Black Scholes Multi choice Flashcards
B
Black-Scholes-Merton assumes that the return from a stock in a short period of time is normally distributed.This means that the stock price at a future time is lognormally distributed
A.
Volatility when multiplied by the square root of t is the standard deviation of the return in a short period of time of length t.It is also the standard deviation of the continuously compounded return in one year.
B
B
The normal distribution runs from minus infinity to plus infinity.N(x)is the area under the distribution between minus infinity and x.
D
When there are dividends it is sometimes optimal to exercise immediately before an ex-dividend date,but it is never optimal to exercise at other times.None of the first three answers are therefore correct.
B
Analysts usually assume that there are 252 trading days in a year for equities.
C
Risk-neutral valuation shows that a derivative can be correctly valued by assuming that the stock grows at the risk-free rate and discounting the expected payoff at the risk-free rate.It follows that C is the correct answer.
C
The VIX index measures the implied volatilities of one-month options trading on the S&P 500 index.
A
The original Black-Scholes-Merton model was designed to value a European option on a stock paying no dividends .
A
Risk-neutral valuation produces a valuation that is correct in all situations not just those where investors are risk-neutral.The expected return on all investments is assumed to be the risk-free rate and the risk-free rate is used to discount expected payoffs.
D
To value a European option we replace the stock price by the stock price minus the present value of all dividends that have ex-dividend dates during the life of the option
The binomial tree valuation method and the Black-Scholes formula are based on the same set of assumptions.As the number of time steps is increased the answer given by the binomial tree approach converges to the answer given by the Black-Scholes-Merton formula.
D
The price relative for the first week is 22/20 or 1.1.The natural log of the price relative is ln(1.1)or 0.09531.Similarly the ln of the price relatives for the other weeks are -0.1466,0.1001,0.1335,and 0.The standard deviation of 0.09531,-0.1466,0.1001,0.1335,and 0 is 0.1138.The volatility per week is therefore 11.38%.This corresponds to a volatility per year of 0.1138 multiplied by the square root of 52 or about 82%.The answer is therefore D.
C
The volatility per month is the volatility per year multiplied by the square root of 1/12 .The square root of 1/12 is 0.2887 and 18% multiplied by this is 5.2%.
