Chapter 12 BlackScholes

Question 1

Black-Scholes is the binomial model with x steps. x is…

Answer 1

x -> infinity

Question 2

Black-Scholes doesn’t use Average return on a stock because

Answer 2

the larger average return is offset by the larger discount rate.

Question 3

Black-Scholes makes a bunch of assumptions:

Answer 3

1. Continuously compounded returns on stock are normally distributed and independent
2. volatility is known and constant
3. future dividends are known
4. risk free rate is known and constant
5. no transaction costs or taxes
6. possible to short sell and borrow at risk free rate

Question 4

Black-Scholes D1 Formula

Answer 4

[ln(S/K) + (r-δ+(1/2)σ^2)T] / σsqrt(T)

ln(prepaidForward on S/ Prepaid Forward on K) + (1/2)σ^2)T / σsqrt(T)

Question 5

Black-Scholes D2 Formula

Answer 5

d1 - σ*sqrt(T)

Question 6

Black-Scholes European Call Formula

Answer 6

Se^(-δt) * N(d1) - Ke^(-rt) * N(d2)

Prepaid Forward on S * N(d1) - Prepaid Forward on K * N(d2)

Question 7

Black-Scholes European Put Formula

Answer 7

• Se(-δt) * N(-d1) + Ke(-rt) * N(-d2)

- Prepaid Forward on S * N(-d1) + Prepaid Forward on K * N(-d2)

Question 8

Black-Scholes can be adjusted to other underlying assets by…

Answer 8

Change δ dividend yield

Question 9

Prepaid Forward Price for a stock with discrete dividends

Answer 9

S - PV(Dividends)

Question 10

Black-Scholes for futures

Answer 10

set delta = r, risk free rate aka Black Formula

Question 11

Option greeks measure what

Answer 11

Change in option price given a change in only one of the inputs

Question 12

Delta (Call vs. Put, In-the-money vs. Out-of-the-money, time)

Answer 12

Option Price Change when stock increases by $1.
Calls -> + and Puts -> -, Higher for in the money, time dilutes the effects of in the money.

formula e^(-rt) * N(d1)

Question 13

Gamma (Call vs. Put, In-the-money vs. Out-of-the-money)

Answer 13

Derivative of Delta, identical call and put means gamma is the same, if a call is deep in the money or deep out of the money, gamma is zero as delta doesn’t change much

Question 14

Vega (Call vs. Put, In-the-money vs. Out-of-the-money, time)

Answer 14

Option Change Price when volatility changes by set amount usually 1 percent point (0.01). PCP-> Same for call and put, higher for at the money options, moderate time higher

Question 15

Theta

Answer 15

Option Price Change when time changes by 1 day or 10 days.

Question 16

Rho (Call vs. Put, In-the-money vs. Out-of-the-money, time)

Answer 16

Option Price Change with respect to interest. Positive for a call and negative for a put. As time increases or options become more in the money, rho’s effect increases

Question 17

Psi (Call vs. Put, In-the-money vs. Out-of-the-money, time)

Answer 17

Option Price Change with respect to dividend yield. + for a put and - for a call. Time increase or options more in the money means Psi’s effect increases

Question 18

Greek measure of a portfolio is

Answer 18

the sum of the individual stock greeks

Question 19

Elasticity of an option

Answer 19

percent change in option/percent change in stock

e(delta)/optionprice / (e/S) where e is dollar change in stock

Question 20

volatility of an option equals the volatility of a stock times what factor?

Answer 20

absolute value of the elasticity

Question 21

Beta or risk premium of an option equals beta of a stock times what?

Answer 21

value of elasticity

Question 22

Sharpe Ratio for an option is the sharpe ratio of a stock times what?

Answer 22

1 because they are the same. SR is risk premium/volatility, and hence the elasticities cancel out.

Question 23

Elasticity of a portfolio is

Answer 23

the weighted average of the individual elasticities where weights are percent of portfolio in one option

Question 24

B of portfolio is

Answer 24

Elasticity of a portfolio times B of the stock.

Question 25

A Calandar spread is

Answer 25

buying options with same strike but different expirations

Question 26

implied volatility

Answer 26

volatility found by using black scholes model and market price

Question 27

risk reversals

Answer 27

implied volatility difference between out of money calls and puts with same delta