• Long 1 call near the money.
• Short 1 call further out-of-the-money (at a higher strike or lower delta).

<Bull call risk graph retrieved from OptionsPlay>

A bull call spread is a bullish strategy that is long one call and short another call at a higher strike. This is a directional strategy that is pushing for the price to go in one direction, which is up. Since it has a short call to help with premium decay, it is more resilient against time crush and IV crush than a single-leg call, however a 1:1 vertical only has capped profit potential.

A bull call spread can be a good play to make if a security is about to test support, such as a Put Wall. Since the max loss is already defined by the price of the debit paid, this defines risk in a way that a stop loss would, but with the added benefit that it cannot shake you out of the trade. 

For the most aggressive version of this strategy, it is opened fully OTM: A call is bought slightly-OTM and another call is written further OTM. As shown here in the visual of an OTM bull call spread, both the max loss (left in red) and max profit (right in green) is limited but the max profit is greater. The max profit of a bull call spread is the distance between call strikes minus the net debit paid. The max loss is the debit paid (the total upfront cost of the spread). 

Advanced: Strategic Considerations

Bull call spreads are often difficult trades to make on index products since (with near perfect certainty) they are bound to have a skew penalty (unfavorable implied volatility amounts at different strikes on the same date). This disadvantage is from the widespread use of covered calls and option collars, which causes the price of further-OTM calls to drop as more and more call writers come in at higher strikes. 

A bull call spread’s time decay (theta) and volatility decay is slowed down in exchange for capping max profit, which is made possible because of some positive time yield from the short call being written as a wingtip.

Regarding the Greeks, if both strikes are bought out-of-the-money, then this is a more aggressive play that always has positive gamma and vega. As a drawback, however, long options also have negative theta (meaning loss of premium from time decay).
However, another way to mitigate against loss from theta is to buy LEAPS, which options with at least 6 months in duration. Buying ITM and then writing a calendar or diagonal in the front can offset most of time decay, especially with a ratio (severely increasing the risk and maintenance if doing so).

Otherwise, there would be arbitrage opportunities from the free optionality of gamma, and there would not be enough of an incentive for counterparties of long options to provide liquidity for those transactions. But if the main strike is in-the-money, then it is a more defensive play since the premium is more durable against time and IV crush, which is a strong decline in implied volatility which affects option pricing. 

Expert: Synthetics

Synthetically, there is nearly perfect logical equivalence between a bull call spread and a credit put vertical. For these strategies to be a logical match, it must swap out puts at the same strikes (long for long and short for short), therefore becoming a credit put vertical (bull put). 

No delta-hedging the underlying security is required for this transposition since it is a vertical. For example, a bull call spread which is long a 470 call and short a 480 call would have logical equivalence (in terms of max profit/loss and the Greeks) as a credit put vertical which is long a 470 put and short a 480 put.

arbitrage: A theoretically risk-free trading strategy. Often this is based on detecting and exploiting mispricings in options. Most mispricings pertain to IV (implied volatility), which is the most inefficient aspect of options pricing. Part of the reason why IV is so inefficient is because the theoretical pricing model for options assumes volatility to remain constant throughout the life of the option contract, which essentially would never happen.

debit: In an option strategy, there is a debit paid from long options or debit spreads. This is the premium paid for the opportunity to hold the position. The debit also functions as the max loss of a long option position. The counterparty receives a credit as time decay income (theta) until the option expires but takes on risks which can lead to losses and be significant if from an open-ended position. 

debit spread: In an option strategy, a debit spread is one that has a net debit (upfront cost) paid for long options. This means that there is an upfront cost which must be outperformed by expiration, however there are rights instead of obligations (which keeps the option holder in control). Unless a debit spread is deep in-the-money, it would be very unlikely for the short leg to be assigned. But if it was, then that assignment would be strongly offset by the long option leg. For out-of-the-money debit spreads, they are long gamma (accelerating directional exposure), long vega (sensitivity to implied volatility), and short theta (which means the premium gradually decays the value of the option over time). This time decay is measured by a first-order Greek known as theta.

