Microsoft PowerPoint - PoF.ppt

The replicating portfolioƒ 201

Under the binomial model,

a derivative will assume at most two values

Ä

we need at most two other securi

ties to match its payoff exactly!

ƒ

The arbitrage pricing theory approach to

the derivative-pricing problem is to

replicate the derivative by tradin

g in the stock and the money market

.

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The initial wealth needed to set up

the replicating portfolio is the no-

arbitrage price of the derivative at time zero!

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Derivate price in the market > no-arbitrage price

Ä

Arbitrage strategy:

• Time 0: Sell the derivative short, set up

the replicating portfolio and invest the

rest in the money market.

• Time 1: Regardless of how the stock price

evolved, we have a zero net position

in the derivative and the money market investment.

ƒ

Derivate price in the market < no-arbitrage price

Ä

Arbitrage strategy:

• Time 0: Buy the derivative, set up the

reverse of the replicating portfolio and

invest the rest in the money market.

• Time 1: Regardless of how the stock price

evolved, we have a zero net position

in the derivative and the money market investment.

Derivative securities: Options - Binomial asset pricing model