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Question 528 DDM, income and capital returns

The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. $P_0$ is the current share price, $C_1$ is next year's expected dividend, $r$ is the total required return and $g$ is the expected growth rate of the dividend.

$P_0=\dfrac{C_1}{r-g}$

The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?

Question 795 option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European put option?

Question 334 option

Which option position has the possibility of unlimited potential losses?

Question 400 option, no explanation

A European put option will mature in $T$ years with a strike price of $K$ dollars. The underlying asset has a price of $S$ dollars.

What is an expression for the payoff at maturity $(f_T)$ in dollars from owning (being long) the put option?

Question 431 option, no explanation

A European put option will mature in $T$ years with a strike price of $K$ dollars. The underlying asset has a price of $S$ dollars.

What is an expression for the payoff at maturity $(f_T)$ in dollars from having written (being short) the put option?

Question 588 option

If trader A has sold the right that allows counterparty B to buy the underlying asset from him at maturity if counterparty B wants then trader A is:

Question 637 option, option payoff at maturity, no explanation

Which of the below formulas gives the payoff $(f)$ at maturity $(T)$ from being short a call option? Let the underlying asset price at maturity be $S_T$ and the exercise price be $X_T$ .

Question 723 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	99	-0.010050	0.990000	-0.010000
2	180.40	0.600057	1.822222	0.822222
3	112.73	0.470181	0.624889	0.375111

Arithmetic average		0.0399	1.1457	0.1457
Arithmetic standard deviation		0.4384	0.5011	0.5011

(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.

(b) $\exp \left( \text{GAGDR} \right) = \text{AALGDR}$ . The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) $\text{GAGDR}^T = \left( P_T/P_0 \right)$ . The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.

(d) $\text{GAGDR} = \exp \left( \text{AALGDR} \right)$ . This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).

(e) $\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)$ . This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.

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