I. Volatility

1. Download three months of daily stock prices for Meta Platforms Inc. (FB) from 8/10/2021 to 11/10/2021 a. from: finance.yahoo.com

2. Following the example in Chapter 15, compute the daily return.

3. Compute the standard deviation.

II. B-S Model

4. Lookup a. the yield on a three-month U.S. T-bill (from Federal Reserve bank).

5. Assuming the standard deviation is what you computed in part 3 and assume today is 11/10/2021, please determine the prices of the call and put that mature on 12/23/2021 and have the exercise price of $330 using the Black-Scholes basics model. a. Hint: When computing output variables, please use cell reference.

6. On 11/10/2021, the option premium of a call that matures on 12/23/2021 with K=$330 is $12.34. The option premium of a put option that has the same exercise price and maturity date is $14.35. Compare the option prices you computed in part 5 with these two trading prices. Are they the same? If they are different, why? III. Implied Volatility

7. Use the call option premium (trading price=$12.34) in part 5 to determine the implied volatility from the call option. a. Hint: You need to use goal seek function in Excel.

8. Assuming the standard deviation is what you computed in part 7 and assume today is 11/10/2021, determine the price of the call that expires on 12/23/2021 with the exercise price of $320 using the Black-Scholes basics model.

9. On 11/10/2021, the option premium of a call that matures on 12/23/2021 with the exercise price of $320 is $18.01. Compare the option price you computed in part 8. Are they the same? If they are different, why? IV. Binominal Tree Model

10. If we use binominal tree model to value the option, assume there are 30 steps (trees), what is u and what is d? (Please use the volatility computed in part I.3.)

V. Summary

Now you finished all the steps above, please go through what you have done and answer the following questions:

a. What variables affect option price (assuming the underlying stock doesnt pay dividend).

b. Among all the variables listed in part a, which one is the most difficult to get?

c. What are two common methods used to obtain the variable in part b.

d. When using Binomial model, there are two states in the future. In the up-state, the stock price is S0u and in the down-state, the stock price is S0d. Now you know u and d are not random. How u and d are determined?