Homework SourseA trader sells 10 call option contracts on a certain stock T
A trader sells 10 call option contracts on a certain stock. The option price is $6, the stock price is $40, and the option’s delta is 0.4. The trader’s portfolio consists of short call and long stock.
A.) Find the number of stocks purchased to make your portfolio delta-neutral.
B.) When the stock price increases by $2, price that your portfolio is delta-neutral by showing that gain and loss are offset.
A trader sells 10 call option contracts on a certain stock. The option price is $6, the stock price is $40, and the option’s delta is 0.4. The trader’s portfolio consists of short call and long stock.
A.) Find the number of stocks purchased to make your portfolio delta-neutral.
B.) When the stock price increases by $2, price that your portfolio is delta-neutral by showing that gain and loss are offset.
A.) Find the number of stocks purchased to make your portfolio delta-neutral.
B.) When the stock price increases by $2, price that your portfolio is delta-neutral by showing that gain and loss are offset.
Solution
A short call option has negative delta hence delta of 1 short call option=-0.4
Total delta of options=10*(-0.4)=-4
Delta of 1 stock=1
Hence,number of stocks needed=4/1=4
If stock price increases by 2
Value of stock position=42*4=168 gain on stocks=168-4*40=8
Value of option position=10*(6-2*0.4)=52 loss on options=10*6-52=8
Hence gain and loss offset each other and portfolio is delta neutral
