Question 1

Which of the following statements is true? Consider options written on a non-dividend-paying stock.

Accepted Answer

A)  All European options have negative theta and positive gamma. 
B)  European calls have negative theta and positive gamma, but European puts may sometimes have positive theta and negative gamma. 
C)  All European options have negative theta and all European calls have positive gamma, but European puts may sometimes have negative gamma. 
D)  All European options have positive gamma and European calls have negative theta, but European puts may sometimes have positive theta. 
A)  All European options have negative theta and positive gamma. 
B)  European calls have negative theta and positive gamma, but European puts may sometimes have positive theta and negative gamma. 
C)  All European options have negative theta and all European calls have positive gamma, but European puts may sometimes have negative gamma. 
D)  All European options have positive gamma and European calls have negative theta, but European puts may sometimes have positive theta.

Question 2

The current stock price is $50, and a put is priced at $3.59201. If the stock rises to $50.10, the price of the put will be $3.549152 and if the stock drops to $49.90, the price of the put will be $3.635261. What is the best estimate of the delta of the put?

Accepted Answer

A)  $- 0.42858$ 
B)  $- 0.43251$ 
C)  $- 0.43055$ 
D)  Cannot be calculated from the given data. 
A)  $- 0.42858$ 
B)  $- 0.43251$ 
C)  $- 0.43055$ 
D)  Cannot be calculated from the given data.

Question 3

You hold a straddle on a stock that you bought a month ago and that still has two months to expiry. Assume the options are European. An unexpected increase of $1 in the price of the stock

Accepted Answer

A)  Will increase the value of your straddle. 
B)  Will decrease the value of your straddle. 
C)  Will have no effect on the value of your straddle. 
D)  Can increase, decrease, or leave unchanged the value of the straddle. 
A)  Will increase the value of your straddle. 
B)  Will decrease the value of your straddle. 
C)  Will have no effect on the value of your straddle. 
D)  Can increase, decrease, or leave unchanged the value of the straddle.

Question 4

The vega of a ________ is highest when it is_________.

Accepted Answer

A)  call; deep in-the-money. 
B)  put; deep out-of-the-money. 
C)  call or put; far away-from-the-money. 
D)  None of the above. 
A)  call; deep in-the-money. 
B)  put; deep out-of-the-money. 
C)  call or put; far away-from-the-money. 
D)  None of the above.

Question 5

A stock is trading at $20. A one-month put with a strike of 19 is valued at $0.360 and has a rho of $- 0.50$ . A decrease of 10 basis points in the interest rate changes the put value by

Accepted Answer

A)  $- 0.005$ . 
B)  $+ 0.005$ . 
C)  $- 0.05$ 
D)  $+ 0.0005$ . 
A)  $- 0.005$ . 
B)  $+ 0.005$ . 
C)  $- 0.05$ 
D)  $+ 0.0005$ .

Question 6

You hold a portfolio of a long position in a call and a long position in a put, both for the same strike and maturity. Which of the following statements is true?

Accepted Answer

A)  When the stock price increases, the delta of the portfolio increases if the call is in-the-money. 
B)  When the stock price increases, the delta of the portfolio decreases if the call is out-of-the-money. 
C)  When the stock price increases, the delta of the portfolio increases whether or not the call is in-the-money. 
D)  There is not enough information to answer this question. 
A)  When the stock price increases, the delta of the portfolio increases if the call is in-the-money. 
B)  When the stock price increases, the delta of the portfolio decreases if the call is out-of-the-money. 
C)  When the stock price increases, the delta of the portfolio increases whether or not the call is in-the-money. 
D)  There is not enough information to answer this question.

Question 7

The gamma of an option is

Accepted Answer

A)  The dollar change in the option delta for a $1 change in the price of the underlying. 
B)  The percentage change in option delta for a 1% change in the price of the underlying. 
C)  The dollar change in the option price for a sudden unit jump change in the price of the underlying. 
D)  The percentage change in the option price for a sudden unit jump change in the price of the underlying. 
A)  The dollar change in the option delta for a $1 change in the price of the underlying. 
B)  The percentage change in option delta for a 1% change in the price of the underlying. 
C)  The dollar change in the option price for a sudden unit jump change in the price of the underlying. 
D)  The percentage change in the option price for a sudden unit jump change in the price of the underlying.

