The Black-Scholes-Merton debate
I have to say the invention of continuous time dynamic hedging was original, but to go from discrete delta hedging to continuous delta hedging is something traders not can use. Loads of quants keep using the continuous delta hedging argument to model everything in risk-neutral world where supply and demand for options themselves do not enter the equation. Yes I am sure it works well on the University campus, but how many options are trading there?
Yes and option formulas existed long before Black-Scholes-Merton. There is also a book in production I understand that will translate some of the less known "ancient" option formula texts into english.
Here an interesting paper I just came over (thank you Koekebakker for showing me this) indicating empirically that option traders very well could price options before 1973
"Traders in the nineteenth century appear to have priced options the same way that twenty-first century traders price options. Stylized facts relating implied volatility to realized volatility, stock prices, and other implied volatilities, are the same in both eras. This paper quantifies how pricing efficiency of the market has evolved over time: implied volatility is more responsive to realized volatility shocks, and the market’s required compensation for being short volatility declined as the market has matured. Modern pricing models and centralized exchanges increased trading activity, but they did not fundamentally alter pricing behavior in the option market."
As we know from Nelson the put-call parity was fully known at least by 1904 (probably much earlier) the same was discrete market neutral delta hedging for atm options, discrete delta hedging was developed further by several other researchers. Several option formulas existed in early 1900. It comes as no surprise that traders could price options very well before 1973, and now the empirical research seems to confirm this.
But I am sure there was option traders blowing up back then as well as now. Great option traders relay on robust hedging principles and not fantasy assumptions that do not hold in practice. In practice we have jumps, liquidity can dry up, both for underlying and not to forget for the options themselves. For example Nelson indicated great option traders that survived in long run tended to be long options not short. To be long options is a simple way to make your portfolio robust from the massive leftover risk even after market neutral delta hedging is taken into account. Hedging options with options is another way to do this. See also Models on Models chapter 2 for details on this.
