Question

You write a call option with X=60 and buy a call with X= 70. The options are on the same stock and have the same maturity date. One of the calls sells for $3; the other sells for $9.

1. Write out the payoff and profit function for this strategy at the option maturity date
2. Draw the payoff graph for this strategy at the option maturity date.
3. Draw the profit graph for this strategy.
4. What is the break even point for this strategy? Is the investor bullish or bearish on the stock?

Answer 1

Payoff function = -max(St - X1, 0) + max(St - X2, 0)

X1 = 60, X2 = 70

Profit function = -max(St - X1, 0) + max(St - X2, 0) + Net premium received

Payoff diagm 20 St 90 go 7o 4 0 -iD - 20 dtagsa m Pro ft 4 St 90 go 50 40

The call option with a lower strike sells for a higher premium. So, the call option with X = 60 has a premium of $9, while the call option with X = 70 has a premium of $3.

Net premium received = 9 - 3 = $6

As long as the stock stays below $60, the investor gets to keep $6

The breakeven for this strategy is Lower Strike + Net premium received = 60 + 6 = $66

The investor starts to lose money beyond the stock price of $66 and his loss is capped at the stock price of $70. Maximum loss is $4.

The investor is bearish on the stock as he has shorted the lower strike call option while limiting his loss by buying a higher strike call option.

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