Question

ption Underlying Asset Strike Type Call Put Call Put Call Call Put Call Put Put Futures Price Contract Size Wheat Corn Silver Crude Oil Gasoline Copper Heating Oil Gasoline Soybeans Natural Gas 64.75 $3.00 $17.25 574.25 $1.75 $2.75 $2.00 $1.75 $10.25 $3.25 $4.5550 $3-2300 $18.6100 $59.1400 $1.7160 $3.2210 $2.0703 $1.7160 5,o00 bu 5,ooo bu 5,000 02 1,000 bbl 42,00o gal 25,000 lb 1,000 bbl 42,000 gal 6 $9.7525 5,000 bu 20 3.0330 10,000 mmBTU ULL SPREAD 5. BUTTERFLY SPREAD Three call options have the same expiration date and strike prices of s14.00, s18.00, and $22.00. Explain how to create a butterfly spread from the above options. Clearly indicate which options should be bought, which ones should be sold, and in what quantities. a. b. Calculate payoff of the spread for the underlying asset prices of $11.0o, $15.00, and $19.00 Please show work

Please show work. This is just a simple butterfly spread. Thank you.

Answer 1

a) A Long Butterfly is an options strategy which consists of 3 options with different strikes such that they are purchased and sold at the same time.

Assume price of 1st option is $3, 2nd option is $2 and 3rd option is $1.

Ignore the volatility column as it is calculated according to black-scholes model.

Buy /Sell Quantity Call /Put/ Stock Strike Days to Expiry Volatility, % Premium Debit / Credit Call 14 365 40.5391 3 X Sell Call 18 365 48.9147 Call 365 Total

In 365 Days At Expiry 35 25 15 05 05 75 175 20 225 25 275 30 325353754

b) Clearly, at the given asset prices, we have the following payoffs:

At $11, payoff is 0

At $15, payoff is $1

At $19, payoff is $3