finance problems, please download and look at them.

13.13. What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months? 5 13.14. What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months? 10 13.22. If the volatility of a stock is 18% per annum, estimate the standard deviation of the percentage price change in (a) one day, (b) one week, and (c) one month. 15 13.23. A stock price is currently $50. Assume that the expected return from the stock is 18% per annum and its volatility is 30% per annum. What is the probability distribution for the stock price in two years? Calculate the mean and standard deviation of the distribution. Determine the 95% confidence interval. 20 13.24. 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, 33.2 5 Estimate the stock price volatility. What is the standard error of your estimate? 13.26. 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% per 10 annum, the volatility is 25% per annum, and the time to maturity is four months. (a) What is the price of the option if it is a European call? (b) What is the price of the option if it is an American call? (c) What is the price of the option if it is a European put? 15 (d) Verify that put-call parity holds. (Note for 12.11! The risk-free rate of interest wit quarterly compounding is 8%. Here 8% is still p.a., per annum. Quarterly rate would be one fourth of it, right!) 20