Lecture 4: Black-Scholes-Merton approach to Option Pricing

Question 1

‘Moneyness’ determines the ? but can’t be known in advance.

If option ends up In the Money, option writer faces a risk ?? with t’ riskiness of underlying asset.

Answer 1

‘Moneyness’ determines the risk but can’t be known in advance.

If option ends up In the Money, option writer faces a risk 1:1 with t’ riskiness of underlying asset.

Question 2

Key to Black-Scholes is the ‘??’ portfolio th’ must offer a ‘?’ rate of return
=> a theoretically correct ? factor is determined.

Answer 2

Key to Black-Scholes is the ‘no-arbitrage’ portfolio th’ must offer a ‘riskless’ rate of return
=> a theoretically correct discount factor is determined.

Question 3

B-S-M Model Assumptions:

1. Share price follows ?:
dS = ????
2. No ?-selling restrictions
3. No ? costs or ?
4. Securities are ??
5. Underlying pays no ?
6. No ? opportunities
7. ? trading
8. r is ? and the ? for all maturities

Answer 3

B-S-M Model Assumptions:
(Many have been relaxed)
1.Share price follows gBm:
dS = µSdt + σSdz
2. No short-selling restrictions
3. No transactions costs or taxes
4. Securities are perfectly divisible
5. Underlying pays no dividends
6. No arbitrage opportunities
7. Continuous trading
8. r is constant and the same for all maturities

Question 4

B-S model address t’ issue of pricing ? options on ?? paying shares.

Answer 4

B-S model address t’ issue of pricing European options on non-dividend paying shares.

Question 5

Assume ALL investors are risk-?

=> appropriate discount rate = ? rate of interest

Answer 5

Assume ALL investors are risk-neutral

=> appropriate discount rate = riskless rate of interest