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Constructing a Bull Call Spread from Options at Different Strikes

Article Quant Q&A · Author: user_456059239
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Summary

The document explains the basic construction of a bull spread using European calls with a common expiration. For the two-call example, the proposed position buys the lower-strike call and sells the higher-strike call. The intuition offered is that the lower-strike call has greater positive delta, while the higher-strike call has less; combining them leaves a net positive delta and therefore bullish exposure, reduced from owning the lower-strike call alone.

The reverse position—selling the lower-strike call and buying the higher-strike call—is described as a bear spread with negative overall delta. The question also asks how to use three options, but the answers give only a brief suggestion of alternating buy and sell legs and do not explain a payoff structure or conditions for a three-leg position. The discussion focuses on directional intuition and does not cover premiums, maximum profit or loss, breakeven, or other factors needed to fully assess the trade.

Key ideas

  • A basic bull call spread buys a lower-strike call and sells a higher-strike call with the same expiration.
  • The lower-strike call typically has greater positive delta than the higher-strike call.
  • The combined position retains positive directional exposure while reducing the delta of the long call alone.
  • Reversing the two legs creates a bear call spread with negative overall delta.
  • A three-leg strategy needs payoff and risk analysis beyond simply alternating long and short positions.

Tags

OptionsDerivatives pricingPosition sizing
Full text
# Bull spread problem


# Bull spread problem












I am new to finance math and I would like to know if my approach to this problem is correct

Consider the following three European call options, all with expiration at time $T$ = 1:

Option $A$ has strike option ($K$) of $10

Option $B$ has strike $15

Option $C$ has strike $20.

Create a bull spread from options A and B.

My understanding is that the spread for this would be buying A, because it is a lower K and selling B because it has a higher K.

Is there a better way to answer this?

Also, how would it work for 3 options, such as A, B,C?

## Answer by nbbo2 (score 0, accepted)

https://quant.stackexchange.com/a/32418

Yes, one way to think of it is to equate the traditional concept of "bullishness" to the modern BSM concept of "delta".

You buy the call at A, so you are "bullish" (positive Delta), now you sell the call at B. The Call at B is less "bullish" than A (smaller Delta) so when you sell it you "lower your bullishness, but stay overall bullish" (reduce Delta by subtracting a smaller number, so the overall Delta stays positive).

The opposite, sell A and buy B, would by definition be called a "bear spread" (negative overall Delta).

This way of thinking also generalizes to 3 options.

## Answer by user219626 (score 0)

https://quant.stackexchange.com/a/32417

I would suggest going through Bull Spread Explained to understand the bull spread better. Theoretically, your understanding is correct when you say that the spread would be buy A and sell B based on the strike price.

This is also a good reference which help you understand the concept nicely.

In case of 3 instruments, I would think of doing either a buy-sell-buy or a sell-buy-sell strategy, which is typically how 3 legged instruments are traded.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.