Portfolio Risk Management Test 2

d<1+Rf<u

True

Delta

(Cu - Cd) / (Us - Ds)

Delta of a Call is between

0 and 1

Delta of a Put is between

-1 and 0

How do you hedge a portfolio using call options

Buy delta number of shares and short 1 call

Pi

(1 + rf - d) / (u - d)

The price of an option

(Pi Cu + (1-Pi) * Cd) / (1 + rf)

The price of an option with two periods

Square Pi and rf and add 2 * Pi to (1-PI)

Rate of return

(new value - old value) / old value

how do you hedge a portfolio using put options

short delta number of shares and buy 1 put

Time Value is always positive

Call Option

Time Value can be negative

Put Option

dividends encourage early exercise

call option

dividends discourage exercise

put option

why do dividends discourage the exercise of a put option

the stock price will decrease after a dividend is paid

To find the price of an option with dividends

(1 - dividend yield) * us (ds)

to find the price of an option with a fixed dividend

u*s - fixed dividend

What kind of model is the binomial pricing model

discrete

what kind of model is the black-scholes pricing model

continuous

the binomial model evenutally becomes the black-scholes model with enough periods

true

discrete return

normal rate of return

continuous return

log(1+discrete)

-1<x<infinity

discrete return

-infinity<x<inifinity

continuous return

the assumptions of the B-S model

1. stock return are log normally distributed

2. constant risk-free rate and constant volatility

3. no taxes and no transaction costs

4. no dividends

5. European option

How do you find the true usable values of d1 and d2

t-distribution chart

if the current stock price is very high

d1 and d2 are = infinity

is the current stock price is close to 0

d1 and d2 are = negative infinity

if the option expires in the money

d1 and d2 are = infinity

in the option expires at the money

d1 and d2 = negative infiniy

in the option expires out of the money

d1 and d2 = negative infinity

if the standard deviation is 0 and the current stock price is larger than the continuous return of the exercise price, OR the exercise price is = 0

d1 and d2 = infinity

if the standard deviation is 0 and the stock price is less than the continuous return of the exercise price

d1 and d2 = negative infinity

call option delta

(change in option price / change of stock price)

greater than 0

call option gamma

(change of delta / change of stock price)

greater than 0

call option Rho

(change in option price / change of interest rate)

greater than 0

call option vega

(change of option price / change in volatility)

greater than 0

what is the only unobservable variable

volatility

call option theta

(change in option price / change in time-to-maturity)

less than zero

which greek variable measures time-value decay

theta

what makes the B-S price equal to the market

implied volatility

as time to expiration increases, the implied volatility increases

true

volatility smile (skew)

implied volatility is low for at the money options and high for in the money and out of the money options

as implied volatility increases, the “expensiveness” of an option decreases

true

Put delta

-1 < x < 0

put gamma

greater than 0

put rho

less than 0

put vega

less than zero

put theta

greater than 0 OR less than 0