volatility crunch will collapse the time value of the put and call premiums.

### Theta

The time decay of an option’s price as the expiration date approaches.
At the close of expiration day, the option’s theta is `0`.
Theta is lower for long expiration periods, which means the option loses time value more slowly
than it would for short expiration periods.
A longer expiration period increases the chance that the combination will expire in the money.
Theta for a straddle is negative (which means the combination loses value over time)
because the options lose value over time due to time decay.

### Gamma

This is the rate of change of delta – the responsiveness of the position to the underlying’s price movement.
In a straddle, gamma is positive, which means delta will increase in the direction of the stock move.
On an upward stock move, a positive gamma dictates that the delta of the straddle becomes increasingly positive,
while on a downward stock move, the straddle’s delta becomes increasingly negative.
You can thus profit from a move in either direction with a straddle.

## Dynamic illustrations

![](straddle_time.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 3, Time decay animation Describing physics of what’s going on with combination’s price when time goes towards expiration.

![](straddle_vola.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 4, Volatility dependency animation Describing physics of what’s going on with combination’s price when an implied volatility rises or falls down.

## Position example on current market conditions

Assume its mid-January and United Technologies (UTX) is trading at `$110.00`.
Buy to open 10 UTX March 03 110 calls for `$2.60` each, buy to open 10 UTX March 03 90 puts for `$3.20` each.
Neglect commissions.

**Net Debit**
: `$2.60 + $3.20 = $5.80`. You pay `$5,800`.

**Potential** **profit**
: `10 x (|strike – stock price| – $580)`

**Maximum loss**
: `$5,800`

**Breakeven point 1**
: `$110 + $5.80 = $115.80`

**Breakeven point 2**
: `$110 – $5.80 = $104.20`

## How to manage position

This is a debit combination with limited risk and unlimited reward.
Here are two things you can do.

### Strong move in underlying stock price

1. If the underlying stock moves beyond the breakeven point,
   you can sell to close the out-of-the-money (OTM) option to recoup a little of the premium.
2. If the ITM leg has gained significant value despite time decay,
   you can sell the ITM option for a substantial profit.
3. You can sell to open an option (put or call) one strike further OTM than the strike for the favored leg,
   thus converting one side of initial straddle into a vertical spread.
   This will compensate you for the initial premium you paid.

### Strong move in underlying stock price that you expect to continue

You could sell to close the OTM option and use the proceeds to buy more contracts of the in-the-money option,
at a strike price of your choosing.

## Variation

If you have a mildly bullish inclination, you can put on a strap, which is a straddle with more calls than puts.
If you have a mildly bearish inclination, you can put on a strip, which is a straddle with more puts than calls.
You’ll make more profit with either variation than you would with a straddle when you correctly guess
the direction of stock movement, but you’ll profit less if you guess incorrectly.

If you already own the underlying stock, you can create a synthetic straddle by purchasing ATM puts.
Similarly, if you have already shorted the stock, you could buy ATM calls.
This works best when the stock price is very close to the option strike price.

## Summary

A straddle limits your losses to some amount between zero and the premium
if the stock price remains between the two breakeven points.
There is no profit limit on the upside, and the downside profit is limited only
to the extent that a stock price can’t fall below zero.
If the stock price moves substantially, your ROI will be smaller
than it would be from a naked long call or put position,
but you would have to correctly guess the direction of the movement to realize the higher ROI.
You might be able to make a profit on a straddle even if the stock price doesn’t move.
This is possible only when the implied volatility of the straddle jumps soon after purchase
and thereby expands premiums (through an increase in time value) above the amount you paid.
You could then sell the straddle for a profit, albeit probably a small profit.



# Strangle

## Strategy name and alternative names

**Strangle**. Alternative shorter names are **Long strangle, poor-man’s straddle**.

## Main characteristics

Neutral position.
It is a combination involving an equal number of out-of-the-money (`OTM`) long puts and long calls with the same expiration date.
It is a debit combination, which means you must pay to put on the position.
The strategy profits when the price of the underlying security moves up or down beyond the breakeven points.

## Options used in the combination

Buy to open one OTM call and simultaneously buy to open one OTM put.
Both options derive from the same underlying stock.
The strike price of the put is below the current stock price by about the same amount as the call strike price
is above the security price.
For example, if the stock price is `100`, you would buy a 95-strike put and a 105-strike call.
The advantage of this combination is that it benefits from volatility, independently of the direction of stock price movement.
Both the put and the call have (potentially) unlimited upsides but limited loss exposure.  
A strangle is like a straddle, except that the put and call in a straddle have the same at-the-money strike price.
Because the strangle uses cheaper OTM options, the total premium is less than that for a straddle, all other things being equal.

