Questions from Business Statistics

Q: If
follows the geometric Brownian motion process in equation (14

If
follows the geometric Brownian motion process in equation (14.6), what is the process followed by (a) y = 2S, (b) y=S2 , (c) y=eS, and (d) y=er(T-t)/S. In each case express the coefficien...

Q: A stock whose price is $30 has an expected return of

A stock whose price is $30 has an expected return of 9% and a volatility of 20%. In Excel, simulate the stock price path over 5 years using monthly time steps and random samples from a normal distribu...

Q: A stock price is currently 50. Its expected return and volatility

A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years? (Hint: ST > 80 when ln...

Q: A stock price is currently $50. Assume that the expected

A stock price is currently $50. Assume that the expected return from the stock is 18% and its volatility is 30%. What is the probability distribution for the stock price in 2 years? Calculate the mean...

Q: Suppose that observations on a stock price (in dollars) at

Suppose that observations on a stock price (in dollars) at the end of each of 15 consecutive weeks are as follows: 30:2; 32:0; 31:1; 30:1; 30:2; 30:3; 30:6; 33:0; 32:9; 33:0; 33:5; 33:5; 33:7; 33:5; 3...

Q: A financial institution plans to offer a security that pays off a

A financial institution plans to offer a security that pays off a dollar amount equal to ST2 at time T, where ST is the price at time T of a stock that pays no dividends. (a) Use risk-neutral valuatio...

Q: Consider an option on a non-dividend-paying stock when

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5%, the volatility is 25% per annum, and the time to maturity i...

Q: Assume that the stock in Problem 15.30 is due to

Assume that the stock in Problem 15.30 is due to go ex-dividend in 1 2/1 months. The expected dividend is 50 cents. (a) What is the price of the option if it is a European call? (b) What is the pri...

Q: Consider an American call option when the stock price is $18

Consider an American call option when the stock price is $18, the exercise price is $20, the time to maturity is 6 months, the volatility is 30% per annum, and the risk-free interest rate is 10% per a...

Q: The appendix derives the key result / Show that

The appendix derives the key result Show that and use this to derive the Black–Scholes–Merton formula for the price of a European put option on a non-dividend-payin...