Bull Call Spread

A bull call spread is an options strategy built from two call options on the same underlying asset with the same expiry date. The trader buys a call at a lower strike and sells a call at a higher strike. The position gains when the underlying price rises, up to a fixed maximum, and the most it can lose is the amount paid to open it.

It is the debit form of the bull spread, and is also called a long call spread or call debit spread. The strategy fits a view that the price will rise moderately. It costs less than buying a call alone, because the premium collected on the call sold pays for part of the call bought, and in exchange the trader gives up any gain above the higher strike.

The two legs are entered together as a single option spread. The long call gives the right to buy the underlying at the lower strike price. The short call creates an obligation to sell at the higher strike if assigned. Between the strikes, the long call gains as the price rises. Above the higher strike, every further dollar gained on the long call is lost on the short call, so the profit is capped.

The choice of strikes sets the character of the trade. A common form buys a call near the current price and sells one further out of the money. A wider gap between strikes raises both the cost and the maximum profit. A narrower gap is cheaper but pays less.

Per share at expiry:

• $K_L$ is the lower strike, of the call bought.
• $K_H$ is the higher strike, of the call sold.
• Net premium paid is the price of the long call minus the price of the short call.

A share trades at $100. A trader buys the $100 call for $4.50 and sells the $110 call for $1.50, both expiring in two months. The net premium is $3.00. The maximum loss is $3.00, reached if the share finishes at or below $100. The maximum profit is (110 − 100) − 3.00 = $7.00, reached at or above $110. The break-even is 100 + 3.00 = $103. On one contract of 100 shares, the trader risks $300 to make at most $700.

If the share finishes at $106, the long call is worth $6 and the short call expires worthless, for a profit of 6 − 3 = $3 per share. A lone $100 call bought for $4.50 would have made only $1.50 at that price, but would keep gaining above $110 where the spread does not.

The spread has positive delta, smaller than that of a single call because the short leg offsets part of the long leg. The effect of time depends on where the price sits. Near the lower strike, the position loses a little value each day through theta. Near or above the higher strike, the passing of time helps, since the spread approaches its full width as expiry nears.

Exposure to implied volatility is reduced in the same way. A fall in volatility lowers the value of both calls, and the loss on one is partly made up by the gain on the other. This makes the spread a common choice when options look expensive. Before expiry the spread is worth less than its full width even when the price is above the higher strike, so the maximum profit is only reached at the end.

• Long call. A single call has unlimited upside but costs more and needs a larger rise to break even.
• Bull put spread. The same view can be expressed by selling a put and buying a lower-strike put for a net credit. With matching strikes and European-style options, the two have nearly the same payoff.
• Covered call. A covered call also sells a call to earn premium but holds shares instead of a long call, so its downside is much larger.
• Bear put spread. The bear put spread is the mirror image for a falling view.

The full premium is lost if the price is at or below the lower strike at expiry. A correct view that arrives too late still results in a loss, because the options have a fixed life. The cap also means the trader does not share in a large rally.

If the contracts are of the American option type, the short call can be assigned early, most often just before an ex-dividend date when it is in the money. The trader must then deliver shares and can exercise the long call to do so, but may owe the dividend. If the price finishes between the strikes at option expiry, the long call is exercised alone and the trader ends up owning shares, with the cost and risk that implies. Trading two options also means paying two bid-ask spreads.