:::cut:::

## Risk profile

![](strangle_exp-pnl-1024x576.png){.thumb}
Figure: Fig. 1, P&L chart: The X axis is price and Y axis is profit/loss. The range of the Y axis is maximum loss to maximum gain with some margin to show overall picture. The domain of the X axis is centered on the midpoint between the two strike prices (i.e., the average of the put and call strike prices).

**Maximum profit**
: If the stock price rises above the call’s strike, the profit on the call leg is unlimited,
and is equal to the difference between the underlying’s price and the call strike price,
minus the premium on the strangle (we’ll ignore commissions).
Upside potential on the call leg is unlimited.
If the stock price falls, the profit on the put leg is virtually unlimited,
and is equal to the difference between the put strike price and the underlying’s price,
minus the premium on the strangle.
(Technically, profit potential on the put leg is limited to the strike price of the put minus the premium,
because a stock price can drop to no lower than zero.)

**Maximum loss**
: Premium paid, which equals the premium on the call plus the premium on the put.
Occurs when the underlying’s price closes between the call and put strikes.

**Breakeven point**
: There are two breakeven points on a strangle.
The upper breakeven point equals the call strike price plus the total premium paid.
The lower breakeven point equals the put strike price minus the total premium paid.

**Key points**
: On a profit/loss chart where the X axis is a base asset price and the Y axis is profit/loss,
the value of the combination is a minimum between the put strike price and the call strike price.
The two strike prices form the base of a truncated V-shaped curve, that is,
two diagonal lines with opposite slopes that rise from the endpoints of the line connecting the put
and call strike prices.
The left leg begins at a point with (X,Y) coordinates of (put strike price, stock price minus strangle premium).
The right leg begins at a point with (X,Y) coordinates of (call strike price, stock price minus strangle premium).
The maximum loss, at any point between the two strike prices, is the strangle premium.
The left (put) leg rises as the stock price falls and is bounded by the y-axis.
The right (call) leg rises without limit as the stock price rises.
The left and right legs cross the X axis at the breakeven points described above.

## Preconditions to open this combination

You would put on a strangle in the hopes that the underlying stock will quickly break out
above the upper breakeven point or break down below the lower breakeven point.
You would choose an underlying stock that is relatively volatile, as this increases the chances
that the stock price will move away from the strike prices (see the vega chart).
You don’t need an opinion on price direction to profit from a strangle, as long as the stock price moves a sufficient amount.
Some traders put on strangles just ahead of a corporate announcement, jury verdict or earnings announcement,
in the hopes the news will move the stock price.
Your biggest fear is that the price of the underlying stock will not move
into the money enough (for either the put or the call) to recoup all your premium.

## Greeks

![](greeks-1024x576.png){.thumb}
Figure: Fig. 2, Strangle greeks

### Delta

Delta is an option’s probable price movement in relation to the price movement of the underlying stock.
The value ranges from `-1` to `1`:

-   `-1` to `0` for a long put;
-   `0` to `1` for a long call;

where `0` means the option (and thus the spread) price is not affected by the stock price,
and `1` means the option prices moves penny for penny in lockstep with the underlying’s price.
At the average strike price of a strangle, the deltas of the put and of the call cancel each other out,
which is why the strangle is delta neutral.
There is a wrinkle when the stock price does not exactly match the average strike price.
If the stock price is above the average strike price, the call will have a slightly higher delta value
than will the put, giving you a positive delta position that, in the short term, gains on the upside
and loses to the downside.
The reverse is true if the stock price is below the average strike price.
This is only a concern if you sell to close the strangle before expiration;
If you hold till expiration, the effect of a slightly non-neutral delta evaporates.

### Vega

Vega is the effect of the underlying stock’s volatility on the option’s price.
For a strangle, higher vega translates into higher option prices, all things being equal.
For example, a vega of `0.3` means that an option’s price will rise by 30 cents for each point increase
in the underlying stock’s implied volatility.
Buying a strangle during periods of high implied volatility can be disadvantageous,
because a volatility crunch will shrink vega and collapse the time value of the put and call premiums.
Vega has a maximum value between strikes.

### Theta

Theta is the time decay of an option’s price as the expiration date approaches.
At the close of expiration day, the option’s theta is `0`.
Theta is lower for long expiration periods, which means the option loses time value more slowly
than it would for short expiration periods.
A longer expiration period increases the chance that the combination will expire in the money.
Theta for a strangle is negative (which means the combination loses value over time)
because the options lose value due to time decay.
Time decay speed is maximum when the underlying’s price is between strikes.

