Question 1. Suppose the closing stock prices 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.
Question 2. A stock price is currently $70. Over each of the next two three-month periods it is expected to go up by 8% or down by 6%. The risk-free rate is 4% per annum with continuous compounding. What is the value of a six-month European put option with a strike price of $72?
Question 3. Calculate the value of a 3-month at-the-money European call option on a stock index when the index is at 1000, the risk-free rate is 4% per annum, the volatility of the index is 20% per annum, and the dividend yield on the index is 2% per annum
Question 4. Currently the stock index currently stands at 1000 and has a volatility of 20%. The risk-free rate is 8% and the dividend yield on the index is 2%. What is the value of a six-month European put option on the index with a strike price of 1050?
Question 5. A call option on a non-dividend-paying stock has a market price of $2.50. The strike price is $13, the stock price is $13, the time to maturity is 3 months, and the risk-free rate is 5% per annum. What is the implied volatility?