
The Pricing of Options and Corporate Liabilities (1973) [pdf] - jpelecanos
https://www.cs.princeton.edu/courses/archive/fall02/cs323/links/blackscholes.pdf
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brockwhittaker
I would reference this as one would reference a physics book from a hundred
years ago — a possibly decent starting point but old knowledge that has been
proven incorrect in dangerous ways.

For example, the Black Scholes model that was developed in 1973 assumes a
normal distribution, which is not only wrong, but an extremely dangerous
misunderstanding of the markets that leads to the underestimation of Black
Swan events and rail risk.

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pash
The Black–Scholes–Merton model does assume a log-normal distribution of price
changes, and the tails of that distribution are not fat enough to account for
the frequency of large price changes observed in real-world markets.

But your criticism is essentially off base. The main reason the
Black–Scholes–Merton model remains the workhorse of derivatives pricing nearly
a half century on, and the reason two of its creators were given a Nobel prize
in 1997, is that the model has proved to be enormously adaptable. One can
relax the assumption of constant volatility in various ways, assuming instead
that volatilty depends on the price level, on other factors, or that it is
itself random. These embellishments retain the Brownian motion and its normal
distribution as the primary source of randomness, but the added volatilty
structure allows for almost arbitrarily fat tails and all sorts of complicated
dependencies in the resulting distribution of price changes.

The fields of mathematical finance and financial engineering are in large part
concerned with coming up with tweaks to the Black–Scholes–Merton model that
provide the complications necessary to price idiosyncratic securities while
maintaining as much of the simplicity of the basic model as possible so that
pricing (usually numerically) remains tractable.

As JumpCrissCross pointed out, there have also been numerous follow-on models
developed that make different assumptions about the basic distribution of
price changes, going back to Merton’s jump-diffusion model of 1980. Most of
these models can still be viewed as embellishments of the Black–Scholes–Merton
model.

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brockwhittaker
Completely agree. My point is that readers should not stop reading at this
source, and to keep digging, as this isn’t the “answer” to valuation.