### Gamma

Gamma is the rate of change of delta – the responsiveness of the position to the underlying’s price movement.
In a strangle, gamma is positive, which means delta will increase in the direction of the stock price movement.
On an upward stock move, a positive gamma dictates that the delta of the strangle becomes increasingly positive,
while on a downward stock move, the strangle’s delta becomes increasingly negative.
You can thus profit from a move in either direction with a strangle,
as long as the stock moves far enough into the money for either the put or the call.

## Dynamic illustrations

![](strangle_time.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 3, Time decay animation: Describes the physics of what happens to the combination’s price as expiration approaches.

![](strangle_vola.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 4, Volatility dependency animation: Describes the physics of what happens to the combination’s price when implied volatility rises or falls.

## Position example

Assume its mid-January and United Technologies (UTX) is trading at `$110.00`.
Buy to open 10 UTX March 03 114-strike calls for `$1.12` each, buy to open 10 UTX March 03 106-strike puts for `$1.23 each`.
Neglect commissions.

-   **Net Debit**: `$1.12 + $1.23 = $2.35`. You pay `$2,350`.
-   **Maximum profit**: `10 x (|ITM option strike price – stock price| – $235)`
-   **Maximum loss**: `$2,350`.
-   **Breakeven point 1**: `$114 + $2.35 = $116.35`.
-   **Breakeven point 2**: `$106 – $2.35 = $103.65`.

## How to manage position

This is a debit combination with limited risk and unlimited reward. Here are some things you can do.

### Strong move in underlying stock price

1. You can sell to close the leg that gained value due to the move in the underlying stock price.
   If time decay hasn’t devalued options significantly, the option in the favored leg has become profitable.
   Alternatively, you can sell the whole spread,
2. You can sell to open an option one to two strikes further in the money than the option that gained value.
   Doing this converts one side of the strangle into a vertical spread, thus compensating you
   for the premium you paid on the strangle, possibly creating a positive risk profile.
3. If the underlying stock moves beyond one of the breakeven points, you can sell
   to close the out-of-the-money (OTM) option to recoup a little of the premium.

### Strong move in underlying stock price that you expect to continue

You could sell to close the OTM option and use the proceeds to buy more contracts of the in-the-money option,
at a strike price of your choice.

## Variations

If you wish to risk more money in order to reduce the distance between the two breakeven points,
you could buy a straddle instead of a strangle.

If you have a mildly bullish inclination, you could buy more calls than puts.
If you have a mildly bearish inclination, you could buy more put than calls.
You’ll make more profit with either variation than you would with a classic strangle
if you correctly guess the direction of stock movement, but you’ll profit less (or lose more) if you guess incorrectly.

## Summary

A strangle limits your losses to some amount between zero and the combination’s premium
if the stock price remains between the two breakeven points.
There is no profit limit on the upside, and the downside profit is limited only to the extent that a stock price can’t fall below zero.
If the stock price moves substantially, your ROI will be smaller than it would be from a naked long call or put position,
but you would have to correctly guess the direction of the movement to realize the higher ROI.
You might be able to make a profit or cut your loss on a strangle even if the stock price doesn’t move beyond a breakeven point.
This is possible only when the implied volatility of the underlying stock jumps soon after purchase
and thereby expands option premiums (through an increase in time value) above the amount you paid.
You could then sell the strangle for a profit, albeit probably a small profit.

A strangle costs less than a straddle, so that less money is at risk per combination.
However, the strangle has a larger distance between breakeven points, so that you need more stock price movement to make a profit.
The strangle expires without value if the ending stock price is between the two strike prices, inclusively.
In a straddle, the expiration value is more than zero unless the ending stock price is equal to the strike price.



# Vertical Bull Debit Call Spread

## Strategy name and alternative names

**Vertical bull debit call spread.** An alternative shorter name is **bull call spread**.

## Main characteristics

Moderately bullish. It is a vertical spread, which means it involves two or more options at different strike prices
with the same expiration date. It is a debit spread, which means you must pay to put on the position.
The strategy profits when the underlying security rises moderately.

## Options used in the spread

Buy to open one at-the-money (ATM) call and simultaneously sell to open one out-of-the money (OTM) call.
Both calls derive from the same underlying stock.
The advantage of this spread is that the credit from the sale of the OTM call partially offsets the debit paid for the ATM call.
Basically, the spread allows you to buy the ATM call at a discount
in exchange for a cap on the maximum profit you can extract from the spread.

