Ch 4: NONLINEAR RISK: OPTIONS Flashcards
The value of a ________________ instrument depends on an underlying asset, which can be a price, an index, or a rate.
Derivative
_____________________ is about combining those with the movements in the risk factors.
Risk Management
_____________________ model provides a closed-form solution, from which these derivatives can be computed analytically.
Black-Scholes (BS) model
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.
c. There are nonlinearities in option payoff.
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.
0.5 ; 1 ; Call
The most important sensitivity is the _______________, which is the first partial derivative with respect to the price.
Delta
Gamma is identical for a call and put with identical characteristics. T or F
True
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.
-0.5 ; -1 ; Put
For ___________________, gamma is the highest, or nonlinearities are most pronounced, for short- term at-the-money options.
Vanilla Options
___________________ is similar to the concept of convexity developed for bonds
Gamma
____________________ bonds, always have positive convexity.
Fixed-Coupon Bonds
________________ can create positive or negative convexity.
Options
_________________________ is beneficial, as it implies that the value of the asset drops more slowly and increases more quickly than otherwise.
Positive Convexity or Gamma
____________________ can be dangerous because it implies faster price falls and slower price increases
Negative Convexity
____________________ in options, whether calls or puts, create positive convexity.
Long Position
____________________ create negative convexity.
Short Positions
In exchange for assuming the harmful effect of negative convexity, option sellers receive the ____________________.
Premium
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
b. -0.5
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
a. Call option expiring in 10 days with strike USD 70
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
a. Buy 65,000 shares
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.
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.
Unlike linear contracts, ______________ are exposed not only to movements in the direction of the spot price, but also in its _______________.
Options ; Volatility
Options therefore can be viewed as “_______________.”
Volatility Bets
The sensitivity of an option to volatility is called the option _________ (sometimes also called lambda, or kappa).
Vega
___________________ are the most sensitive to volatility
At-the-money Options
_________ decreases with maturity and ___________ increases with maturity.
Vega ; Gamma
_____________ is highest for long-term at-the-money options.
Vega
____________ is the sensitivity to the domestic interest rate.
Rho
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.
The Value of the Call
An increase in the _______________ decreases the growth rate of the underlying asset, which is harmful to the value of the call.
Dividend Yield
The variation in option value due to the passage of time is called ____________.
Theta or Time Decay
