Dear Quant Finance Community,

I have been reading a considerable amount of material regarding the BSM model and I am fascinated by the evolution of the model and options trading industry. However, from what I have read, there are some controversial topics that seem to have no definite conclusions. I was hoping that persons in the Quant Finance Community may be willing to share their insight.

What I have learned is that the notion of a self-financing replicating strategy (e.g. dynamic hedging) was not an original idea for Black and Scholes. They recognise this in their 1972 publication, pointing out that Thorp and Kassouf already discovered this (and were applying it in the markets way before options became standardised on the CBOE in 1973).

It is pointed out in various texts that the main difference between Thorpe and Kassoufs work and Black and Scholes work, is that Black and Scholes observed that a combination of “delta” long shares over a very (instantaneous) short period of time should earn a return equal to a riskless investment.

But what does not make sense to me is that Black and Scholes would not have “observed” this if Merton didn’t point it out to them by introducing the notion of continuous-time dynamic hedging? Only under the continuous-time and continuous trading assumption (along with other unrealistic assumptions) does the no-arbitrage hypothesis kick in, where only the risk-free rate remains as the expected return of a perfectly hedge portfolio?

This makes me question why the work of Black and Scholes took precedence over Thorp and Kassoufs work? It would seem that Black and Scholes didn’t actually invent anything novel? But they had the vital input from Merton which validated the general ideas at the time? I am making a presumption of course, and would appreciate constructive negative or positive feedback.

If my presumption is correct, what then was Black and Scholes real contribution? I can understand why Merton got the economic equivalent of the Nobel prize for his Ito calculus contribution, but why did Scholes also get the prize (Fischer had passed away but would also have receive the prize if alive)?

What I also find highly suspicious is that the BSM model only works in a risk-neutral world (where investors have no risk/reward preferences) and other unrealistic assumptions hold. Of course risk preferences are moot if one can perfectly dynamically hedge, but one cannot actually do this in real markets. Furthermore, intuitively anyone who studies the problem understands that volatility is never constant and it cannot be predicted (it can only be forecasted which is a poor methodology for traders). If traders (buy side and sell side) intuitively understand that geometric Brownian motion is not a reflection of reality, and that volatility is not constant and cannot be predicted; then surely expected return based on risk preferences are actually very important?

The problem is that expected return cannot be observed or measured, which isn’t conducive to deriving a close-form solution for option pricing. Perhaps Black, Scholes and Merton knew this and had to find a way to “get rid” of the notion of expected returns?

This also makes me think that the market reintroduced the inescapable reality of risk preferences (i.e. expected return) into what we today call implied volatility? Now market makers and traders manipulate IVol to reflect their risk preferences related to unknown future underlying pricing outcomes. Market pricing of options reflects this. No longer does sigma represent volatility in accordance with GBM assumptions. Rather sigma represents whatever traders and market-makers believe the future may or may not hold which is purely subjective or based on sophisticated mathematical and statistical guesswork. Traders, market makers and quants are now financial alchemists in their own right?

Is there something wrong with my thinking? I would really appreciate your feedback if anyone has the time and interest to respond.

With thanks and appreciation in advance!