:::cut:::

## Risk profile

![](vbcs_exp-pnl-1024x576.png){.thumb}

**Maximum profit**
: Equals the strike price of the OTM call minus the strike price of the ATM call
minus the net premium paid minus commission.
Achieved when underlying’s price rises to or above the OTM call’s strike price.

**Maximum loss**
: Net premium paid plus commission. Occurs when underlying’s price is not greater than the ATM call strike price.

**Breakeven point**
: Strike price of ATM call plus net premium.

**Key points**
: On a profit/loss chart (see below) where the X axis is price and the Y axis is profit/loss,
the value of the spread from left to right (lower to higher prices) is constant
at maximum loss until the underlying’s price exceeds the ATM call’s strike price.
The line representing the value of the spread increases diagonally as you move to the right (increasing price).
The value is zero at the breakeven point, and reaches its maximum value at the strike price of the OTM call.
Further increases in strike prices have no effect on the profit/loss of the spread, which remains constant.

## Preconditions to open this spread

You would put on a bull call spread in the hopes that the underlying stock will rise to the strike price of the OTM call by expiration date.
You would choose an underlying stock that is relatively volatile, as this increases the chances
that the stock price will move toward the OTM call’s strike price (see the vega chart).
Since your potential maximum loss is limited, downside volatility has only a limited risk,
so you need not fear it as much as you would with a naked short call position (which has an unlimited risk).

You would also choose an expiration date that is not too close, since the time value of the OTM call collapses faster
than that of the ATM call as the expiration date approaches, assuming the stock price is still near the ATM call’s strike price.
The discount on the spread derives from the decay of an option’s time value as the expiration date approaches (see theta decay chart).
If you bought just the ATM call, your debit would equal the intrinsic value (if any) of the call plus its time value (ignoring commissions).
By shorting the OTM call, you receive a credit equal to the time value.
Therefore, the time values of the two calls partially cancel each other out.

The offset is partial because time value is greatest at the ATM call strike price.
The effect is to buy the ATM call option at a discount,
which means a higher return on investment when the stock price is above the breakeven point.
The breakeven point is lower in the bull call spread as compared to a naked long call,
thanks to the credit provided by shorting the OTM call.

## Greeks

![Vertical bull call spread greeks](vbdcs_greeks-1024x576.png){.thumb}
Figure: Fig. 2, Vertical bull call spread greeks

### Delta

An option’s probable price movement in relation to the price movement of the underlying stock.
The value ranges from `0` to `1` for a long call or short put, where `0` means the option price is not affected by the stock price,
and `1` means the option prices moves penny for penny in lockstep with the underlying’s price.
A short call or long put have a delta between `0` and `-1`, reflecting that these options have values
that move in the opposite direction from those of the underlying stock.
Delta increases for ATM options as the expiration date approaches.
For a bull call spread, delta is initially positive, as the value of the spread increases when the underlying stock price rises.

### Vega

The effect of the underlying stock’s volatility on the option’s price.
Higher vega translates into higher option prices, all things being equal.
For example, a vega of `0.3` means that an option’s price will rise by 30 cents for each point increase
in the underlying stock’s implied volatility.
In a bull call spread, vega is positive for options with a short expiration period
but is less positive for options with longer expiration periods.

### Theta

The time decay of an option’s price as the expiration date approaches.
At the close of expiration day, the option’s theta is `0`.
Theta is lower for long expiration periods, which means the option loses time value more slowly
than it would for short expiration periods.
A longer expiration period increases the chance that the option will expire in the money.
Theta is negative (which means the spread loses value over time) for a bull call spread
if the underlying’s price is below the breakeven point;
Theta becomes positive (i.e., the spread’s price grows with time) when the underlying asset price rises above the breakeven point.

### Gamma

This is the rate of change of delta — the responsiveness of the position to the underlying’s price movement.
In a bull call spread, gamma is positive below the breakeven point,
which leads to delta growth when the underlying price approaches the breakeven point.
Above the breakeven point, gamma becomes negative, thereby decreasing delta.

## Dynamic illustrations

![](vbdcs_time.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 3, Time decay animation Describes the physics of what happens to the spread’s price as expiration approaches.

![](vbdcs_vola.mp4){style="width: 100%; height: 100%;" autoplay="autoplay" loop="loop" controls="controls"}
Figure: Fig. 4, Volatility dependency animation Describes the physics of what happens to the spread’s price when implied volatility rises or falls.

