4 ms·

> theory of random walks, risk neutral pricing, and the black scholes option pricing formula to be the most significant findings Random walks, heck yes! Black

by srean 10y ago

> theory of random walks, risk neutral pricing, and the black scholes option pricing formula to be the most significant findings Random walks, heck yes! Black Scholes not so much. Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously. There's way too much fluctuation in practice than a Gaussian process would fit/predict. So I would put it as: mathematically sound enough, empirically not quite so.

JumpCrisscross 10y ago
> Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously. Options theory is popularly misunderstood. Makes being a former options trader fun and annoying. First, the impact. You can model almost anything as an option. Equity? Call option on a firm's assets struck at the liabilities. (Literally anything else? A portfolio of Arrow–Debreu options [0].) Modern risk models, and these include some very successful ones, would not work without Black Scholes. Second, no professional uses a Gaussian assumption without knowing what they're doing. (In any case, people started re-writing Black Scholes for other curves since at least the 1990s.) No model can economically ascertain every possible risk. One must always choose risks one considers negligible. This is true in finance as in life. Sometimes we choose to ignore the wrong risks. When that happens, it's easier to blame highfalutin math than admit "I didn't think about that". No amount of "fat tailing" will substitute rigorous risk management. Case in point: the multitude of funds launched after 2008 focussing on "black swans" and "fat tails". Pretty much all of them lost money [3]. They missed--with everyone else--Dubai's near default, Greece's actual default, the 2010 Flash Crash, 2011's summer volatility, China's 2015 crash, the following August's international crash, Brexit or practically anything else that one might consider both significant and unexpected. (No shit.) The real "magic" in Black Scholes? It's not the distribution. It's volatility. Modern models expand this once single term into a multidimensional beast [4]. This is the other reason for the prevalence of Gaussian assumptions. Traders trade computation of the distribution for computation of the volatility surface. The latter (tau) almost always dominates the former (delta) in terms of what's being mispriced. [0] https://en.wikipedia.org/wiki/Arrow–Debreu_model https://en.wikipedia.org/wiki/Arrow–Debreu_model [1] https://en.wikipedia.org/wiki/Portfolio_insurance https://en.wikipedia.org/wiki/Portfolio_insurance [2] https://en.wikipedia.org/wiki/Tulip_mania https://en.wikipedia.org/wiki/Tulip_mania [3] http://www.businessinsider.com/watch-out-investors-the-black-swan-funds-arent-that-good-2009-6 http://www.businessinsider.com/watch-out-investors-the-black... [4] http://edoc.hu-berlin.de/series/sfb-649-papers/2005-20/PDF/20.pdf http://edoc.hu-berlin.de/series/sfb-649-papers/2005-20/PDF/2...
- srean 10y ago
  Vehemently agree, in particular this > no professional uses a Gaussian assumption without knowing what they're doing I would say Black Scholes set the theme, but the details had to be modified quite a bit. Unmodified BS is BS. 'Fat tailing' would be very unlikely to give one a better prediction accuracy. It can, however, give one a better appreciation of the risk.
  - JumpCrisscross 10y ago
    > Unmodified [Black Scholes] is BS Black-Scholes-Merton is a theory. Analogous to Newtonian mechanics or textbook thermodynamics. They all need modification to work in the real world. That doesn't make them BS. > [Using a fat-tailed distribution] can, however, give one a better appreciation of the risk How does one choose a model and parameters for events which are, by definition, hard to predict? Keep in mind that most "black swans" arise from unforeseen dimensions of risk. There's the "my stock lost 90% of its value" fat tail versus "the damn exchange went bust". There's "my clearing bank is broke" and "the Russians invaded my country".

by srean 10y ago

JumpCrisscross 10y ago

> Its a fantastic toy model, but over all I think, it did more harm than good. People took its thin tail behavior too seriously. Options theory is popularly misunderstood. Makes being a former options trader fun and annoying. First, the impact. You can model almost anything as an option. Equity? Call option on a firm's assets struck at the liabilities. (Literally anything else? A portfolio of Arrow–Debreu options [0].) Modern risk models, and these include some very successful ones, would not work without Black Scholes. Second, no professional uses a Gaussian assumption without knowing what they're doing. (In any case, people started re-writing Black Scholes for other curves since at least the 1990s.) No model can economically ascertain every possible risk. One must always choose risks one considers negligible. This is true in finance as in life. Sometimes we choose to ignore the wrong risks. When that happens, it's easier to blame highfalutin math than admit "I didn't think about that". No amount of "fat tailing" will substitute rigorous risk management. Case in point: the multitude of funds launched after 2008 focussing on "black swans" and "fat tails". Pretty much all of them lost money [3]. They missed--with everyone else--Dubai's near default, Greece's actual default, the 2010 Flash Crash, 2011's summer volatility, China's 2015 crash, the following August's international crash, Brexit or practically anything else that one might consider both significant and unexpected. (No shit.) The real "magic" in Black Scholes? It's not the distribution. It's volatility. Modern models expand this once single term into a multidimensional beast [4]. This is the other reason for the prevalence of Gaussian assumptions. Traders trade computation of the distribution for computation of the volatility surface. The latter (tau) almost always dominates the former (delta) in terms of what's being mispriced. [0] https://en.wikipedia.org/wiki/Arrow–Debreu_model https://en.wikipedia.org/wiki/Arrow–Debreu_model [1] https://en.wikipedia.org/wiki/Portfolio_insurance https://en.wikipedia.org/wiki/Portfolio_insurance [2] https://en.wikipedia.org/wiki/Tulip_mania https://en.wikipedia.org/wiki/Tulip_mania [3] http://www.businessinsider.com/watch-out-investors-the-black-swan-funds-arent-that-good-2009-6 http://www.businessinsider.com/watch-out-investors-the-black... [4] http://edoc.hu-berlin.de/series/sfb-649-papers/2005-20/PDF/20.pdf http://edoc.hu-berlin.de/series/sfb-649-papers/2005-20/PDF/2...

srean 10y ago
Vehemently agree, in particular this > no professional uses a Gaussian assumption without knowing what they're doing I would say Black Scholes set the theme, but the details had to be modified quite a bit. Unmodified BS is BS. 'Fat tailing' would be very unlikely to give one a better prediction accuracy. It can, however, give one a better appreciation of the risk.
- JumpCrisscross 10y ago
  > Unmodified [Black Scholes] is BS Black-Scholes-Merton is a theory. Analogous to Newtonian mechanics or textbook thermodynamics. They all need modification to work in the real world. That doesn't make them BS. > [Using a fat-tailed distribution] can, however, give one a better appreciation of the risk How does one choose a model and parameters for events which are, by definition, hard to predict? Keep in mind that most "black swans" arise from unforeseen dimensions of risk. There's the "my stock lost 90% of its value" fat tail versus "the damn exchange went bust". There's "my clearing bank is broke" and "the Russians invaded my country".