Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different...

The paper reviews the option pricing model constructs of Bachelier and Black-Scholes Merton, concluding the latter model approximates the former. The paper demonstrates that certain critiques of the Bachelier model outlined in the 1960s and 1970s are not sound; and Bachelier's model can be...