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To remain riskless it must be frequently adjusted or “rebalanced”.

In particular, we would have to rebalance continuously!

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However,

we will obtain a riskless rate of return on our portfolio

which by absence of arbitrage is equal to our riskless interest rate from the money market account.
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This is the key element in the

BS arguments and leads to their

pricing formulas.
Derivative securities: Options - Black-Scholes modelBlack-Scholes model: Main ideas

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