Question

Question 3. A 1-year European put option on a stock with strike price of $50 is quoted as $7; a 1-year European call option on the same stock with strike price $30 is quoted as $5. Suppose you long one put and short one call (one option is on 100 share).

a) Draw the payoff diagram for your put position and call position.

b) After 1-year, stock price turns out to be $45. What is your total payoff? What is your total profit/loss?

Answer 1

a) Payoff diagram for the long put position is as below

Strike price is $50, option price is $7

From the payoff diagram you can see that the premium paid $7 and hence it is in the negative side. When the the stock prices less than 50 the long put option will be e in profit. When the price goes below 50 then what we lose the premium paid.

Payoff diagram for short call option is as below

Strike price $30 and option price is $5

From the diagram I can see e that for short call option the gain is $3. When the price of the stock goee below 35 then the option premium price goes down and the loss is unlimited.

b) when the stock price is $45, the long put option will be in the money and the short call option will be out of the money. However, the cost price of the long put will be $50-$7 = $43 ( as the option price paid is the cost of the option, the buyer will get profit only if the stock goes below $43). Hence on long put option, the buyer will be in net loss of $2 when the price after 1year is $45.

Similarly, on the short call option, the net price for the seller is $30+$5 =$35. When price goes above $35, the seller of call option gets loss. Hence on the short call option, the seller will be in net loss of $10.

Hence, the total loss if a person buys both these options will be $12.