Self Study Questions Topic 5

Question 1

Binomial Option Pricing Hedge Ratio (also a proof)

Answer 1

Question 2

Pseudo Probability Measure

Answer 2

Question 3

One Period Binomial Option Pricing Equation

Answer 3

Question 4

Nomeclature for 1 period binomial model

Answer 4

Question 5

Two Period Binomial Option Pricing Equation

Answer 5

Question 6

Three Period Binomial Option Pricing Equation

Answer 6

Question 7

Pseudo Probability Measure P’

Answer 7

Question 8

N-period binomial option pricing equation

Answer 8

Question 9

Working out B

Answer 9

combination function - number of periods = superscript and number of ups = subscript
x the pseudo probability to power of number of ups x (1-pseudo probability to the power of number of downs)

Question 10

Calculating Z statistic for Normal Distribution

Answer 10

1. mean
2. std deviation
3. Z statistic = (a - mean) divided by SD

Question 11

Min binomial ‘ups’ for positive payoff

Answer 11

ROUND UP
(given on formula sheet)

Question 12

Put-Call Parity

Answer 12

Question 13

Upper Option Price Bounds (European)
also a proof

Answer 13

Question 14

Lower bounds for European CALL price (no dividends) (proof also)

Answer 14

use discrete - time in periods, rate is per period

use continuous - time in years, rate is annual

Question 15

Lower bounds for European PUT price (no dividends) (proof also)

Answer 15

use discrete - time in periods, rate is per period

use continuous - time in years, rate is annual

Question 16

Lower bounds for European option prices WITH dividends

Answer 16

-payment of dividends detracts from share price

(just a +D on both of the bounds)

Question 17

Put Call Parity (European options WITH dividends)

Answer 17

Question 18

Bounds for American options prices

Answer 18

Question 19

American option price relationships

Answer 19

Question 20

Early Exercise of American Options
No dividends

Answer 20

Question 21

Early Exercise of American Options
Other cases and with dividends

Answer 21

Question 22

C subscript u

Answer 22

u = 1 + proportional change in price

Question 23

C subscript d

Answer 23

d = 1 + proportional change in price

Question 24

mean for the normal distribution

Answer 24

number of periods multiplied by the correct pseudo probability

Question 25

Std deviation for normal distribution

Answer 25

square root of mean multipled by (1 - pseudo probability)

Question 26

Z statistic for normal distribution

Answer 26

a - the mean all divided by standard deviation

Question 27

Locating Arbitrage Opportunities

Answer 27

- arise when wrongly priced locate via: 1. under/over pricing vs some models/estimations 2. priced outside of theoretical lower/upper bounds 3. non-conformity of prices with put-call parity

Question 28

derivative

Answer 28

financial asset existence depends upon other asset measure (underlying) worth depends on movements in underlying

Question 29

option

Answer 29

right but not obligation to buy/sell underlying class of derivative at predetermined price (exercise price) with reference to expiry date

Question 30

call vs put

Answer 30

CALL = RIGHT TO BUY PUT = RIGHT TO SELL

Question 31

European vs American

Answer 31

European = exercised on expiry American = exercised any point up to & including expiry date American option = has value greater or equal to European (more freedom and less constraints)

Question 32

Attributes/Parameters define option/contribute to value

Answer 32

1. price of underlying 2. exercise price 3. volatility 4. time to maturity 5. risk free rate (6. dividends)

Question 33

why never exercise an American Call Option Early

Answer 33

1. loss time value - unlimited upside, limited downside 2. pay strike early is inefficient - pay later = lower the present value Call american = Call european

Question 34

why sometimes exercise an American Put Option Early

Answer 34

1. immediate receipt of strike price = cash now, invest risk free 2. limited upside remaining = max is E, underlying low - time value is then small 3. no dividends = no benefit Put american greater than or equal to put european