Question 1

When there are dividends: choose one)

Accepted Answer

D

Question 2

For equities it is usually assumed that the number of trading days in the year is:

Accepted Answer

The number of trading days in a year for equities is usually assumed to be 252. This accounts for weekends and public holidays when stock exchanges are closed.

Question 3

The risk-free rate is 5% and the expected return on a stock is 12%. A derivative can be valued by: choose one)

Accepted Answer

In financial theory, the correct approach to valuing derivatives (or any financial asset) is to discount the expected payoff at the risk-free rate, not at the asset's expected return rate. This is because the risk-free rate represents the time value of money without any risk, which is the appropriate baseline for discounting. The expected growth rate of the stock price should match the risk-free rate when valuing derivatives to ensure that the valuation is not biased by the stock's risk premium.

Question 4

A 7-month European put option on the stock of Telstra has an exercise price of $4.80. The current stock price is $4.50, the risk-free rate is 8% per annum, and the volatility is 30% per annum. Calculate the price of the put option using the Black-Scholes-Merton formula. _ _ _ _ _ _ _ _

Accepted Answer

The answer of A 7-month European put option on the...

Question 5

In the Black-Scholes-Merton option pricing formula, Nd₁) denotes: choose one)

Accepted Answer

The notation Nd₁) in the Black-Scholes-Merton formula represents the cumulative distribution function (CDF) for a standard normal distribution, which gives the area under the normal distribution curve to the left of the value d₁. This corresponds to the probability that a normally distributed random variable takes on a value less than or equal to d₁.

Question 6

A stock price is $100. Volatility is estimated to be 20% per year. What is the estimate of the standard deviation of the change in the stock price in one week? choose one)

Accepted Answer

The standard deviation of the change in stock price in one week is calculated as $100 * 0.20 * sqrt(1/52) = $2.77.

Question 7

The Black-Scholes-Merton model assumes: choose one)

Accepted Answer

The Black-Scholes-Merton model, a fundamental concept in financial mathematics for pricing options, assumes that the stock price at a future time follows a lognormal distribution. This assumption allows for the stock price to only take positive values, reflecting the reality of stock prices in financial markets.

Question 8

The VIX index measures choose one)

Accepted Answer

The VIX index measures the market's expectation of 30-day forward-looking volatility conveyed by S&P 500 stock index option prices, thus it reflects implied volatilities for options trading on the S&P 500 Index.

Question 9

What is the price of the put option in the previous question if there is a dividend payment of $0.40 in 3 months? _ _ _ _ _ _ _ _

Accepted Answer

The answer of What is the price of the put...

Question 10

The Black, Scholes and Merton pathbreaking papers on stock option pricing were published in: choose one)

Accepted Answer

The Black-Scholes model, which is a fundamental concept in financial mathematics for pricing options, was introduced in a paper published in 1973 by Fischer Black and Myron Scholes. Robert Merton also contributed to the development of the theory around the same time, leading to the model often being referred to as the Black-Scholes-Merton model.

Question 11

Volatility can be defined as: choose one)

Accepted Answer

Volatility in finance is typically defined as the standard deviation of the return of an investment, often measured with continuous compounding, over a specific period, usually one year. This measures the dispersion of returns around the mean return and is a common measure of risk.

Quiz 13: Valuing Stock Options: the Black-Scholes-Merton Model