Question 1

The share price of Ajax Inc. is currently $105. The share price a year from now will be either $130 or $90 with equal probabilities. The interest rate at which investors can borrow is 10%. Using the binomial OPM, the value of a call option with an exercise price of $110 and an expiration date one year from now should be worth ________ today.
A)$11.59
B)$15.00
C)$20.00
D)$40.00

Accepted Answer

The binomial option pricing model calculates the option price by considering the possible future outcomes and their probabilities. The expected future price is $110, and the present value of the expected payoff is $11.59 when discounted at the risk-free rate of 10%.

Question 2

Research suggests that option pricing models that allow for the possibility of ________ provide more accurate pricing than does the basic Black-Scholes option pricing model.
I. early exercise
II. changing expected returns of the share
III. time varying share price volatility
A)II only
B)I and III only
C)II and III only
D)I, II and III

Accepted Answer

The Black-Scholes option pricing model assumes that options are only exercised at expiration and that the expected returns of the underlying shares are constant. However, in reality, the option holder may decide to exercise the option before expiration, and the share price volatility may change over time. Therefore, option pricing models that allow for the possibility of early exercise and time-varying share price volatility provide more accurate pricing than the basic Black-Scholes model that assumes constant expected returns and no early exercise.

Question 3

You are considering purchasing a put option on a share with a current price of $33. The exercise price is $35 and the price of the corresponding call option is $2.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be ________.
A)$2.25
B)$3.91
C)$4.05
D)$5.52

Accepted Answer

The answer of You are considering purchasing a put option...

Question 4

Which one of the following will increase the value of a put option?
A)A decrease in the exercise price
B)A decrease in time to expiration of the put
C)An increase in the volatility of the underlying share
D)An increase in share price

Accepted Answer

An increase in the volatility of the underlying share increases the value of a put option because it raises the potential for the share price to fall below the exercise price, increasing the likelihood of a profitable exercise.

Question 5

In the Black-Scholes model if an option is not likely to be exercised both N(d1) and N(d2) will be close to ________. If the option is definitely likely to be exercised N(d1) and N(d2) will be close to ________.
A)1; 0
B)0; 1
C)-1; 1
D)1: -1

Accepted Answer

In the Black-Scholes model, N(d1) represents the probability of the option being exercised and N(d2) represents the probability of the option being in the money at expiration. If an option is not likely to be exercised, it means that it is out of the money, and therefore N(d1) and N(d2) will be close to 0. On the other hand, if an option is definitely likely to be exercised, it means that it is in the money, and therefore N(d1) and N(d2) will be close to 1. Therefore, the best choice is B, where N(d1) and N(d2) are close to 0 and 1, respectively.

Question 6

In the Black-Scholes model as the share's price increases the values of N(d1) and N(d2) will ________ for a call and ________ for a put option.
A)increase; decrease
B)increase; increase
C)decrease; increase
D)decrease; decrease

Accepted Answer

As the share's price increases, the probability of the option being exercised (i.e. N(d1)) increases for call options, and decreases for put options. Therefore, the values of N(d1) will increase for call options and decrease for put options. Similarly, the probability of the option expiring in-the-money (i.e. N(d2)) increases for both call and put options as the share's price increases, but at a slower rate for put options. Therefore, the values of N(d2) will increase for call options and decrease for put options.

Question 7

If you have an extremely 'bullish' outlook on the share market, you could attempt to maximise your rate of return by ________.
A)purchasing out-of-the-money call options
B)purchasing at-the-money bull spreads
C)purchasing in-the-money call options
D)purchasing at-the-money call options

Accepted Answer

Purchasing out-of-the-money call options gives the holder the right to buy the underlying asset at a certain price on or before a certain date. If the asset price rises, the call option will become more valuable, and the holder can sell it for a profit.

Question 8

Of the variables in the Black-Scholes OPM, the ________ is not directly observable.
A)price of the underlying asset
B)risk-free rate of interest
C)time to expiration
D)variance of the underlying asset return

Accepted Answer

The variance of the underlying asset return is not directly observable and needs to be estimated. It is typically estimated using historical or implied volatility. The other variables, including the price of the underlying asset, risk-free rate of interest, and time to expiration, are observable or known.

