Skip to content

Call spread payoff capped at 20

Question

Find a portfolio of vanilla options with this payoff at expiry: zero if the spot is below 100100, spot minus 100100 for spot between 100100 and 120120, and a flat 2020 for spot above 120120.

Short answer

Buy a call struck at 100100 and sell a call struck at 120120. Below 100100 both are worthless; between 100100 and 120120 only the long call pays S−100S-100; above 120120 the payoffs give (S−100)−(S−120)=20(S-100)-(S-120)=20. This bull call spread is model-free.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.38, p.20; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free