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27/08/2022
Problem 5. Valuing Stock Options: The Black-Scholes-Merton Model (10 marks)
This is a Bloomberg-based exercise. Before making any calculations, please do the following:
Go to the Trading Room and login in Bloomberg (G42 2.16 at Gold Coast Campus and N50 0.32E at Nathan Campus). You can find the Trading Room timetable in the folder “Bloomberg Activities” under “Course Content” on [email protected] In the same folder, you can also find materials which will be useful for your work with Bloomberg. Search for the share of Google (Bloomberg ticker: GOOGL). Download daily price data for the Google share price over the last 250 trading days. Go to the Options Monitor showing option contracts on the Google share (Use OMON <Go> ). Find the put and the call options with o Expiration in October 2017 and o Strike price $940 Make screenshot(s) showing the prices of these options. Hint: You can make screenshots and email them to yourself via GRAB <Go>. Use LR <Go> to obtain a LIBOR value for the same day as the option price data. Choose the USD LIBOR with time horizon closest to the time-to-maturity of the options. Document with a screenshot.
Once you have this data, you can start with the calculations:
(a) Calculate with Excel the daily returns of the Google share and calculate afterwards their standard deviation over the last 250 days. (b) Convert the daily volatility to volatility per annum. (c) Use the Black-Scholes-Merton pricing formulas for European options and calculate the theoretical prices of a European call and a European put option with expiration in October 2017 and strike price of $940 on the Google share. Use the LIBOR rate you have downloaded as a proxy of the risk-free rate. (d) Insert the Black-Scholes-Merton prices you just calculated in the put-call-parity. Does it hold? (e) How would the result of (c) change if a dividend of $2 is expected in four months? (f) Compare the Black-Scholes-Merton prices you calculated in (c) with the prices of these options given in Bloomberg (use the average of bid and ask price as the Bloomberg price). Are there any deviations between the theoretical prices you have calculated and the prices given in Bloomberg? If yes, what could be possible reasons for these deviations?
Hint: There are no dividends announced for August, September and October 2017.
Additional submission requirements for problem 5: Additionally to your calculations, please insert in the Word file that you will submit the screenshots you have made showing the spot price, option prices and LIBOR which you used. Upload the Excel file showing the calculation of the standard deviation in (a).
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