You must select a non-Dividend Paying Stock and this stock **must** be
approved by me since no overlap is allowed since stocks must be unique to each
student.

I choose Google

Select a non-dividend paying stock for which at least six calls and six puts have traded on a day for expiration of May or June. Once you have selected this stock, download the following on the same day:

- The stock price and its price history for the past five years
- The call and put option prices for the
following:
- The Strike price closest to the current stock price

- The Strike price just below the Strike price in Part a.

- The Strike price just below the Strike price in Part a.

- Of course, all three strike prices
- The current date and maturity date of the options
- The government rate with maturity period closest to the maturity of the options (from www.federalreserve.org)

You will use this option data for Assignments 1 to 5

You should consider the following positions (including synthetic positions):

- Purchased and written (sold) calls and puts and strike prices
- Purchased and written (sold) Bull Money Spreads with all combinations of calls and puts and strike prices
- Purchased and written (sold) Straddles with all combinations of calls and puts and strike prices
- Purchased and written (sold) Butterfly spreads with call and puts (all three strike prices are needed)

Consider all positions specified in Referenced Option Trading Strategies above and assume that the stock price may go up 20% by maturity or down 20% by maturity.

- Specify the most profitable position if the stock goes up 20%
- Specify the most profitable position if the stock goes down 20%
- Discuss the risk of taking the most profitable position versus simply buying the stock (for the up 20% case) or shorting the stock (for the down 20% case)

Be sure to justify all your positions with Excel calculations, including any profit diagrams you feel are necessary to justify your conclusions.

Consider all the positions specified in Referenced Option Trading Strategies above. You must specify the following:

- The price(s) at maturity for which each position has zero profits (the breakeven price(s))
- The price(s) at maturity where the profit
diagrams cross for the following combinations:
- The purchased call versus the purchased bull money spread with calls

- The purchased put versus the written (sold) bull money spread with puts

- The purchased straddle centered at the middle strike price versus the purchased butterfly spread with calls

You cannot use Excel graphs to approximate these prices - you must determine the exact prices.

Based on these prices, provide a discussion to a client demonstrating why certain strategies should be used within a specified price range at maturity.

Assume that the behavior of stock prices over the last three years (from the date you obtained the option data) provides your best guess as to the behavior of prices going forward. You should use this data to calculate the mean, standard deviation (“volatility’) and skew based on the daily rate of return (in log form).

Using the Monte Carlo simulation procedure discussed in class, generate 100 possible prices of your stock at expiration of the option. Based on this, generate the following for all positions specified in Referenced Option Trading Strategies and the simple long or short position in the stock:

- The mean, standard deviation, skew and kurtosis of all positions based on the dollar performance of each strategy
- The mean, standard deviation, skew and kurtosis of all positions based on the rate of return performance of each strategy

Based on this data (as well as your conclusions from Assignments One and Two), provide a recommendation to your client as to which position should be taken, completely justifying your reasoning.

Assume that you have a friend that firmly believes that the stock follows a binomial process. This friend wants to hedge 100 call option contracts at each strike price (your friend is a stupid trader who does not know how to hedge his risk from selling these call options - be sure to charge him an enormous consulting fee). You should provide the following:

- A discussion on the pros and cons of assuming a stock follows a binomial process
- The investment in the underlying stock and the investment in government securities for each call option that will hedge the trader’s positions
- An explanation on why the trader must change his hedge on a daily basis until he ends up liquidating his (written) position in each call option
- The implied range of Put prices at each strike price

Your friend suddenly changes his mind and now firmly believes that the stock follows a Geometric Brownian motion (i.e., the Black-Scholes-Merton process we used in class). He still wants to hedge 100 call option contracts at each strike price. You should provide the following:

- A discussion on the pros and cons of assuming a stock follows a binomial process
- The investment in the underlying stock and the investment in government securities for each call option that will hedge the trader’s positions
- An explanation on why the trader must change his hedge on a daily basis until he ends up liquidating his (written) position in each call option
- The implied range of Put prices at each strike price

Assume that the date is April 3^{rd} and your
ignorant friend want to go long in the SP500 E-Mini contract for June 2019. This contract is $50 times the Index Value
and matures on June 15^{th} (73 days).

Your friend has no idea what he should pay for this contract (really – charge him an enormous fee). You have the following information

- The Spot Price of the S&P 500 is 2,873.40
- The (average) dividend yield is 1.83% per annum on the S&P 500
- The three-month treasury yield is 2.37% per annum

Based on this information, provide your friend with the “fair” futures price (the futures price at which no money changes hands) and why this price must always be correct.

Calculating non-Dividend Paying Stock

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