Self Study Questions Topic 8

Question 1

C from the BSM model
european call

Answer 1

Question 2

d1 from the BSM model
(ON FORMULA SHEET)

Answer 2

Question 3

d2 from the BSM model

Answer 3

Question 4

getting from an annually compounded rate to continuously

Answer 4

ln (1+ annually compounded rate)

Question 5

put call parity

Answer 5

Question 6

stochastic

Answer 6

just means random

Question 7

Properties of stochastic processes

Answer 7

1. Markov - no memory (expected value depends only on the previous value)
2. Martingale - expectation is the future is where we are today (conditional expectation of random variable is the value today)

Question 8

key properties of the Brownian motion (definition)

Answer 8

1. starts with zero
2. continuous paths
3. independent increments
4. normal increments
5. variance grows linearly with time
6. markov and martingale properties

Question 10

Itô’s Lemma

Answer 10

first derivative multiplied by dX and then 0.5 of second derivative multiplied by dt

Question 11

key assumptions behind BSM

Answer 11

1. underlying follows a lognormal random walk
2. risk free interest rate is a known function of time
3. no dividends
4. continuous and effective delta hedging
5. no transactions costs
6. no arbitrage opportunities

Question 12

log returns

Answer 12

Question 13

varying standard deviation

Answer 13

increase = increased value
higher standard deviation = greater upside risk

Question 14

calculating implied standard deviaiton

Answer 14

trial & error

if value < C then increase std deviation

if value > C then decrease std deviation

std deviation = 0.5 good starting

Question 15

Brownian Motion & Standard form of scaled BM with drift & pricing options

Answer 15

• BM = continuous time limit process
• starts discrete n -> infinity = continuous

Question 16

BM with drift equation

Question 17

BM with drift scaled equation

Answer 17