Question 8

You expect a sizable jump in the stock price but are not sure of the direction in which the stock will go. Which of the following alternatives would be best?

Accepted Answer

A)  Buy call options. 
B)  Buy put options. 
C)  Sell a straddle. 
D)  Buy a call and delta hedge it. 
A)  Buy call options. 
B)  Buy put options. 
C)  Sell a straddle. 
D)  Buy a call and delta hedge it.

Question 9

A stock is trading at $132. A one-month call with a strike of $125 costs $9.773 and has a theta of $- 30.53$ . The passage of one trading day ( $\approx 0.004$ years) will cause the call value to, approximately,

Accepted Answer

A)  Rise by $0.04$ . 
B)  Fall by $0.003$ 
C)  Fall by $0.122$ . 
D)  Fall by $0.04$ 
A)  Rise by $0.04$ . 
B)  Fall by $0.003$ 
C)  Fall by $0.122$ . 
D)  Fall by $0.04$

Question 10

Consider options written on a non-dividend-paying stock. Deep in-the-money put options may

Accepted Answer

A)  Have negative gamma and positive theta if they are European in style. 
B)  Have negative gamma and negative theta if they are American in style. 
C)  Have positive gamma and positive theta if they are European in style. 
D)  Have positive gamma and positive theta if they are American in style. 
A)  Have negative gamma and positive theta if they are European in style. 
B)  Have negative gamma and negative theta if they are American in style. 
C)  Have positive gamma and positive theta if they are European in style. 
D)  Have positive gamma and positive theta if they are American in style.

Question 11

Gamma is a risk measure that is related to the volatility (particularly jump-risk) of the underlying stock. Which of the following is most valid?

Accepted Answer

A)  When you buy vanilla call options it is useful to hedge away gamma to minimize jump risk. 
B)  When you sell vanilla put options it is useful to hedge away gamma to minimize jump risk. 
C)  Both (a) and (b). 
D)  Neither (a) nor (b). 
A)  When you buy vanilla call options it is useful to hedge away gamma to minimize jump risk. 
B)  When you sell vanilla put options it is useful to hedge away gamma to minimize jump risk. 
C)  Both (a) and (b). 
D)  Neither (a) nor (b).

Question 12

The absolute value of theta is highest for options

Accepted Answer

A)  That are deep out-of-the-money. 
B)  That are near-the-money. 
C)  That are deep in-the-money. 
D)  There is not enough information to determine the answer. 
A)  That are deep out-of-the-money. 
B)  That are near-the-money. 
C)  That are deep in-the-money. 
D)  There is not enough information to determine the answer.

Question 13

For options that are at-the-money, which of the following statements is typically valid as maturity nears?

Accepted Answer

A)  Gamma increases as does theta. 
B)  Gamma increases and theta decreases. 
C)  Gamma decreases and theta increases. 
D)  Gamma and theta both decrease. 
A)  Gamma increases as does theta. 
B)  Gamma increases and theta decreases. 
C)  Gamma decreases and theta increases. 
D)  Gamma and theta both decrease.

Question 14

The current price of a call is $5 and the stock is trading at $50. The delta and gamma of the call are 0.5 and 0.05, respectively. If the stock price increases to $50.50, then approximate the new call price using the information given:

Accepted Answer

A)  $5.24375 
B)  $5.25 
C)  $5.25625 
D)  $5.2625 
A)  $5.24375 
B)  $5.25 
C)  $5.25625 
D)  $5.2625

Question 15

You hold a portfolio of a long position in a call and a short position in a put, both for the same strike and maturity, both written on a non-dividend paying stock. Which of the following statements is most correct?

Accepted Answer

A)  The delta of the portfolio increases when the stock price increases. 
B)  The delta of the portfolio stays the same when the stock price increases. 
C)  The delta of the portfolio decreases when the stock price increases. 
D)  The delta of the portfolio may increase or decrease when the stock price increases. 
A)  The delta of the portfolio increases when the stock price increases. 
B)  The delta of the portfolio stays the same when the stock price increases. 
C)  The delta of the portfolio decreases when the stock price increases. 
D)  The delta of the portfolio may increase or decrease when the stock price increases.