## Position example

Assume Apple (AAPL) is trading at `$120`.
Buy to open 10 AAPL March 120 calls for `$3.20`, sell to open 10 AAPL March 125 calls for `$1.40`.
Neglect commissions.

**Net debit:** `$3.20 – $1.40 = $1.80`. You pay `$1,800`.
If you expect AAPL to go up to near `$130` by expiration, you might instead sell to open 10 AAPL March `$130` calls.

**Maximum profit:** `10 x ($500 – $180) = $3,200`.

**Maximum loss:** `$1,800`.

**Breakeven point:** `$120 + $1.80 = $121.80`.

## How to manage position

Since this is a debit spread with limited risk and reward, you don’t need much management, but here’s what you can do.

### Strong rise in underlying stock price

You could buy to close the OTM call and sell to open an OTM call with the next higher strike price.
Alternatively, you could refrain from buying the higher strike call, converting the position into a long call.
Lastly, you could simply close out the spread once the stock price hits the OTM call’s strike price, since this represents maximum profit.

### Stock price not expected to rise much

You could write extra OTM calls to lower the net cost and the breakeven point.
The resulting long call ladder spread has unlimited risk.

### Stock price expected to reverse after hitting strike price of OTM call

You can convert to a bear call spread (which see) by selling to close the long call and buying
to open a new long call with a strike higher than that of the short call.
This position profits from a price decline and has limited profit, limited loss potential.

## Variation

You can put on a bull call spread using two OTM calls with different strike prices above the current stock price.
You buy the lower-strike call and sell the higher-strike one.
For example, if the stock price is `$120`, you buy the `$125` call and sell the `$130` call.
This can be extremely profitable on a percentage basis if the stock price explodes in your favor.
Of course, the probability of a total loss is much greater,
because the breakeven point lies further away from the current price of the underlying.

## Summary

The bull call spread limits your losses if the underlying stock price drops, and limits your profits if the stock price rises.
If the stock price rises but never hits the OTM call’s strike price,
your ROI will be larger than it would be from a naked long call position.
The bull call spread is also an effective way to buy options at a discount.
We’ve ignored commissions, but in the real world, you’ll pay more commissions
with the spread than you would with a naked long call position.



Option Expiration and Pinning
=============================

Options trading can appear intimidating to some traders.
To make money, you must understand how option values fluctuate, the risks of option positions and the regulations pertaining to option expiration.
You can have option positions that expire after periods ranging from one day to more than a year.
Understanding the mechanics of option expiration will save you from unpleasant surprises.

:::cut:::

## Option Expiration

Long option position holders have the right to buy or sell (via calls or puts, respectively) a specified amount of some asset,
such as securities, commodities, currencies and contracts, at a stated price – the strike price – on
or before the expiration date (American-style options) or only on the expiration date (European-style options).
An option *seller* – the short position – earns the option’s price, known as the premium,
but may be forced to purchase or sell (because of puts or calls, respectively)
the underlying asset should the option long position exercise the option.
Call options can possess *intrinsic value*, which is any excess of the underlying asset’s price relative to the strike price.
Put options gain intrinsic value when the underlying asset’s price is less than the strike price.
Options also have *time value* that is based on their possibility of gaining intrinsic value.
Time value decreases to zero by the time the expiration date arrives.

### Unexpected Purchases

Most put and call long positions never exercise their options – they simply cash out by selling the option or,
if *out of the money*, letting it expire worthlessly.
However, if you don’t sell your options with intrinsic value before they expire, they will execute
and you’ll end up buying (via calls) or selling (via puts) the underlying asset.
Options expiration dates are on a Friday at the close of trading.
Suppose you own seven stock calls with intrinsic value – *in-the-money* options – and neglect to sell them before they expire.
On the following Monday, you’ll receive notice of your purchase of 700 of the underlying shares.
If your brokerage account doesn’t contain sufficient cash to pay for the shares, your broker makes a margin call,
meaning you must quickly deposit money or it will sell the underlying shares,
forward the proceeds to the call short position holder and charge commissions (and possibly penalty fees) to your account.
If this happens a couple of times, don’t be surprised if your broker closes your account.

