Skip to content

Mispriced calls at strikes 1000, 1010, 1020

Question

Three calls on the same underlying and expiry are quoted as follows:

StrikePrice
10004
10103.5
10202.75

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 3.5>12(4+2.75)3.5 > \tfrac12(4+2.75). Buy the 1000 and 1020 calls and sell two 1010 calls: this butterfly has a non-negative payoff everywhere, yet you receive 2(3.5)−4−2.75=0.252(3.5)-4-2.75 = 0.25 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 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