In: Finance
3. Options contracts for corn are listed below. A single option contract is for 5,000 bushels, but prices are quoted per bushel. For example, if someone wanted to purchase a December 2018 put option with a strike price of $3.60, then the premium would be $400 (= $0.08 x 5,000 bushels). The maturity dates are the same as the futures contracts.
Expiration | Strike | Call | Put |
DEC 2018 | $3.60 | $0.41 | $0.08 |
DEC 2018 | $3.70 | $0.35 | $0.12 |
DEC 2018 | $3.80 | $0.30 | $0.17 |
DEC 2018 | $3.90 | $0.26 | $0.22 |
DEC 2018 | $4.00 | $0.22 | $0.29 |
DEC 2018 | $4.10 | $0.19 | $0.36 |
DEC 2018 | $4.20 | $0.16 | $0.43 |
Firm A needs to purchase 10,000 bushels of corn in December 14, 2018. The current price per bushel of corn is $3.60. Assume the firm cannot pass on any increased costs due to changes in price to their customers.
Suppose Firm A decides to purchase option contracts to protect itself from corn prices above $3.90 per bushel.
(a) What will be the total premium Firm A has to pay for these contract(s)?
(b) What would be the total payoff if the price of corn at maturity is $3.70?
(c) What would be the total payoff if the price of corn at maturity is $4.00?
(d) What would be the total payoff if the price of corn at maturity is $4.20?
Call option gives the holder the right to purchase a particular amount(lot size) of underlying stock at a strike price on the expiration date.
Put option gives the holder the right to sell a particular amount(lot size) of underlying stock at a strike price on the expiration date.
In this case firm A would buy 2 lots(10,000 bushels) of Call options of strike $3.9 with premium of $0.26 of december maturity.
A) Total premium = premium * number of bushels =0.26 * 10000 = $2600
B) At maturity spot price: $3.7 Strike price= $3.9
Payoff = (spot price - strike price) * 10000 bushels = ($3.7 - $3.9) * 10000 = - $2000
Total payoff = Payoff - Premium = -$2000 - $2600 = -$4600
C) At maturity spot price: $4 Strike price= $3.9
Payoff = (spot price - strike price) * 10000 bushels = ($4.0 - $3.9) * 10000 = $1000
Total payoff = Payoff - Premium = $1000 - $2600 = -$1600
B) At maturity spot price: $4.2 Strike price= $3.9
Payoff = (spot price - strike price) * 10000 bushels = ($4.2 - $3.9) * 10000 = $3000
Total payoff = Payoff - Premium = $3000 - $2600 = $400