Lecture 7

Question 1

Define options and distinguish between a European and American option

Answer 1

A call (put) option gives its owner the right to buy (sell) stock at a specified
exercise or strike price (K) on or before a specified maturity date (T)

European options are exercised only at maturity; American options can be
exercised on or at any time before maturity.

Question 2

Outline differences in being long and short on a call/put option and provide the profitability formula for each

Answer 2

Question 3

Please outline:
Covered call strategy
Naked put writing
Protective put strategy

Answer 3

Covered call strategy:
This strategy involves buying the underlying stock and simultaneously selling a call option on the same stock. This is done to generate income from the premium of the call option while holding the stock

Naked put:
Selling a put

Protective put:
Buying a stock and purchasing a put option for the same stock. To protect against downside risk while maintaining upside potential.

Question 4

Please outline straddle and butterfly spread

Answer 4

Straddle: Simultaneously buying a call option and a put option with the same strike price and expiration date. To profit from significant price movements in either direction (volatility).

Butterfly spread: Buying two options with the same expiration date but different strike prices (K1 and K3) and selling two options with a strike price in the middle K2, where K2 = (K1+K3)/2

Question 5

Please list and explain the formulas for put-call parity options (European, American & dividend-paying)

Answer 5

European:
P+S = C+K * Exp(-rfT)

American:
P+S = C+K * Exp(-rfT) + E

Dividend paying:
P+S * exp(-qT) = C+K * Exp(-rfT)

Question 6

What are the determinants of option prices?

Answer 6

Question 7

Please find the expected value today of the following call

Answer 7

Answer in notes

Question 8

Consider a 1-year European call option with a strike price of $90
written on a non-dividend-paying stock whose current price is $90.
Suppose that at the end of year 1 the stock price either increases to
$110 or decreases to $70. The annual risk-free interest rate is 9%.
What is the price of this option?

Answer 8

Show workings
Price:

Question 9

What is the Black-Scholes formula?

Answer 9

Question 10

Find the price of the call according to Black-Scholes using the following data:
Stock price (S0) = 100
Strike Price (K) = $105
Time to Maturity (T) = 1 year
Risk-free rate = 0.05
Volatility = 0.20

Answer 10

Show all steps:
C0 = $7.97

Question 11

What is the formula for p (risk-neutral outcome) when solving the binomial tree?

Answer 11