Call spread payoff capped at 20
Question
Find a portfolio of vanilla options with this payoff at expiry: zero if the spot is below , spot minus for spot between and , and a flat for spot above .
Short answer
Buy a call struck at and sell a call struck at . Below both are worthless; between and only the long call pays ; above the payoffs give . 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.
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Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
- Option Trading Strategies: Spreads, Combinations, and Payoff Engineering
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