Question 9

If you know that a call option will be profitably exercised then the Black-Scholes model price will simplify to ________. A)S₀ - X B)X - S₀ C)S₀ - PV(X) D)PV(X) - S₀

Accepted Answer

When a call option is profitably exercised, the holder of the option will buy the underlying asset at the strike price X and sell it at the market price S. Therefore, the profit from exercising the option is S - X. In the Black-Scholes model, the price of the option is represented by S₀. To get the profit from exercising the option, we need to subtract the strike price X from S₀, which gives us S₀ - X. However, we also need to take into account the time value of money, so we need to discount the strike price X by the risk-free rate to get the present value of X, which is PV(X). Therefore, the simplified Black-Scholes model price when a call option is profitably exercised is S₀ - PV(X), which is equivalent to choice C.

Question 10

A high dividend payout will ________ the value of a call option and ________ the value of a put option.
A)increase; decrease
B)increase; increase
C)decrease; increase
D)decrease; decrease

Accepted Answer

A high dividend payout reduces the value of the underlying asset, which in turn reduces the value of a call option (since the holder wants the price to go up) and increases the value of a put option (since the holder wants the price to go down).

Question 11

A one dollar increase in a share's price would result in ________ in the call option's value of ________ than one dollar.
A)a decrease; less
B)a decrease; more
C)an increase; less
D)an increase; more

Accepted Answer

A one dollar increase in a share's price typically results in an increase in the call option's value, but by less than one dollar due to the option's delta being less than 1.

Question 12

Hedge ratios for long call position are ________ and hedge ratios for long put positions are ________.
A)negative; negative
B)negative; positive
C)positive; negative
D)positive; positive

Accepted Answer

The hedge ratio for a long call position is positive because the holder of a long call option benefits from an increase in the price of the underlying asset. So, to hedge the risk of the underlying asset moving in the opposite direction, the investor would buy a certain number of shares of the underlying asset, and the hedge ratio would be positive. Conversely, the hedge ratio for a long put position is negative because the holder of a long put option benefits from a decrease in the price of the underlying asset. So, to hedge this risk, the investor would sell a certain number of shares of the underlying asset, and the hedge ratio would be negative. Therefore, option C is correct.

Question 13

Perfect dynamic hedging requires ________.
A)a smaller capital outlay than static hedging
B)less commission expense than static hedging
C)daily rebalancing
D)continuous rebalancing

Accepted Answer

Dynamic hedging requires continuous monitoring and rebalancing of the hedging portfolio to ensure a perfect hedge. While it may require a larger capital outlay and more commission expense compared to static hedging, the ability to adjust the hedge as the market conditions change can lead to better risk management and potential profits. Daily rebalancing may not be sufficient to maintain a perfect hedge in all market conditions.

Question 14

If a share price increases, the price of a put option on the share will ________ and the price of a call option on the share will ________.
A)decrease; decrease
B)decrease; increase
C)increase; decrease
D)increase; increase

Accepted Answer

When the share price increases, the price of a put option decreases as the probability of the share price falling below the strike price decreases. On the other hand, the price of a call option increases as the probability of the share price exceeding the strike price increases. Therefore, the correct answer is (B): decrease for a put option, increase for a call option.

Question 15

The Black-Scholes hedge ratio for a long call option is equal to ________.
A)N(d1)
B)N(d2)
C)N(d1) - 1
D)N(d2) - 1

Accepted Answer

The Black-Scholes hedge ratio for a long call option is equal to the delta of the option, which is denoted by N(d1), where N() is the cumulative distribution function of a standard normal distribution. The choices provided seem to be incorrectly formatted, but option A is the closest to representing the delta of a call option, which is N(d1), without the subtraction or additional terms found in the other options.

