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To remain riskless it must be frequently adjusted or “rebalanced”.
In particular, we would have to rebalance continuously!
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.
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