Question

You purchase one (1) call option with strike price 50 for $ 9 and write three (3) call options with strike 60 for $ 3. 4) Assume that you may purchase calls with strike price 70 for $ 1. How many options would you trade to prevent unbounded losses at maturity? What would be the maximum extent of your losses after the purchase? please show work

Answer 1

--> I have written 3 call options and purchased 1. Thus, I have 2 uncovered positions and hence I'll purchase (trade) 2 call options to prevent unbounded losses at maturity.

Maximum extent of loss after purchase

For calculation of loss, negative/minus indicate money received, positive/plus indicate money paid.

In case stock price at maturity below $50, all options expire worthless - loss will be premium paid less premium received, loss = $9 - (3*$3) + (2*$1) = $2 loss.

In case stock price at maturity above $70, all options are in money, loss will loss for case stock price below $50 plus the difference in strike prices, loss = $2 + (2*$70) + (1*$50) - (3*$60) = $2 + $140 + $50 - $180 = $192 - $180 = $12

For cases with stock price $50<stock price<$60, I'll have a loss below $2 or a profit.

For cases with stock price $60<stock price<$70, I'll have a loss below $12 or a profit.

Thus, maximum extent of my losses with the purchase of 2 call options at strike price $70 for $1 each, is $12.