Question

You have an exclusive contract to supply oranges to Juice&Co. and you are expected to deliver 10,000 oranges in one year from now at the market price in place at that time. Your production cost to farm and harvest the 10,000 oranges will be $2,000 in one year. Today’s market price for one orange is $0.52. Assume that the continuously compounded risk free interest rate is 6%..

You expect the price of oranges to be between $0.50 and $0.55 next year, and you have decided to hedge your risk using one year European options: you buy 10,000 put options with strike price $0.52 for $84 (per option) and sell 10,000 call options with strike price $0.54 for $74 (per option).

1. a) What is the total cost of your options portfolio?

2. b) Determine the range of possible net profits you can get from your supply contract and

   options portfolio one year from now. Show your work in detail.

Answer 1

Asnwer to (a)

since we have bought the put option with strike price of $0.52 we have to pay premium of $84

Further, we have sold the call option with strike price of $0.54 we will received the premium of $74

Hence total cost of option portfolio is ($84 - $74) = $10

Answer to (b)

scenario 1 where orange price will be $0.5 after one yera.

profit from supply contract

proceedes from supply of orange $0.5 * 10,000 = $5,000

cost of harvesting = $2,000

hence, net profit = $3,000

payoff from option contracts

we have bought put option contract with strike price of $0.52 and spot after one year is $0.5 hence we will receive $0.02 per orange. Hence, total payoff uder put contract will be $200 (10,000*$0.02)

we have sold the call option contract withstrike price of $0.54 and spot after one year is $0.5 hence call option contract will lapse and payoff will be nil

hence total payoff under option potrfolio = $200

however, cost of option portfolio is $10

hence, profit = $190

scenario 2 where orange price will be $0.55 after one yera.

profit from supply contract

proceedes from supply of orange $0.55 * 10,000 = $5,500

cost of harvesting = $2,000

hence, net profit = $3,500

payoff from option contracts

we have bought put option contract with strike price of $0.52 and spot after one year is $0.55 hence put option contract will lapse and payoff will be nil

we have sold the call option contract withstrike price of $0.54 and spot after one year is $0.55 hence we have to pay $0.01 per orange to call option buyer. Hence, pay off will be (10,000*-$0.01) = -$100

hence total payoff under option potrfolio = -$100

however, cost of option portfolio is $10

hence, profit = -$110 or Loss of = $110