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Pricing a Call Spread as the Difference Between Its Legs

Article Quant Q&A · Author: DoonieCaan
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Summary

A call spread that is long a lower-strike call and short a higher-strike call can be priced by subtracting the short call’s value from the long call’s value. Each option is priced separately, then the signed values are combined to obtain the strategy’s price.

The explanation connects this calculation to no-arbitrage pricing: portfolios with the same payoff should have the same value. It does not address the question about how to calculate the spread’s delta, and it gives no numerical example or discussion of practical pricing details such as exercise style, dividends, or transaction costs.

Key ideas

  • Price a call spread by subtracting the value of the short call from the value of the long call.
  • No-arbitrage reasoning links a strategy’s value to the combined values of its component options.
  • The document does not explain how to calculate the spread’s delta.

Tags

OptionsDerivatives pricingArbitrage
Full text
# Pricing for basic option strategies


# Pricing for basic option strategies












If I am trying to price a strategy, say for example a call spread where we are long a call, strike L and short a call strike M, would the pricing formula simply be the Black-Sholes price for the Call at Strike L subtract the Black Scholes price for a call at Strike M?

Is it really that simple or am I missing something?

Furthermore, the Delta would be 0 when the price is < l or > m, but in between l and m, would it just be the average of each leg?

## Answer by Julie Taylor (score 1)

https://quant.stackexchange.com/a/69892

That is correct and actually many of the proofs in option pricing use this concept in order to arrive at a price, for example, by using a replicating portfolio of some stock and bonds, we can adjust our portfolio weights such that the payoff is exactly the same as an option, therefore by no arbitrage principles, this portfolio must be the same as the option. Similar principle here, you have a spread strategy which can be constructed by two calls, so the cost should be just the cost of individual constituents.

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.