Question

In: Finance

3. Options contracts for corn are listed below. A single option contract is for 5,000 bushels,...

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?

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago
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