### Unexpected Assignments

A put short position who doesn’t repurchase an *in-the-money* put before expiration faces *assignment*.
That means you’ll have to buy the underlying asset at the strike price, and if your account is underfunded,
you’ll receive a margin call.
A short position in call that expires in the money must deliver the underlying asset on the Monday after expiration.
If you don’t already have the asset in your account, the broker will buy it for you using your margin deposit.
Note that short option positions may be assigned before expiration, as long as they are in the money.
You can sidestep problems regarding asset delivery and payment by closing an option position by the end of trading on the expiration date.
It’s a good idea to leave standing orders with your broker to close out in-the-money option positions at expiration.
This causes your broker to execute a *market-on-close* order, selling the options you own or buying back your short options.
Either way, the broker closes your option positions and frees you from automatic purchase or sale of the underlying asset.

## Pinned Stock Options

*Pinning* is the phenomenon observed on option expiration days in which underlying stocks tend
to close right at a strike price of an option (closing *at-the-money*).
This behavior is not seen on non-expiration dates nor for stocks without options.
Pinning creates certain risks for both public option traders and for option market makers (OMMs) – specialist dealers
who earn commissions by buying from public sellers and selling to public buyers,
thus ensuring the existence of a liquid market for options.

### Trading Risks

On option expiration date, a trader with a long position in ITM options will have a choice:
close out the option position before the end of the day – receiving an amount of cash per option determined
by the difference between the option strike price and the current stock price;
or hold the position through the close and then receive (via a call)
or sell (via a put) the underlying stock from/to the OMM.
The risk of holding an option that is pinned near a strike price is that it could suddenly flip
from ITM to out-of-the-money at the last second, leaving the option holder with a worthless position.

### OMM Risks

OMMs in general wish to avoid holding outright positions in an option,
because they do not want to undertake price risk – they make their money from commissions, not from gains and losses.
Since OMMs must stand ready to buy and sell puts and calls, they prefer a neutral posture with respect to prices.
This preference is what drives the mechanism of pinning on expiration day.

### Mechanism of Pinning

As the market approaches its close on expiration day, ITM call holders may sell their positions to lock in a profit.
OMMs are obligated to buy these calls, but do not want to take on the price risk associated with holding the calls.
Therefore, OMMs will hedge away this risk by short-selling the underlying stock into the close,
thereby neutralizing price risk – the short stock position loses value as the long option position gains,
protecting the OMM from price moves in a strategy known as *delta hedging*.
Short selling tends to depress prices by increasing supply, so stock prices that were above the strike price are pressured downward toward the strike.
The reverse situation occurs for put holders when stock prices are just below the strike near expiration:
if the put holders sell their options, the OMM will neutralize price movements by buying underlying stocks, resulting in upward stock price pressure.
The see-sawing of offsetting pressures is why stock prices get pinned to option strike prices at expiration.


# Day trading options

The term “day trading” assumes that a trader opens and closes positions within a single trading session and doesn’t take positions overnight.

Also, when talking about day trading, people generally think of instruments such as – equities, ETFs and futures. Not options.

However, let’s analyze whether we can use options for day trading and, if so, we should consider how to adjust trading styles
and which nuances to focus on while trading options within such a short time frame.

:::cut:::

## Day trading requirements

First, let’s consider which conditions an instrument must satisfy to be traded within a day without taking positions overnight.
The most important are:

- Relatively high volatility
- Enough liquidity
- Acceptable commissions

Volatility is required to allow a trader to catch a relatively large price move.
Certainly, we could say that volatility may be “scaled” if an instrument can be traded with leverage,
but in this article, we consider non-leveraged trading.

Liquidity is required to allow a trader close his position at any moment with a tight bid/ask spread.
When analyzing liquidity level, we must take into account the size which we trade.
If we trade only one contract, then liquidity is not an issue in most of the instruments you might want to trade.
Besides the quantity of contracts which you can buy/sell in any given moment, an important metric is the size
of the spread between best market orders. You pay half of the spread to the market each time when buying/selling at market price.

Commissions is not only an instrument property as it mostly depends on your broker/FCM.
The only requirement is that commissions must not kill a significant part of your profit.

Now let’s take a look at whether options satisfy these requirements.

## Options price volatilities

The heading above is a bit misleading for anyone who knows something about the implied volatility concept.
This paragraph is not about IV/HV of an option’s underlying instrument; it is about the volatility of the option’s price itself. Here we are considering options not as a derivative, but as an independent security.

To start, let’s take three options on the S&P 500 futures index, which are being traded at the moment of writing this article.
We consider three options, one is at-the-money, and two (call and put) are out of the money.
For each of the options, we build a candlestick chart for daily prices from the beginning of the instrument’s lifecycle to the current day.
We can see on the chart that price movements are significant, sometimes moving more than 100% in one day.

