Question

5. ) A call option on an S&P 500 futures contract has an exercise price of 1490; the call premium is currently $6.50. On the same date, a put option on the S&P 500 futures contract has an exercise price of 1490; the put premium is currently $7.50. The two options have the same expiration date.

1. Is the current index value greater than or less than 1490. How do you know?

2. Assume that the S&P 500 index is 1485 at expiration:

• Should the call option be exercised or should it be left to expire? What is the net ($) gain or loss after accounting for the premium paid to purchase the option?

• Should the put option be exercised or should it be left to expire? What is the net ($) gain or loss after accounting for the premium paid to purchase the option?

Answer 1

Sol:

A) Under call option, if the share price / market price is higher than strike price / exercise price then only the option will be exercised otherwise it will be lapsed.

Given, strike price = 1490

Therefore, to exercise the option the share price should be more than strike price i.e > 1490.

Hence,Current index value should be greater than 1490 in order to exercise the future contract.

Under put option, if the strike price is higher than share price then only the option will be exercised otherwise it will get lapsed.

Given, strike price = 1490

Inorder to exercise the option , the share price should be lower than 1490.

Hence, Current Index value should be lower than 1490 inorder to exercise the future contract.

B)

Option Share price/Market price Strike price/ Exercise price Action Payoff Net profit & loss = Payoff - premium

Call 1485 1490 Lapse 0 0- 6.5 = $ -6.5

Put 1485 1490 Exercise 5 5- 7.5 = $ -2.5

  

Net  loss = $ 9

i) Under call option , S&P 500 is below the strike price at expiration. It is called "out of money". Therefore, option is worthless to exercise and also ceases to exist because it is cheaper to buy the shares in the open market. Due to which the trader need to sell it prior to expiry.

$ 6.5 is the net loss after accounting for the premium paid to purchase the option.

ii) Under put option, the option will be exercised only when the strike price will be higher than the share/ market price. S&P 500 is below the strike price at expiration. The option is worth exercising. It is called " In the money". In this case, there is chance to earn a profit.

And the determination of profitability is based upon the premium paid and commission paid.

$ 2.5 is the net loss after accounting for the premium paid to purchase the option.