Black-Scholes Model/Equations - The numbers, Mason!

[Anti Snigger]

So, I've been interested in the mathematics behind the stock market, and last night I discovered The Black-Scholes Model. I'm admittedly pretty intrigued by this as someone who studies math, and I'm just curious if anyone here is familiar with these equations and how they're applied in practice.
Using 1D Brownian motion to model stonks is so retarded to me that it wraps around to based for me and I totally believe that it could work.

 

[Waifu Denier]

Black-Scholes is bullshit because it still assumes a normal distribution of stock returns, which is unrealistic given both tail risk and the assumption that large price shifts must be lower in probability than small ones. But if you want a practical lesson. look at how Myron Scholes, half of the eponymous model, was part of LTCM which blew up spectacularly and lost 4.6 billion dollars in a few days.

 

[Anti Snigger]

Black-Scholes is bullshit because it still assumes a normal distribution of stock returns, which is unrealistic given both tail risk and the assumption that large price shifts must be lower in probability than small ones. But if you want a practical lesson. look at how Myron Scholes, half of the eponymous model, was part of LTCM which blew up spectacularly and lost 4.6 billion dollars in a few days.

Yeah I noticed the use of normal distributions throughout, I guess that's a valid criticism. At least in physics, for large enough systems you can model any inherent randomness as normal because the erraticism all cancels out.

 

[Waifu Denier]

Yeah I noticed the use of normal distributions throughout, I guess that's a valid criticism. At least in physics, for large enough systems you can model any inherent randomness as normal because the erraticism all cancels out.

You try applying a normal distribution to stock returns and you will get regular 10+ sigma events, and anyone with common sense will realize that the chance of the stock market crashing like Black Monday being that of the earth suddenly randomly gravitationally collapsing into a black hole is extremely flawed. If any of these pricing models could be used for reliable (risk adjusted) profit above the market return, they would be trade secrets kept hidden by Renaissance rather than something any schmuck can look up and apply online.

 

[Anti Snigger]

You try applying a normal distribution to stock returns and you will get regular 10+ sigma events, and anyone with common sense will realize that the chance of the stock market crashing like Black Monday being that of the earth suddenly randomly gravitationally collapsing into a black hole is extremely flawed. If any of these pricing models could be used for reliable (risk adjusted) profit above the market return, they would be trade secrets kept hidden by Renaissance rather than something any schmuck can look up and apply online.

Yeah, as I've been learning this stuff, I've been trying to keep in mind that any idea I have is at a minimum late as fuck if not wrong, given the resources put into studying things. I'm not investing at all, I'm kind of just looking at it from an academic perspective for now

 

[herefortheactualthreads]

blah blah blah reznov la la la bowman

 

[N Space]

You try applying a normal distribution to stock returns and you will get regular 10+ sigma events, and anyone with common sense will realize that the chance of the stock market crashing like Black Monday being that of the earth suddenly randomly gravitationally collapsing into a black hole is extremely flawed. If any of these pricing models could be used for reliable (risk adjusted) profit above the market return, they would be trade secrets kept hidden by Renaissance rather than something any schmuck can look up and apply online.

I have always thought that isn't the case simply because the barrier of entry is so fucking high. I personally did a project in my advanced probability graduate course to merely define Ito's Integral, I didn't get into any uses or theorems regarding it, let alone the definition, examples or solutions for SDEs (Stochastic Differential Equations) which is what Black-Scholes is. This is absolutely not a thing any schmuck can look up and use.

 

[N Space]

Yeah I noticed the use of normal distributions throughout, I guess that's a valid criticism. At least in physics, for large enough systems you can model any inherent randomness as normal because the erraticism all cancels out.

God bless the Central Limit Theorem.

 

[Waifu Denier]

I have always thought that isn't the case simply because the barrier of entry is so fucking high. I personally did a project in my advanced probability graduate course to merely define Ito's Integral, I didn't get into any uses or theorems regarding it, let alone the definition, examples or solutions for SDEs (Stochastic Differential Equations) which is what Black-Scholes is. This is absolutely not a thing any schmuck can look up and use.

The barrier of entry is high but you have to remember that even if only a small portion of people will ever understand something like how to apply a maximum Lyapurnov exponent to index analysis, the absolute number of people will still be in the thousands of new graduates every year who will then enter the industry and to the myriad companies that try everything to gain a market advantage. It isn't hard for a few companies to amass a large amount of leverage (literally) in strategies they think will be highly profitable.

 

[Thorndyke Special]

If any of these pricing models could be used for reliable (risk adjusted) profit above the market return, they would be trade secrets kept hidden by Renaissance rather than something any schmuck can look up and apply online.

I agree with your overall point, but once in a blue moon things have been studied but never put into practice. One example that spring to mind is the fact that academics had proven that a diversified portfolio of junk bonds yielded higher (even with the inevitable bankruptcies) than a portfolio of AAA bonds two decades before Mike Milken put these studies into practice and reaped billions in reward.

These days, though, it's very likely that you're correct and any ev+ models discovered will instantly be deployed and guarded with religious fervor.

 

[Waifu Denier]

I agree with your overall point, but once in a blue moon things have been studied but never put into practice. One example that spring to mind is the fact that academics had proven that a diversified portfolio of junk bonds yielded higher (even with the inevitable bankruptcies) than a portfolio of AAA bonds two decades before Mike Milken put these studies into practice and reaped billions in reward.

These days, though, it's very likely that you're correct and any ev+ models discovered will instantly be deployed and guarded with religious fervor.

I would actually agree with your point. I do think there are many ways to gain an advantage over the market, but for the ordinary layman, or even skilled and experienced individual, it isn't something that's often feasible, because you are in competition against organizations with large pools of talent and resources.