defined risk: In an option strategy, if risk is defined then it is structured so that it has a max loss (capped total loss on a trade) rather than potentially unlimited loss.

delta: A first-order Greek that measures the sensitivity of an option's price to directional movement in the underlying security. Factoring out nonlinear dynamics, the instantaneous value of one delta is worth one share of a stock. This means that if the option on a stock is 40 delta, such as a 40 delta long call or a 40 delta short put, then instantaneously it has the same profit/loss dynamics of being long 40 shares. 

gamma: A second-order Greek which compares changes in delta (directional exposure) to changes in the underlying. In general, gamma means the acceleration of directional exposure. Gamma is also one of the main properties of an option: All long options are long gamma. In a way, gamma is thought of as the magic of options because the size of directional exposure (delta) increases as it is right about direction (therefore increasing profits), and it decreases when it is wrong about direction (therefore decreasing losses). But the cost for this magic is time decay. The connection to market makers is that when they are long gamma (market gamma is positive) then they trade against the direction of the trend to lock in profits after they have favorable moves with increased size thanks to gamma. This is why positive market gamma tends to create an environment of reduced or reducing realized volatility (smaller overall price moves).

Greeks: An option Greek is a type of risk metric that compares the change in one thing to a change in the other. A first-order Greek is the change in one thing compared to a change in the price of an option. The major first-order Greeks are delta (sensitivity to direction), vega (sensitivity to implied volatility), and theta (sensitivity to time decay). 

hedge: To hedge is to set up precautionary or defensive measures which partially compensate against heavy losses or limit further losses. A well-designed hedge is asymmetrical to the larger position it is protecting—in a way that it suddenly increases in size if the larger position takes on losses. A hedge does not aim at being perfect and would generally be content near a limit of recovering a portion of the losses from what it is protecting.

ITM (in the money): An option is in-the-money if it would still have some [intrinsic] value if the option expired with the underlying price where it currently is. Being in the money is entirely about the strike price beating the underlying price. ITM options cost more than options at or out of the money; they also have less extrinsic value. Additionally, ITM options have more deltas (immediate directional risk).

IV (implied volatility): The expected percentage range over a year with 68.3% confidence. This is based on options pricing at one standard deviation. Long options benefit from increases in implied volatility and short options benefit from decreases in implied volatility. In general, when implied volatility increases it means that the expected percentage range is getting larger. When implied volatility is applied to lengths of time other than one year, then this is called the expected move.

IV crush: A sharp drop in implied volatility which causes the price of an option to deflate. Short options benefit from IV crush and long options lose value from IV crush.

liquidity: A market environment that allows for the ready conversion of cash into an asset and an asset back into cash, with minimal extra costs or restrictions. What primarily helps to establish liquidity is a large number of buyers and sellers active in trading an investment product. When a security is liquid, it has a reasonably tight bid/ask spread, which helps to keep transaction costs low. In addition to tight spreads, high liquidity is often signified by a large amount of volume or open interest. However, some securities might only be liquid for deceptively short periods of time, such as a stock which has a tight bid/ask spread around earnings or a major economic event, but then one that later traps traders when the bid/ask spread widens. Trading liquid products, especially options, helps to keep agility high and transaction costs low, both of which are important components of profitable trading.

long call: To be long (buy and hold) an option contract which has limited risk and unlimited potential gains from moves up in the underlying price. The max loss is the cost of the call. Going long on a call is a simple way to gain upside exposure to movement in an underlying security, however the underlying security (such as a stock) must outperform the premium placed on that call by the options market. In other words, a long call must beat the options market in order to profit. If closed early (well before expiration) then a long call must outpace the expected move (priced in by the options market) for a specific period of time. All long calls have long gamma and long vega but short theta. It is uncommon to exercise calls rather than simply close them for a profit, however a long call is frequently understood as a right to exercise (trade in the long call to be long 100 shares) if above the specified strike price. Synthetically, a long call becomes logically equivalent to a long put if also short 100 shares.

