Ch 4: NONLINEAR RISK: OPTIONS

Question 1

The value of a ________________ instrument depends on an underlying asset, which can be a price, an index, or a rate.

Answer 1

Derivative

Question 2

_____________________ is about combining those with the movements in the risk factors.

Answer 2

Risk Management

Question 2

_____________________ model provides a closed-form solution, from which these derivatives can be computed analytically.

Answer 2

Black-Scholes (BS) model

Question 3

Why is the delta normal approach not suitable for measuring options portfolio risk?

Example 1

a. There is a lack of data to compute the variance/covariance matrix.
b. Options are generally short-dated instruments.
c. There are nonlinearities in option payoff.
d. Black-Scholes pricing assumptions are violated in the real world.

Answer 3

c. There are nonlinearities in option payoff.

Question 3

The delta of an at-the-money call option is close to ____. Delta moves to ___ as the call goes deep in the money. It moves to zero as the ____ goes deep out of the money.

Answer 3

0.5 ; 1 ; Call

Question 4

The most important sensitivity is the _______________, which is the first partial derivative with respect to the price.

Answer 4

Delta

Question 4

Gamma is identical for a call and put with identical characteristics. T or F

Answer 4

True

Question 5

The delta of an at-the-money put option is close to ____. Delta moves to ____ as the put goes deep in the money. It moves to zero as the ______ goes deep out of the money.

Answer 5

-0.5 ; -1 ; Put

Question 6

For ___________________, gamma is the highest, or nonlinearities are most pronounced, for short- term at-the-money options.

Answer 6

Vanilla Options

Question 7

___________________ is similar to the concept of convexity developed for bonds

Answer 7

Gamma

Question 8

____________________ bonds, always have positive convexity.

Answer 8

Fixed-Coupon Bonds

Question 9

________________ can create positive or negative convexity.

Answer 9

Options

Question 10

_________________________ is beneficial, as it implies that the value of the asset drops more slowly and increases more quickly than otherwise.

Answer 10

Positive Convexity or Gamma

Question 11

____________________ can be dangerous because it implies faster price falls and slower price increases

Answer 11

Negative Convexity

Question 12

____________________ in options, whether calls or puts, create positive convexity.

Answer 12

Long Position

Question 13

____________________ create negative convexity.

Answer 13

Short Positions

Question 14

In exchange for assuming the harmful effect of negative convexity, option sellers receive the ____________________.

Answer 14

Premium

Question 15

A 90-day European put option on Microsoft has an exercise price of $30. The current market price for Microsoft is $30. The delta for this option is close to ______.

Example 2

a. -1
b. -0.5
c. 0.5
d. 1

Answer 15

b. -0.5

Question 16

Which of the following IBM options has the highest gamma with the current market price of IBM common stock at USD 68?

Example 3

a. Call option expiring in 10 days with strike USD 70
b. Call option expiring in 10 days with strike USD 50
c. Put option expiring in 10 days with strike USD 50
d. Put option expiring in 2 months with strike USD 70

Answer 16

a. Call option expiring in 10 days with strike USD 70

Question 17

A bank has sold USD 300,000 of call options on 100,000 equities. The equities trade at 50, the option strike price is 49, the maturity is in three months, volatility is 20%, and the interest rate is 5%. How does the bank delta hedge? (Round to the nearest thousand share).

Example 4

a. Buy 65,000 shares
b. Buy 100,000 shares
c. Buy 21,000 shares
d. Sell 100,000 shares

Answer 17

a. Buy 65,000 shares

Question 18

A portfolio of stock A and options on stock A is currently delta neutral, but has a positive gamma. Which of the following actions will make the portfolio both delta and gamma neutral?

Example 5

I. Buy call options on stock A and sell stock A.
II. Sell call options on stock A and sell stock A.
III. Buy put options on stock A and buy stock A.
IV. Sell put options on stock A and sell stock A.

Answer 18

d. Negative gamma is achieved by selling an option, so the correct answer must be either b) or d). Selling a put also creates positive delta, however, so this has to be offset by selling the stock.

Question 19

Unlike linear contracts, ______________ are exposed not only to movements in the direction of the spot price, but also in its _______________.

Answer 19

Options ; Volatility

Question 20

Options therefore can be viewed as “_______________.”

Answer 20

Volatility Bets

Question 21

The sensitivity of an option to volatility is called the option _________ (sometimes also called lambda, or kappa).

Answer 21

Vega

Question 22

___________________ are the most sensitive to volatility

Answer 22

At-the-money Options

Question 23

_________ decreases with maturity and ___________ increases with maturity.

Answer 23

Vega ; Gamma

Question 24

_____________ is highest for long-term at-the-money options.

Answer 24

Vega

Question 25

____________ is the sensitivity to the domestic interest rate.

Answer 25

Rho

Question 26

The _______________ increases as interest rate increases, as the underlying asset grows at a higher rate, which increases the probability of exercising the call, with a fixed strike price.

Answer 26

The Value of the Call

Question 27

An increase in the _______________ decreases the growth rate of the underlying asset, which is harmful to the value of the call.

Answer 27

Dividend Yield

Question 28

The variation in option value due to the passage of time is called ____________.

Answer 28

Theta or Time Decay