![](cnds_4months-1024x576.png)
Figure: ES mini 2200 put and call daily prices, 4 months

Now let’s build the chart for intraday data, 10 minute periods:

![](cnds_1day-1024x576.png)
Figure: ES mini 2200 put and call prices within one day

The day was selected randomly, 2016-11-22.
It’s easy to see that the price range of the put option for this day was between 22 and 27.5 points or more than 20%.

In other words, the option’s price changed significantly more than the underlying’s.
Therefore, options price volatility is more than enough to allow traders to use them as a speculative security for day trading.

### Note

The charts above were built for option strikes which now are at the money.
If an option is far in or out of the money, then it’s price will not be so volatile.

## Options liquidity

Liquidity of a single option is always lower than the liquidity of its underlying. There are several reasons for this.

1. The number of options is bigger than the number of underlyings by thousands of times.
   For example, right now (when this article was written) there are 6 options series for the ES mini December futures.
   Each series contains about 400 options.
   Even if we assume that the number of people who trade options is equal to the number of people trading futures (the underlying),
   their interest is dispersed on all the different options.
2. In reality, the number of people who trade options is much fewer than number of traders for linear instruments

### Near the money liquidity concentration

The further the strike is from the money, the less liquidity exists at that strike.
If we open a big position in an ATM option, we must remember that it might become harder to close that position
if the underlying price changes significantly causing the option to be far in or out of the money.

To demonstrate this let’s visualize some data from the CME Group website.
This is a time and sales report, a simple table containing the following columns:

- Trade time
- Trade instrument (call/put and strike)
- Trade price
- Number of contracts in trade

We want to understand at which strikes the most trades are concentrated.
The best way to visualize such kind of information is a histogram.
We’ve built two: the first shows a distribution of the number of trades,
while the second illustrates a distribution of the number of traded contracts.

![](strikes_hist-1024x576.png)
Figure: Number of trades per strike in one day

As expected, most trades occurred near the ATM strike. The black dashed line on both charts denotes current underlying price.

But since we are talking about intraday trading, it’s not likely that the liquidity of a particular contract will change significantly in one day.

### Spreads

What really can affect the performance of intraday options trading is the bid/ask spread.
Let’s compare the spread of the underlying (ESZ16 futures) with that of the corresponding ATM call option.

Right now the spread in ESZ16 futures orders book is 0.25 or 12.5 $ and this is equal to the minimum price step,
denoted in contract specification.
Contract nominal value at current price is 2200/0.25\*12.5 = $110,000. The spread in futures then is equal to 12.5/110000 = 0.011%.

[http://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500_contract_specifications.html](http://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500_contract_specifications.html)

On the other hand, the current price of an ATM call for this futures contract with expiration in two weeks is about 16 points.
Price step of this contract is also 0.25 = 12.5$.
Spread can’t be less than the price step.
Thus minimum bid/ask spread is 0.25/16 = 1.56%, which is huge in comparison to the spread for its underlying futures contract.

## Commission

Commissions are mostly a property of the brokerage firm, not the contract.
In our understanding, commissions must be at least smaller than half of the contract’s price step.

## Day trading options, conclusion

Near the money options can be used as a speculative instrument for intraday trading.
When selecting the appropriate contract, it’s worth it to pay attention to the following things:

- average size of the bid/ask spread
- how far an option’s strike is from underlying’s price; always try to select ATM option for best liquidity
- how many contracts traded per day on average



# How to read P&L Charts (part 1)

The question considered in this article might seem too obvious, and one might say that there is nothing to discuss.
But our user support experience tells us that often people who are entirely new in options spent excessive time
on trying to figure out options payoff profiles.
Having a well-developed skill of reading options risk profiles (alternative terms are P&L profiles, payoff function profiles) is essential to successful options trading.

For sure, sooner or later everyone will understand all the details, but we think that with this article we may accelerate this process.

:::cut:::

## P&L of a position in a linear asset. Numbers.

First, we assume stocks, bonds, indexes, commodities, ETFs and even futures are all linear assets.
They all (except futures) have their “own price,” which doesn’t directly (formally) depend on any other asset.
Futures price depends on its underlying asset price in a linear way, thus we also assume futures as a linear instrument.

Assume you have $100 in cash.
You then decide to buy a stock with a current price of $100.
Therefore, your portfolio will consist of 1 share, and you will be glued to computer/smartphone monitoring the price of the stock.
What you are doing is simple and straightforward.
You just observe the price, and since you have only one share, you know that the value of your portfolio entirely coincides with the stock price.
Then you simply compare the current value of the portfolio with your initial investment ($100) to calculate your P&L.

