Question 1

Higher _________, higher ________

Accepted Answer

Higher implied volatility generally leads to higher option prices because it indicates a greater expected fluctuation in the underlying asset's price, increasing the potential for profit.

Question 2

Francis has a long position on the underlying asset and has sold a number of call options with the following binomial tree:

Given the current asset price is $20 and r is 5%, what is the price of the this call option?

Accepted Answer

The answer of Francis has a long position on the...

Question 3

The current value of an underlying asset is $80.The strike price of a call option with one month to expiration is $85.There is a 20% chance that in one month the value of the underlying asset will be $75 and an 80% chance that it will be $90.
a)What is the expected value of the underlying asset and the corresponding rate of return?
b)What is the hedge ratio and the corresponding value of the call given r = 0.02%?

Accepted Answer

The answer of The current value of an underlying asset...

Question 4

The current stock price is $568.36, a one-year call option with a strike price of $500 is $102, and the risk-free rate is 2%.What should be the price of a one-year put option with the same strike price?

Accepted Answer

The answer of The current stock price is $568.36, a...

Question 5

Create a table illustrating the range of payoffs of a protective put strategy for the following values of an underlying asset: 60, 70, 80, 90, 100.The strike price of all options in the strategy is $80 and the current value of the underlying asset is $80.

Accepted Answer

The answer of Create a table illustrating the range of...

Question 6

Toronto Skaters' stock is now worth $100.In one month, it will either be $80 or $120.Given that the monthly risk-free rate is 2%, what is the corresponding value of the call? (Assume a strike price $105)

Accepted Answer

We can use the risk-neutral valuation method to calculate the value of the call option.

First, we calculate the risk-neutral probabilities of the stock being worth $80 or $120 in one month using the risk-free rate:

p(down) = (1 + r - u)/(u - d) = (1 + 0.02 - 0.8)/(1.2 - 0.8) = 0.4/0.4 = 1
p(up) = (1 + r - d)/(u - d) = (1 + 0.02 - 0.2)/(1.2 - 0.8) = 0.82/0.4 = 2.05

Next, we calculate the expected value of the stock in one month under the risk-neutral probability measure:

E(S) = p(up) * $120 + p(down) * $80 = 2.05 * $120 + 1 * $80 = $280

Then, we discount the expected stock price back to the present using the risk-free rate:

V(0) = (1 + r)^(-1) * [p(up) * max(S(1) - K, 0) + p(down) * max(S(2) - K, 0)]
where K is the strike price of $105

V(0) = (1 + 0.02)^(-1) * [2.05 * max($120 - $105, 0) + 1 * max($80 - $105, 0)]
V(0) = $10.78

Therefore, the corresponding value of the call option is $10.78. The best choice is C.

Question 7

Toronto Skaters' stock is now worth $100.In one month, it will either be $80 or $120.Given that the monthly risk-free rate is 2%, how many calls does the investor need to sell to hedge a long position in Toronto Skaters' stock? (Assume a strike price of $105)

Accepted Answer

The answer of Toronto Skaters' stock is now worth $100.In...

Question 8

Assume the current value of the underlying asset is $20 and the value of the underlying asset tomorrow can either be $15 or $25.What is the risk-neutral probability of generating a 2% return on the asset?

Accepted Answer

The risk-neutral probability of generating a 2% return on the asset is 0.54. This is because the expected return on the asset is $20 * 0.54 + $25 * 0.46 = $20.28, which is a 2% return on the current value of the asset.

Question 9

Briefly explain how to replicate the payoff of a risk-free asset using put-call parity.

Accepted Answer

The answer of Briefly explain how to replicate the payoff...

Question 10

_________is an estimate of the ________ of the underlying asset based on observed option prices.

Accepted Answer

The answer of _________is an estimate of the ________ of...

Question 11

VIX can be used

Accepted Answer

VIX (CBOE Volatility Index) is a measure of the expected volatility of the S&P 500 index over the next 30 days, based on the prices of options on the index. It is commonly used as a gauge of market sentiment and is often referred to as the "fear index." It is not used to price interest rate volatility nor to estimate the risk of default premium of the underlying debt.

Question 12

Marie wants to determine the fair value of a put option with a strike price of $20 due to expire in 2 years.A call with the same strike price and expiration is worth $5.The risk-free rate is 4%.What would you tell Marie is the fair value of the put option? Assume: continuous compounding and value of the underlying asset is $22

Accepted Answer

The answer of Marie wants to determine the fair value...

Question 13

You have been provided with the following information:
$\bullet$S = $25
$\bullet$Exercise price = $20
$\bullet$Risk-free rate = 1%
$\bullet$Volatility is 20%
$\bullet$The option expires in one year.
Based on this information, what is the value of the corresponding call option?
(NOTE: if using the appendix A-1 to solve for the N(d1)and N(d2)values you should truncate d1 and d2 to two decimal places and round down.

Accepted Answer

The answer of You have been provided with the following...

Question 14

Create a table depicting the payoffs for a collar given Xput = $50, S = $55, and Xcall = $60.Assume the value of the asset in 2 months will be: $40, $50, $55, $60, $75, $80.

Accepted Answer

The answer of Create a table depicting the payoffs for...

Question 15

Which of the following statements is correct?

Accepted Answer

Risk neutral refers to the state of ignoring the risk involved in determining expected rates of return.

Quiz 12: Options

Higher _, higher

Francis has a long position on the underlying asset and has sold a number of call options with the following binomial tree: Given the current asset price is $20 and r is 5%, what is the price of the this call option?