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You are long 3 contracts of 1-yr futures on the S&P 500 index with delivery price...

You are long 3 contracts of 1-yr futures on the S&P 500 index with delivery price of $3,00, long 3 contracts of 1-yr put options on the index with strike of $2,400, and also short 3 contracts of 1-yr call options on the index with strike of $4,000. What will be your payoff at expiry if the index price (S_T) is $5,000?

Solutions

Expert Solution

The payoff is going to be the sum of payoffs from 9 contracts. Let us break the problem into three sub-parts - each consisting of three contracts as mentioned in the problem.

  1. Long 3 contracts of 1-year futures with delivery price of $3,000: - I'm obligated to purchase at $3,000 when the price is $5,000. Hence, the payoff on each contract is $2,000. Total payoff is $6,000.
  2. Long 3 contracts of 1-year put option on index with strike of $2,400: - Given the index price at expiry is $5,000 more than the strike price $2,400, the put options are not going to be exercised. Hence, there is no payoff.
  3. Short 3 contracts of 1-year call option on index with strike of $4,000: - Given the index price at expiry is $5,000 more than the strike price $4,000, I lose my right to purchase the index at $4,000 by shorting the call option because the other party would exercise the call option. I lose $1,000 on each contract. Total loss is $3,000.

Hence, adding the three, the total payoff is $3,000.

jeff jeffy answered 1 year ago
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