THE GREEKS

Question 1

BSM Formula Inputs

Answer 1

1. S- asset price (delta)
2. Volatility- Vega
3. Interest Rate- Rho
4. Passage of TIme- Theta
5. X- exercise price
6. Gamma- rate of change in delta as stock price changes

Question 2

Delta and Calls

Answer 2

Positively Related
Delta > 0

Measures change in call price for $1 change in underlying.
Prices up 1, Delta of 0.5, call price expected to move 50 cents.

Question 3

Delta and Puts

Answer 3

Negatively Related

Delta < 0

Question 4

Vega and Calls

Answer 4

Positively Related
Vega > 0

Higher volatility always positively impacts price of options

Question 5

Vega and Puts

Answer 5

Positively Related

Vega > 0

Question 6

Rho and Calls

Answer 6

Positively Related
Rho > 0

As rates increase, call values increase

Question 7

Rho and Puts

Answer 7

Negatively Related
Rho < 0

As rates decrease, put values decline.

Question 8

Theta and Calls

Answer 8

Value - > $0 as call -> maturity.

Negatively related

Theta < 0

Question 9

Theta and Puts

Answer 9

Value - > $0 as put -> maturity.

Positively related

Theta < 0

Question 10

Theta’s input

Answer 10

passage of time

Question 11

Delta’s input

Answer 11

Asset price

Question 12

Vega’s input

Answer 12

Volatility

Question 13

Rho’s input

Answer 13

risk-free rate

Question 14

Delta Def

Answer 14

Change in price of an option for a 1 unit change in price of underlying stock.

Question 15

Far out of the money call, delta approaches

Answer 15

0

Question 16

Far in the money call, delta approaches

Answer 16

e^(-dividend yield*T)

Question 17

Far out of the money put, delta approaches

Answer 17

0

Question 18

Far in the money, put delta approaches

Answer 18

-e^ (-dividend yield*T)

Question 19

Dynamic Hedging/Delta Neutral Hedging

Answer 19

Combining a long stock position with short calls so portfolio value doesn’t change with stock price.

of short calls needed = # shares hedged / Delta of call

Delta < 1 so always need more calls than shares.

Question 20

Dynamic Hedge Formula

Answer 20

of short calls needed =

shares hedged / Delta of call

Question 21

Gamma

Answer 21

rate of change in delta as stock price changes

positive for both calls and puts

largest when option is ATM and close to expiration

Small for deep ITM and deep OTM options not close to expiration

Question 22

Gamma and Calls

Answer 22

Positively related

Question 23

Gamma and Puts

Answer 23

Positively related

Question 24

Gamma risk

Answer 24

when stock price jumps abruptly (a violation of BSM assumption)

Question 25

Implied volatility

Answer 25

of continuous returns on underlying stock is “volatility” from BSM model that makes model value = market price

Volatility “implied” by option price.