November 9th, 2014, 4:31 pm
It's dangerous to try to read an authors mind, in this case Brown, but since he has been MIA from this forum for quite a while, I will give it a shot.If you read the orig. BS paper, you will find the BS formula derived in two different ways: (i) a delta-hedging argument, and (ii) a CAPM argumentThe CAPM model is a market equilibrium model -- why this would be considered the most important, I have no clue and probably would disagree.See wikipedia for more about CAPM.The delta-hedging argument constructed an instantaneously riskless position out of the stock and the option. The rate of return of that position was equated to a Tbill rate of return. Perhaps this could be labeled the market efficiency argument.Completely efficient markets presume (among other things) that all investments with the same payoffs in every state of the world should have the same price -- this is called the Law of One Price. Merton and others turned the delta-hedging argument around to show that, equivalently, a marketed option could be replicated by dynamic trading in the stock and bond.To avoid offering an arbitrage opportunity, the replicated option must cost the same as the marketed option.These are all fuzzy distinctions in the context of this model, however.For example, the delta-hedging argument is also a no-arbitrage argument.Market efficiency is really a concept distinct from the Law of One Price -- read `Efficient market hypothesis' at wikipedia.But the spirit of the quote -- that there are many routes to the BS formula -- is well-known and uncontested.Finally, markets can be efficient, offer no arbitrage opportunities, and follow an equilibrium model -- all with the BSM model being FALSE. Indeed, in the real world, securities markets are highly efficient and offer few arbitrage opportunities, and the BSM model is definitely false. HTH
Last edited by
Alan on November 8th, 2014, 11:00 pm, edited 1 time in total.