5 - BS continued

Question 1

BS with dividend payment, what must be done before the BS formula can be applied?

Answer 1

PV of dividend must be subtracted from stock price at time zero
S0- D e^(-r x t)

Question 2

why would an american option be exercised early?

Answer 2

high dividends and low time value

Question 3

can american calls be valued using BS?

Answer 3

no not really, corresponding EU calls can be valued at every dividend date and maturity; and the highest of these values can give a lower bound to the value of a US option.

Question 4

can american puts be valued using BS? what can be used to value a put in combination with BS?

Answer 4

no because exercise may be optimal on other dates outside of dividend dates, use put-call-parity

Question 5

what does term structure of implied volatility mean?

Answer 5

the relationship between implied volatility and the time to expiration (straight line)

Question 6

what does the volatility smile/skew refer to?

Answer 6

the relationship between implied volatility and exercise price (curved line)

Question 7

What are the five greeks and what do they tell us?

Answer 7

delta - small changes in stock price
gamma - large changes in stock price
rho - interest
theta - time
vega - volatility

Question 8

what figure from the BS formula give you the delta value? what is the range of this figure? what does the value tell us?

Answer 8

N(d1)
0-1
the hedge ratio

Question 9

how does the delta/ N(d1) differ for a call or a put?

Answer 9

call delta is positive

put delta is negative

Question 10

how does the call value react to delta? why?

Answer 10

when delta moves towards 1 call price increases, as the stock price has increased relative to X
when delta moves towards 0 call price decreases, as the stock price has decreased relative to X

Question 11

at what value of delta is the call in/out of the money?

Answer 11

1 = in the money
0 = out of the money

Question 12

when would you expect to see the greatest change in delta? when does it change less?

Answer 12

when the call is close to the money the change in delta is the greatest when stock price changes a little

when the call is far in/out of the money the delta does not change as much

Question 13

what does a large gamma tell us? what does this mean for the delta and hedging?

Answer 13

that the call price is more sensitive to large stock movements. the delta is more sensitive and moves faster, means that it’s difficult to hedge

Question 14

when is gamma greatest? when does it change the most

Answer 14

both answers are; when option is at the money.

Question 15

based on time, when does gamma increase the most?

Answer 15

closer to expiration

Question 16

how does rho differ for call and put options?

Answer 16

call - positive

put - negative

Question 17

when does the rho value move/change the most?

Answer 17

at the money

Question 18

when vega increases, what happens to the price of calls? puts?

Answer 18

both increase

Question 19

when does vega change the most? (have the greatest impact on option value)

Answer 19

when option is at the money

Question 20

when is a large or small theta good/bad?

Answer 20

larger theta - more time is good for call and bad for put

small theta - less time is bad for call and good for put

Question 21

when does theta change the option price most? when is time decay at its greatest?

Answer 21

when the option is at the money

Question 22

what does delta hedging/ delta neutral entail?

Answer 22

holding shares and selling calls to maintain risk free position

Question 23

with delta hedging which value tells you the number of shares held per option sold?

Answer 23

delta - N(d1)