Question 16

Which of the following is a true statement?
A)The actual value of a call option is greater than its intrinsic value prior to expiration.
B)The intrinsic value of a call option is always greater than its time value prior to expiration.
C)The intrinsic value of a call option is always positive prior to expiration.
D)The intrinsic value of a call option is greater than its actual value prior to expiration.

Accepted Answer

The actual value of a call option (often referred to as its market price) can be greater than its intrinsic value prior to expiration because it includes time value, which accounts for the potential of the option to increase in value before it expires.

Question 17

According to the put-call parity theorem, the payoffs associated with ownership of a call option can be replicated by ________.
A)shorting the underlying share, borrowing the present value of the exercise price and writing a put on the same underlying share and with the same exercise price
B)buying the underlying share, borrowing the present value of the exercise price and buying a put on the same underlying share and with the same exercise price
C)buying the underlying share, borrowing the present value of the exercise price and writing a put on the same underlying share and with the same exercise price
D)shorting the underlying share, lending the present value of the exercise price and buying a put on the same underlying share and with the same exercise price

Accepted Answer

According to the put-call parity theorem, owning a call option can be replicated by buying the underlying asset, borrowing the present value of the exercise price, and buying a put option with the same exercise price and expiration date.

Question 18

The current share price of Alcoa is $70 and the share does not pay dividends. The instantaneous risk free rate of return is 6%. The instantaneous standard deviation of Alcoa's shares is 40%. A put option on this share with an exercise price of $75 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold ________ shares of stock per 100 put options to hedge your risk.
A)30
B)34
C)69
D)74

Accepted Answer

The answer of The current share price of Alcoa is...

Question 19

The delta of a put option on a share is always ________.
A)between zero and -1
B)between -1 and 1
C)positive but less than 1
D)greater than 1

Accepted Answer

The delta of a put option ranges between zero and -1. This is because the delta of a put option reflects the change in the price of the option for every one-point change in the price of the underlying share. As the price of the underlying share decreases, the value of the put option increases, resulting in a negative delta. Since the price of the underlying share can only decrease up to zero, the delta of a put option cannot be less than zero. On the other hand, since the price of the put option can only increase up to its strike price, the delta cannot be greater than -1.

Question 20

What combination of variables is likely to lead to the lowest time value?
A)Short time to expiration and low volatility
B)Long time to expiration and high volatility
C)Short time to expiration and high volatility
D)Long time to expiration and low volatility

Accepted Answer

The time value of an option decreases as the time to expiration gets shorter. Low volatility also contributes to a lower time value because there is less chance for the underlying asset's price to move significantly. Therefore, the combination of short time to expiration and low volatility is likely to lead to the lowest time value.

Quiz 14: Options and Risk Management

Research suggests that option pricing models that allow for the possibility of ________ provide more accurate pricing than does the basic Black-Scholes option pricing model. I. early exercise II. changing expected returns of the share III. time varying share price volatility

Which one of the following will increase the value of a put option?

In the Black-Scholes model if an option is not likely to be exercised both N(d1) and N(d2) will be close to . If the option is definitely likely to be exercised N(d1) and N(d2) will be close to .

In the Black-Scholes model as the share's price increases the values of N(d1) and N(d2) will for a call and for a put option.

If you have an extremely 'bullish' outlook on the share market, you could attempt to maximise your rate of return by ________.

Of the variables in the Black-Scholes OPM, the ________ is not directly observable.

If you know that a call option will be profitably exercised then the Black-Scholes model price will simplify to ________.

A high dividend payout will the value of a call option and the value of a put option.

A one dollar increase in a share's price would result in in the call option's value of than one dollar.

Hedge ratios for long call position are and hedge ratios for long put positions are .

Perfect dynamic hedging requires ________.

If a share price increases, the price of a put option on the share will and the price of a call option on the share will .

The Black-Scholes hedge ratio for a long call option is equal to ________.

Which of the following is a true statement?

According to the put-call parity theorem, the payoffs associated with ownership of a call option can be replicated by ________.

The delta of a put option on a share is always ________.

What combination of variables is likely to lead to the lowest time value?