Mispriced calls at strikes 1000, 1010, 1020
Question
Three calls on the same underlying and expiry are quoted as follows:
| Strike | Price |
|---|---|
| 1000 | 4 |
| 1010 | 3.5 |
| 1020 | 2.75 |
These prices admit an arbitrage. How many dollars can you lock in for certain?
Short answer
$0.25. Call prices must be convex in strike, but . Buy the 1000 and 1020 calls and sell two 1010 calls: this butterfly has a non-negative payoff everywhere, yet you receive to put it on.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
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
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