OTM: An option is out-of-the-money if it would have zero value expiring with the underlying at its current price. When an option is out-of-the-money, its entire price is made of extrinsic value, which is a premium that option buyers are willing to pay for an opportunity to make a profit.

Put Wall: The Put Wall is our major support level, which measures the most amount of negative gamma in the market. This shows us what the bottom of the probable trading range is (the lower bound). 

security: Any investment product that can be traded on an exchange, such as but not limited to stocks, futures, ETFs, options, bonds, mutual funds, and treasuries. 

short call: To be short (sell to open and hold) a call. Unless otherwise hedged, the owner of the short call has unlimited risk and only limited potential gains, which makes this an extremely dangerous strategy in isolation. If left to expire, a short call will achieve max profit if the price ends up underneath the strike price. Shorting a call is a way to express a thesis that one is “not bullish” such as what might be justifiably the case if testing a Call Wall from underneath; being “not bullish” is different than being bearish. For a short call to be profitable, the underlying security must underperform the premium placed on that call by the options market. In other words, a short call profits when the underlying security fails to beat the options market. To be closed early for a profit, there needs to be a decrease in implied volatility or the underlying must have increased less than the options market has priced in for that specific period of time. All short calls have short gamma and short vega but long theta. Short options also come with obligations instead of rights, which means that, at any time, shares can be assigned (100 short shares for each contract); assignment usually only happens when in-the-money and near expiration). Synthetically, a short call becomes logically equivalent to a short put if the trader is also long 100 shares.

stop loss: In trading, a stop loss is a predefined exit point to close a trade at a max loss if the trade goes badly. Stop losses, unless otherwise specified, are market orders, which means they can transact at a worse point than expected if the underlying is moving fast or it is illiquid (lacking a high amount of buyers and sellers).

strike: The price that an option is based on. A long call will expire worthless if the price of the underlying security finishes underneath the strike price, and a long put will expire worthless if the underlying finishes above the strike price.

theta: The measurement of how much an option's price changes relative to time. Often used to mean time decay, theta gets stronger in an accelerated fashion as the time of an option runs out. If long an option, then time decay causes net losses (unless more is earned from increases in implied volatility or sharp and favorable price movements). And if short an option, then time decay causes net profits (unless more is lost from increases in implied volatility or sharp and unfavorable price movements).

vega: A first-order Greek which measures the sensitivity of an option to changes in implied volatility (the expected percentage range based on option prices with 68.3% confidence). When we say extrinsic value, this pertains directly to vega and theta (the sensitivity of an option to time decay). As options run out of time on the contract, vega decreases. This is why we often see short duration options with very high implied volatility amounts: the higher implied volatility is balanced out by a smaller slice of vega, which is the influence of implied volatility on the price of an option.

vertical spread: Any option strategy which has all contracts expiring on the same date. In contrast to a horizontal spread (calendar) or diagonal spread (combination of vertical and horizontal strikes), vertical spreads are usually the most directional and also the easiest to manage. With vertical strategies, the main edge at play is usually skew (differences in implied volatility for different strikes on the same date). Implied volatility is the expected percentage range over the next year—based on option prices—with 68.3% confidence.

wingtip: A wingtip is what we call the endpoint of an options strategy where it is furthest out of the money (OTM). A reference to a wingtip is always to the furthest-OTM strike in a strategy. If the main leg on a vertical strategy (both options on the same date) is a credit (a premium is received for taking on some risks and potential obligations), then a long-option wingtip protects against some short gamma risk (directional risk that can increase and accelerate). The cost of defining the risk is giving up some of the premium collected. In order for risk to become defined with main credit legs, then at least as many further-OTM long contracts would need to be written.

writing: We say “write” when a trader sells an option to open a new position. Simply saying “to sell” an option is unclear, as that could mean either selling-to-close or selling-to-open a new position. The most common example of writing is the covered call strategy, which is buying 100 shares in a stock and then selling-to-open a short call on that same stock. In general, writing is to accept an obligation, and there is time-decay income in exchange for that risk (as well as the risk of assignment which is being delivered shares that can create a jump in directional risk).