The replicating portfolio 208The replication argument depends on several assumptions:Short positions are allowed(unlimited credit).Shares of stock can be subdividedfor sale or purchase.Essentially satisfied because optionpricing and hedging (replication)typically involve lots of options.
The interest rate for investing isthe same as the interest rate forborrowing; we use a constant risk-free rate which is assumed to be thesame for all maturities.Is close to being true for large institutions.
The purchase price of stock is the same as the selling price, i.e.there is zero bid-ask spread.Is not satisfied in practice.
No transaction costs, taxes, ...
At any time,the stock can take only twopossible values in the nextperiod.In the Black-Scholes model, this assumption is replaced by the assumptionthat the stock price is a geometric Brownian motion. Empirical studies of stock price returns have consistentlyshown this not to be the case!Derivative securities: Options - Binomial asset pricing model