MGMT_41150_Homework2_20_02_2024 no solutions

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Purdue University *

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41150

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Finance

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Apr 3, 2024

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Homework#2 - 150 Points Total *Due in class on March 19 th . Please type as much as possible of your answers using your computer, to aid grading. Whenever needed (e.g., if you need to write equations), feel free to do so by hand. Bear in mind that if these equations are difficult to read, I may not understand what you wrote. **You may work in groups of up to 4 people . If you work in a group, you should submit only one copy of the homework. Make sure each one of you is listed at the top of the page (with their full names, and email address clearly legible). To keep things simple I am going to ask that if you plan on working with others, you choose from colleagues in your same section. Note: Working in group is not a requirement, and I do not grade homework submitted by individuals differently from homework submitted by groups. ***Please print this HW one-sided and write in the space provided (I will try to leave plenty of space, but use an additional page if you need to). ****Please show all work for full credit!
Q1 (20 points) The current spot price of gold is $1,315 per ounce. The 11-month risk free rate is 0.75% (annualized, continuously compounded). Your broker quotes you an 11-month futures contract at $1,391. Assume storage costs are $0.23 monthly per ounce, paid at the end of the storage period. What is the correct theoretical futures price? What is the arbitrage trade/profit (per contract) using the price you were quoted? (Reminder: gold contracts are based on 100 ounces of gold)
Q2 (25 points) You are looking at options on Dumbledore Corporation with 14 months until expiration and a strike price of $85. The risk free rate for 14 months is 4.5% (annualized with continuous compounding). The firm is not expected to pay any dividends over the next 14 months, and the current stock price is $92.78. The price of the call option is $13.06 and the put option is $2.11. Find the arbitrage trade given these prices and show the profit for each contract.
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Q3 (25 points) You are looking at options on Ravenclaw Corporation with 13 months until expiration and a strike price of $50. The risk free rate for maturities between 1 and 13 months is 2.5% (annualized with continuous compounding). The firm is expected to pay a dividend of $1.20 each quarter over the next 13 months (i.e. a $1.20 dividend in 3, 6, 9 and 12 months), and the current stock price is $48.11. The price of the call option is $3.14 and the put option is $4.79. Find the arbitrage trade given these prices and show the profit for each contract.
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Q4 (45 points) Use the data below to answer questions a) through d) for Malfoy Corporation, which is currently trading for $31 per share: Call Options Put Options Strike Bid Price Ask Price Strike Bid Price Ask Price $20 $12.15 $12.33 $20 $0.76 $0.89 $25 $7.26 $7.39 $25 $1.05 $1.18 $30 $2.55 $2.66 $30 $1.84 $1.97 $35 $1.46 $1.59 $35 $5.67 $5.81 $40 $0.88 $0.97 $40 $10.79 $10.95
4.1 Find the cost of a butterfly spread using the call options with strikes of 25, 30 and 35. Draw the profit diagram and show the profit for the ending stock price in the appropriate ranges.
4.2 Find the cost of a straddle using options with a strike price of 30. Draw the profit diagram and show the profit for the ending stock price in the appropriate ranges. 4.3 Find the cost of a strangle using the options with strikes of 20 and 40. Draw the profit diagram and show the profit for the ending stock price in the appropriate ranges.
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Q5 (35 points)
A US investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?