Econ 337 Spring 2019 Homework #3 Due 2/21/19 70 points
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1 Econ 337 Spring 2019 Homework #3 Due 2/21/19 70 points For the following questions use the attached futures and options data. Assume historical expected basis of -$0.30 per bushel and a commission of $0.01 per bushel for both crops. Show the math and draw the graph. 1. A speculator buys a put option on Dec corn futures. What does she pay for the option? At what price does she breakeven (where her return is equal to zero)? If the Dec corn futures price falls to, what is her return? She pays the $ premium and the $0.01 commission for a total of $ Her breakeven price is equal to Strike Price Premium Commission = - $ $0.01 = $ If the Dec corn futures price falls to, her return is: Max(0, Strike Price Futures Price) Premium Commission = Max(0, - ) - $ $0.01 = Max(0, ) - $ $0.01 = - $ $0.01 = $ Put - - $9.00 $10.00 Futures Price
2 2. A hedger (producer) buys a put option on Dec corn futures. What is her floor price with the option in place? If the Dec corn futures price falls to, what is her net price? Floor Price = Strike Price + Basis Premium Commission = - $ $ $0.01 = $ If the Dec corn futures price falls to, her net price is equal to her floor price, $ To see this, look at the graph. She receives $2.70 from the cash market ( - $0.30, futures + basis) and she receives $ from the put option (see the return from put option in question 1). Cash Net Put - - $9.00 $10.00 Futures Price
3 3. Instead of buying that put option, the producer does a short hedge. What is her floor price with the short hedge in place? If the Dec corn futures price falls to, what is her net price? Floor price with a short hedge is the expected price with a short hedge. Expected Price = Futures Price + Basis Commission = $4.02 $0.30 $0.01 = $3.71 If the Dec corn futures price falls to, her net price is $3.71. Net Price = Cash + Futures Return = (Futures + Basis) + (Old Futures Futures Commission) = ( $0.30) + ($4.02 $0.01) = $ $1.01 = $3.71 Cash Net - - $9.00 $10.00 Futures Price Hedge
4 4. If the speculator in question 1 also sold a call option on Dec corn futures, does that change her breakeven price? If so, what is the new breakeven price? Yes, her breakeven price changed. From question 1, her original breakeven price was $ The change is due to selling the call option. At her old breakeven price, she now receives the premium on the call minus the commission ($ = $ $0.01). So her new breakeven price is now at $3.7975, her old breakeven plus the call return. Put - - $9.00 $10.00 Futures Price Net Call
5 5. If the hedger in question 2 also sold a call option on Dec corn futures, does that change her floor price? If so, what is the new floor price? Yes, her floor price changed with the addition of the call option premium less the commission. New Floor Price = Old Floor Price + Call Option Premium- Commission = $ $ $0.01 = $ Old Net New Net - - $9.00 $10.00 Futures Price Call
6 6. A speculator buys a call option on Dec corn futures. What does she pay for the option? At what price does she breakeven? If the Dec corn futures price falls to $3.50, what is her return? If the Dec corn futures price rises to, what is her return? She pays the premium and commission, $ $0.01. So she pays $ Her breakeven price is equal to: Strike Price + Premium + Commission = + $ $0.01 = $ Her return is: Max(0, Futures Price Strike Price) Premium Commission At $3.50 futures, her return is: Max(0, $ ) - $ $0.01 = Max(0, -$0.50) - $ $0.01 = - $ $0.01 = -$ At $5 futures, her return is: Max(0, - ) - $ $0.01 = Max(0, ) - $ $0.01 = - $ $0.01 = $ Call - - $9.00 $10.00 Futures Price
7 7. A hedger (processor) buys a call option on Dec corn futures. What is her ceiling price with the option in place? If the Dec corn futures price falls to $3.50, what is her net price? Ceiling Price = Strike Price + Basis + Premium + Commission = - $ $ $0.01 = $ If the Dec corn futures price falls to $3.50, her option will expire worthless and her net price is: Net Price = Cash + Premium + Commission = Futures + Basis + Premium + Commission = $ $ $ $0.01 = $ Cash Call Net - - $9.00 $10.00 Futures Price
8 All prices and premiums are listed in dollars per bushel Dec Corn Futures Price 4.02 Options Strike Price Premium Options Strike Price Premium Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call Put Call
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