Estimate the stock price volatility. What is the standard error of your estimate?

Solution Preview

See the attached file.

Question:
Suppose that observations on a stock price (in dollars) at the end of each of 15 consecutive weeks are as follows:
Estimate the stock price volatility. What is the standard error of your ...

Solution Summary

This post explain how to estimate stock price volatility

1. Suppose the closing stockprices for 10 consecutive trading days are $20.00, $20.10, $19.90, $20.00, $20.50, $20.25, $20.90, $20.90, $20.90, $20.75. Estimate the volatility of the stock per annum.
2. A stockprice is currently $70. Over each of the next two three-month periods it is expected to go up by 8% or down by 6%

Volatility cannot be directly observed for calculation purposes of the option pricing model. Therefore, it may be determined from:
historic volatility.
forward-looking volatility.
implied volatility.
any of the above.

3. Using the values of St, K, rf , and T specified below, use your spreadsheet and trial and error (or Solver) to estimate the implied volatility (accurate to four decimal places) of a call with a price of $7.2568.
St = $60.00
K = $60.00
rf = 0.02
T = 0.3333 (3 months).

The Dow Jones Industrial Average on January 12, 2009 was 8474 and the price of the March 84 call was $4.50. Assume the risk-free rate is 3.2%, the dividend yield is 2% and the option expires on March 20, 2009 (Note that the options are on the DJI dividend by 100.)
Q1: Use Derivagem to calculate the implied v

Using the data in the following table, estimate (a) the average return and volatility for each stock, (b) the covariance between the stocks, and (c) the correlation between these two stocks.
Realized Returns
Year Stock A Stock B
1998 -10% 21%
1999 20% 30%
2000 5% 7%
2001 -5% -3%
2002 2% -8%
2003 9%

For a call option on a non-dividend paying stock, the strike price is $29, the stockprice is $30, the risk-free rate is 6% per annum, the volatility is 20% per annum and the time to maturity is 3 months. What is the price of the call option?
a. $2.02
b. $2.35
c. $2.67
d. $2.89
e. None of the above.

Option: Which of the following events are likely to increase the market value of a call option on a common stock? Explain.
a. An increase in the stock's price.
b. An increase in the volatility of the stockprice.
c. An increase in the risk-free rate.
d. A decrease in the time until the option expires.

AD 13: The Dow Jones Industrial Average on August 15, 2008 was 11,660 and the price of the December 117 call was $3.50. Assume the risk-free rate is 4.2%, the dividend yield is 2% and the option expires on December 25 (options markets are closed the day after Christmas).
Q1: Use Derivagem to calculate the implied volatility o

1. Assume that the CAPM is a good description f stockprice returns. The market expected return is 7% with 10% volatility and the risk-free rate is 3%. New news arrives that does not change any of these numbers but it does change the expected return of the following stocks:
Expected Return Volati