The Black-Scholes-Merton Model – questions
• The original Black-Scholes and Merton papers on stock option pricing were published in which year?
• 1983
• 1984
• 1974
• 1973
• Which of the following is a definition of volatility?
• The standard deviation of the return, measured with continuous compounding, in one year
• The variance of the return, measured with continuous compounding, in one year
• The standard deviation of the stock price in one year
• The variance of the stock price in one year
• A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the standard deviation of the change in the stock price in one week?
• $0.38
• $2.77
• $3.02
• $0.76
• What does N(x) denote in the B-S formula?
• The area under a normal distribution from zero to x
• The area under a normal distribution up to x
• The area under a normal distribution beyond x
• The area under the normal distribution between -x and x
• What was the original Black-Scholes-Merton model designed to value?
• A European option on a stock providing no dividends
• A European or American option on a stock providing no dividends
• A European option on any stock
• A European or American option on any stock
• A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the expected value of the continuously compounded return in one year?
• 6%
• 8%
• 10%
• 12%
• When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock
• 20N(0.1)-19.7N(0.2)
• 20N(0.2)-19.7N(0.1)
• 19.7N(0.2)-20N(0.1)
• 19.7N(0.1)-20N(0.2)
• When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock
• 19.7N(-0.1)-20N(-0.2)
• 20N(-0.1)-20N(-0.2)
• 19.7N(-0.2)-20N(-0.1)
• 20N(-0.2)-20N(-0.1)
• The volatility of a stock is 18% per year. Which is closest to the volatility per month?
• 1.5%
• 3.0%
• 5.2%
• 6.3%
• When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true?
• The binomial tree price converges to a price slightly above the Black-Scholes-Merton price as the number of time steps is increased
• The binomial tree price converges to a price slightly below the Black-Scholes-Merton price as the number of time steps is increased
• Either A or B can be true
• The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased
[I know I haven’t done binomial trees but have a go at this question anyway. I won’t test on non-covered material, so don’t worry].