## Putting the numbers on a chart

Now let’s put the example above on a chart. Let’s take a look at figure 1.
The x-axis is the per share price. The y-axis denotes our portfolio P&L
The chart we are going to build shows the relationship between the P&L and the stock price.

![](fig1.png){.thumb}
Figure: Fig. 1, P&L of 1$ price movement up and down

The blue point corresponds to the very moment when we’ve just bought the share.
Price at that moment is $100, and therefore the P&L is zero.

If the price moves from $100 to $101, then our portfolio will be worth $1 more than the initial cash amount; thus, the P&L is $1.
The green dot on figure 1 corresponds to this scenario.
Its coordinates on the plot are $(x;y) = (101;1)$.

On the other hand, if the price goes down to $99, then the P&L will be -$1; the red dot on the figure corresponds to this scenario,
its coordinates are $(99;-1)$.

Similarly, with a bigger price move of let’s say, $2 instead of $1, we can see that On figure 2,
the stock price changes to $102 (green dot) or $98 (red dot).

![](fig2.png){.thumb}
Figure: Fig. 2, P&L of 2$ price movement up and down

Moving onto figure 3, we see that all the points are lying on a straight line.
No matter how much the share price changes, the P&L points on the chart will always be lying on this line.

![](fig3.png){.thumb}
Figure: Fig. 3, All dots are lying on a single line

This means that P&L has a linear relationship with the price.
In teenager math form, this would be $y = Qx$, where $y$ is the P&L of the portfolio, $x$ is the stock price change, $Q$ is the number of shares

The P&L of the portfolio is the number of shares multiplied by the P&L of a single share. Therefore, we can substitute $p - p_{0}$ for $x$,
where $p_{0}$ is the purchase price (for a long position) and $p$ is the current stock price.
We can now rewrite the formula as:

$y = Qx = Q (p - p_{0})$ **(1)**

This equation describes the direct dependence of the portfolio P&L on the share price.

What if we own 2, 3, etc. shares?
The $Q$ in the formula above will be $Q = 2$ or $ 3 $ so $y = 2(p - p_{0}), y = 3(p - p_{0})$ and so on.

On figure 4, we’ve added the line corresponding to a portfolio of 2 shares.
Note the angles between the P&L lines and the x-axis.
The more shares in the portfolio, the bigger angle is, and the faster you earn or lose money.
For 1 share, the portfolio P&L angle is 45 degrees, while for two shares, the angle is 63 degrees.

![](fig4.png){.thumb}
Figure: Fig. 4, Different angles for different position sizes (number of shares in portfolio)

## Changing the open price

In the example above, the stock was bought at $100.
What would the chart look like if the position was purchased at $99?
How do we redraw the P&L line? The line will be the same as before, just shifted to the left by 1, as shown in figure 5.

![](fig5.png){.thumb}
Figure: Fig. 5, Different open prices

## Closing the position

What if the stock price rose to $101 and the holder decided to sell it and close position? What will our chart look like then?

We can think of selling the position as a separate short position and draw them both on the chart (figure 6).
When you buy and sell a security intraday, your broker actually keeps both positions separate.
In effect, you own both the original long and the offsetting short – even though you only see cash.
Only after the trades are settled and cleared, are these positions will be collapsed on your broker’s books.

![](fig6.png){.thumb}
Figure: Fig. 6, Short position

For a short position, the $Q$ in our equation (1) is negative, $Q = -1$.
Thus, the P&L for a short position is $y = -1(p - p_{0})$ and its chart is shown in figure 7.
Since this is a short position, $p_{0}$ represents the sold price and $p$ still represents current price.

The total P&L of the portfolio, green line, is the sum of the red and blue dashed lines on the chart.
Literally we need to sum red and blue lines at each point.
The green line is, therefore, a constant, regardless of how the price changes going forward as the sum is always 1.
The position is closed and we have a $1 profit in cash.

![](fig7.png){.thumb}
Figure: Fig. 7, Total P&L of closed position

The beauty and usefulness of P&L charts are that you can quickly estimate your P&L no matter where price is going.
You see the whole picture in one chart.

Examples considered in this article are simple, but using them, we’ve explained the basic principles of building P&L charts.
Understanding these concepts will be essential when we explain more advanced options concepts in future articles.


Blog #options-mechanics

Bear Call Spread

Straddle

Strangle

Vertical Bull Debit Call Spread

Option Expiration and Pinning

Day trading options

How to read P&L Charts (part 1)

Last thing