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Maximum gain on 200 shares with two short calls

Question

You buy 200200 shares of a stock at $230 and, against them, sell one contract (100100 shares) of a December $240 call for $10.50 and one contract of a December $250 call for $9.50, both with the same expiry. Assuming any call in the money at expiry is exercised, what is the strategy's maximum profit?

Short answer

$5000. The premiums bring in (10.50+9.50)×100=$2000(10.50+9.50)\times100=\text{\char36}2000. At any price of $250 or more, 100100 shares are called away at $240 (gain $1000) and 100100 at $250 (gain $2000), so the most you can make is 2000+1000+2000=$50002000+1000+2000=\text{\char36}5000.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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