The development of the Black-Scholes model for option valuation (Black-Scholes (1973), Merton (1973)) earned Merton and Scholes the 1997 Nobel Prize in Economics “for a new method for determining the value of derivatives” (Nobel Prize press release), and at the time, it was considered “a significant ‘break-through in attacking the option problem” (Merton (1973)). However, shortly after its publication, it was discovered that its assumptions were unrealistic (Latané and Rendleman (1976)). Among them was the assumption of constant volatility, since the volatility implied by the model turns out to be dependent on expiration dates and strike prices. These serious drawbacks have led to a current critical movement regarding the Black-Scholes model, advocating for its abandonment and even its elimination as a subject of study in Quantitative Finance. However, the Black-Scholes model remains fundamental to many subsequent developments, especially those related to implied volatility, since it is defined from the Black-Scholes formula (“the wrong number which, plugged into the wrong formula, gives the right answer,” according to Rebonato (1999)).
Therefore, the question we pose is this: Should the Black-Scholes model be considered, as Merton believed, a significant breakthrough, or is it, on the contrary, a failed model that should be abandoned and forgotten?
References:
- Black, F. and M. Scholes (1973): “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, 81 (3): 637–654.
- Latané, H. A. and R.J. Rendleman (1976). “Standard Deviations of Stock Price Ratios Implied in Option Prices”. Journal of Finance, 31(2), 369–381.
- Merton, R.C. (1973): “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science, 4 (1), 141-183.
- Rebonato (1999): “Volatility and Correlation in the Pricing of Equity, FX and Interest Rate Options”, Wiley.
