Question

Consider an option strategy where the investor simultaneously buys one call with an exercise

price of $100, sells two calls with an exercise price of $110 and buys one call with an exercise

price of $120 all with the same expiration date. Calculate the payoff of the strategy when

spot price of the underlying is less than $100, between $100 and $110, between $110 and

$120, and greater than $120 at expiration. Draw a payoff diagram for this strategy. What is

the bet being made with this strategy? (This is all the info they gave me)

Answer 1

This is an example of long butterfly call spread, it can be created by buying one in-the-money call option with a low strike price selling (short) of two at-the-money call options, and buying one out-of-the-money call option with a higher strike price

The cost of creating long butterfly call spread = Price of call option of strike price $100 – 2 * Price of call option of strike price $110 + Price of call option of strike price $120

Payoff from call option if stock price is more than the strike price = Stock price – Strike price

Payoff from call option if stock price is less than the strike price = 0

Profit/ (loss) = payoff – call price

Payoff from selling the call option if strike price is more than stock price = Strike price – stock price

Payoff from selling the call option if strike price is less than stock price = 0

Profit/ (loss) = Call price – payoff

Stock Price at Expiration	Long 1, 100 Call Payoff at Expiration	Short 2, 110 Calls Payoff at Expiration	Long 1, 120 Call Payoff at Expiration	Net Payoff at Expiration
90	0	0	0	0
100	0	0	0	0
105	5	0	0	5
110	10	0	0	+ 10
115	15	2*-5 = -10	0	+5
120	20	2 *-10 =-20	0	0
130	30	2 *-20 =-40	10	0

The investor will make highest profit if the Stock Price at Expiration is equal to $110. Therefore investor is betting for that.