Question

The 1-week call options on the Alibaba stock with strike prices of $185, $190, and $195 are $10, $7, and $5.5, respectively. An investor longs a butterfly spread using these three options. Specifically, he longs 100 call options with the strike price $185, shorts 200 call options with the strike price $190, and longs 100 call options with the strike price 195. What is the investor's maximum gain from this strategy?

Answer 1

Investment in this butterfly spread= Premium received from call option of strike price 190- Premium Paid for call option of 185 and 195

=7*200-100*(10+5.5)=$-150

Now, Payoff when underlying price is at $180 at expiry= (Payoff from call option of $185+ Payoff from call option of $190+ Payoff from call option of $195)-150

=0+(180-190)*0+0-150=$-150

Now, Payoff when underlying price is at $185 at expiry= (Payoff from call option of $185+ Payoff from call option of $190+ Payoff from call option of $195)-150

=0+200*0+0-150=$-150

Payoff when underlying price is at $190 at expiry= (Payoff from call option of $185+ Payoff from call option of $190+ Payoff from call option of $195)-150

=100*(190-185)+200*(190-190)+100*0-150=$350

Payoff when underlying price is at $195 at expiry= (Payoff from call option of $185+ Payoff from call option of $190+ Payoff from call option of $195)-150

=100*(195-185)+200*(190-195)+0-150=$-150

Payoff when underlying price is at $200 at expiry= (Payoff from call option of $185+ Payoff from call option of $190+ Payoff from call option of $195)-150

=100*(200-185)+200*(190-200)+100*(200-190)-150=$350

Hence, at various strike price we have seen that, your maximum gain from this strategy is $350.