Interpreting a Capped Call Payoff as a Call Spread

Summary

The payoff that rises with the underlying above a lower strike and then stops increasing can be decomposed into a long call at the lower strike and a short call at a higher strike. The upper strike is the lower strike plus the payoff cap. This identity makes the payoff easier to understand and value using familiar option components.

The answer recommends pricing each call with the standard Black–Scholes framework and combining their values. The document gives the algebraic decomposition but no numerical example, assumptions, or discussion of early exercise, dividends, or market inputs. Its valuation suggestion therefore applies in the setting where the chosen Black–Scholes assumptions and option specifications are appropriate.

Key ideas

• A capped call payoff can be represented as a call spread with strikes separated by the cap amount.
• The position is long the lower-strike call and short the higher-strike call.
• The spread representation allows valuation by pricing the two calls separately and taking their difference.

Tags

# interpret payoff


# interpret payoff












How can the payoff f = min(max(S - K1, 0), K2) be interpreted?

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/77727

Note that $$min(max(S-K_1,0),K_2)=max(S-K_1,0)-max(S-(K_1+K_2),0)$$ so this is the payoff of a call spread (you're long the $K_1$ strike and short a $K_1+K_2$ strike). Then you can use standard Black-Scholes on each option to get your results.

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