Question

You are an options trader with an investment bank. It appears that the S&P500 index will trade between 2700 and 2500 for the next few months. How can you use options to create a profitable investment opportunity?

1 )Please explain in detail.

2) Show the payoff and profit in a graph.

Answer 1

If the S&P500 index is expected trade within a range of 2700 and 2500, then a short strangle can be constructed to make a profit.

1) Selling a short strangle include selling a call option with strike price equal to the upper bound of the range and a put option with strike price equal to the lowe bound of the range.

Sell a call option with strike, X = 2700

Sell a put option with strike, X = 2500

We receive premium for selling this strangle.

Lets say, call option is selling for $25. C = 25

And, put option is selling for $27. P = 27

2. The maximum profit is the total premium = C + P = 25 + 27 = $52

This happens when S&P500 expires within the range.

Upper breakeven point = 2700 + 52 = 2,752

Lower breakeven point = 2700 - 52 = 2,648

Call option payoff = -max(St - X, 0) = -max(St - 2700, 0)

Put option payoff = -max(X - St, 0) = -max(2500 - St, 0)

Short strangle payoff = Call option payoff + Put option payoff

Short strangle payoff = -max(St - 2700, 0) -max(2500 - St, 0)

Short strangle profit = Short strangle payoff + Total premium received

Short strangle profit = -max(St - 2700, 0) -max(2500 - St, 0) + 52

Screenshot with formulas