Question 16

Which of the following statements is valid for European options?

Accepted Answer

A)  The gamma of a call is positive and that of a put is negative. 
B)  The gamma of a call is negative and that of a put is negative. 
C)  The gamma of a call is negative and that of a put is positive. 
D)  The gamma of a call is positive and that of a put is positive. 
A)  The gamma of a call is positive and that of a put is negative. 
B)  The gamma of a call is negative and that of a put is negative. 
C)  The gamma of a call is negative and that of a put is positive. 
D)  The gamma of a call is positive and that of a put is positive.

Exam 17: The Option Greeks

Which of the following statements is true? Consider options written on a non-dividend-paying stock.

The current stock price is $50, and a put is priced at $3.59201. If the stock rises to $50.10, the price of the put will be $3.549152 and if the stock drops to $49.90, the price of the put will be $3.635261. What is the best estimate of the delta of the put?

You hold a straddle on a stock that you bought a month ago and that still has two months to expiry. Assume the options are European. An unexpected increase of $1 in the price of the stock

The vega of a ________ is highest when it is_________.

A stock is trading at $20. A one-month put with a strike of 19 is valued at $0.360 and has a rho of −0.50- 0.50−0.50 . A decrease of 10 basis points in the interest rate changes the put value by

You hold a portfolio of a long position in a call and a long position in a put, both for the same strike and maturity. Which of the following statements is true?

The gamma of an option is

You expect a sizable jump in the stock price but are not sure of the direction in which the stock will go. Which of the following alternatives would be best?

A stock is trading at $132. A one-month call with a strike of $125 costs $9.773 and has a theta of −30.53- 30.53−30.53 . The passage of one trading day ( ≈0.004\approx 0.004≈0.004 years) will cause the call value to, approximately,

Consider options written on a non-dividend-paying stock. Deep in-the-money put options may

Gamma is a risk measure that is related to the volatility (particularly jump-risk) of the underlying stock. Which of the following is most valid?

The absolute value of theta is highest for options

For options that are at-the-money, which of the following statements is typically valid as maturity nears?

The current price of a call is $5 and the stock is trading at $50. The delta and gamma of the call are 0.5 and 0.05, respectively. If the stock price increases to $50.50, then approximate the new call price using the information given:

You hold a portfolio of a long position in a call and a short position in a put, both for the same strike and maturity, both written on a non-dividend paying stock. Which of the following statements is most correct?

Which of the following statements is valid for European options?

Overview

Futures Markets

Pricing Forwards and Futures I

Pricing Forwards Futures II

Hedging With Futures Forwards

Interest-Rate Forwards Futures

Options Markets

Options: Payoffs Trading Strategies

No-Arbitrage Restrictions

Early-Exercise Put-Call Parity

Option Pricing: an Introduction

Binomial Option Pricing

Implementing the Binomial Model

The Black-Scholes Model

Mathematics of Black-Scholes

Beyond Black-Scholes

Path-Independent Exotic Options

Exotic Options II: Path-Dependent Options

Value at Risk

Swaps and Floating Rate Products

Equity Swaps

Currency and Commodity Swaps

Term Structure of Interest Rates: Concepts

Estimating the Yield Curve

Modeling Term Structure Movements

Factor Models of the Term Structure

The Heath-Jarrow-Morton HJM and Libor Market Model LMM

Credit Derivative Products

Structural Models of Default Risk

Reduced-Form Models of Default Risk

Modeling Correlated Default

Filters

The vega of a is highest when it is_.

A stock is trading at $20. A one-month put with a strike of 19 is valued at $0.360 and has a rho of $- 0.50$ . A decrease of 10 basis points in the interest rate changes the put value by

A stock is trading at $132. A one-month call with a strike of $125 costs $9.773 and has a theta of $- 30.53$ . The passage of one trading day ( $\approx 0.004$ years) will cause the call value to, approximately,