Microsoft PowerPoint - PoF.ppt

One-period binomial modelƒ 200

To rule out arbitrage we must assume: 0 < d < 1+r < u.

ƒ

Positivity of stock prices

Ä

d > 0.

ƒ

If d

≥

1+r

Ä

Arbitrage strategy:

• Time 0: Borrow from the money market in order to buy the stock. - Time 1: Even in the worst case, the

value of the stock will be higher

than or equal to the value of

the money market debt and has a

positive probability of being

strictly higher since u > d

≥

1+r.

ƒ

If u

≤

1+r

Ä

Arbitrage strategy:

• Time 0: Sell the stock short and

invest the proceeds in the money

market.

• Time 1: Even in the best case, th

e cost canceling the short position

will be less than or equal to the value of the money market investment and has a positive probab

ility of being strictly less since d

< u

≤

1+r.

Derivative securities: Options - Binomial asset pricing model