12) The Black-Scholes Model

Question 1

What are the assumptions of the Black-Scholes Model

Answer 1

The assumptions are:
* money can be borrowed and lent at a constant risk-free interest rate r
* the share price follows a Geometric Brownian Motion with constant expected growth rate µ and volatility σ
* there are no transaction costs
* the share does not pay dividends
* financial contracts are perfectly divisible (e.g. we can buy/sell any fraction of a share)
* there are no restrictions on short selling

Question 2

If Π = V − ∆S, what is dΠ

Answer 2

Question 3

Describe the proof that

Answer 3

Question 4

From the following equation how can we eliminate risk

Answer 4

Question 5

What are the detailed steps in deriving the Black-Scholes equation

Answer 5