Question

Consider:

(a) Stock trades for $100;

(b) Calls with exercise prices of $90, $100, and $110 trade at prices of $17.11, $10.69, and $6.10 respectively.

If a person buys a $90 call, writes two $100 calls, and buys a $110 call, what is her higher break-even point? The answer is 108.17, how do you solve this?

Answer 1

Higher Break Even Point occurs at the of call option with highest strike price ie., $110

Thus Net Benefit/(Loss from Premium of buying and writing Calls = - Premium paid on $90 Call + Premium received on $100 Calls - Premium Paid on $110 Call

Net Benefit/(Loss) from Premium of buying and writing Calls = - 17.11 + 10.69 * 2 - 6.10

Net Benefit/(Loss) from Premium of buying and writing Calls = - 1.83

Higher Break Even Point = Higher Strike Price + Net Benefit/(Loss)

Higher Break Even Point = 110 - 1.83

Higher Break Even Point = $108.17

Proof at $108.17:

$90 Call option will get exercised = thus payoff = Stock Price at expiration - Call Strike Price = $108.17 - 90 = $18.17

$100 Call option will get exercised by holder = thus payoff = (-Stock Price at expiration + Call Strike Price)*2 = (-$108.17 + 100) = -$16.34

$110 Call option will not get exercised = thus payoff = 110 - 108.17 = $1.83

Thus add all payoff's = $18.17 - 16.34 + 1.83 = $0 (there is not profit and no loss)

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