optimization
i like physics, i like maths, i like coding. you can find all three in the black-scholes equation. the partial differential equation is complicated, but the gist is that you can treat a stock like a physics object undergoing brownian motion. it’s a fascinating interdiscplinary discovery. it is a partial differentiated equation responsible for most of the modern markets. it is the first equation you learn in any computational finance class.
we look at in in the context of options markets. an option is a derivative (something based on another underlying financial asset). it is usually leveraged in theory (with exposure many times over). but somehow, we can obtain the price of options exactly. all parts of the equation are constant and assumed correctly (most of the time) except for volatility. the equation for a log-price of an asset is a mathetmical certainty. the stationarity return distribution is true ninety-nine dot nine percent of the time. returns are independent. asset prices are normally distributed. we’re one variable away from exactly predicting all of the options market.
and in that sense, the beauty is gone. they say options traders are volatility traders because it is the only variable that is still not fixed. everything else comes from some source data. options traders became work hounds. did you know options traders dont blow up anymore? this derivative with astounding leverage… does not blow up anymore! there are circuit breakers limiting instantaneous price moves, a tremendous amount of liquidity, tail risk estimating options models, fully electronic and automated options, equities and money markets to hedge on, and now most edge cases are covered publically. options traders price volatility and make minute changes to models.
the entirety of human ingenuity (including a nobel prize) has been dedicated to making sure markets run efficiently. absolutely despite that, we cannot price real estate accurately. we are off 5-10% of what should be market value. we can have all the data in the world (zillow) and still be unable to do it. we can look in hindsight and ask how the hell did do some things happen. how did china mess up their covid policy so spectacularly bad?
what is the right way? what is the wrong thing to do? i recently have learned a lot about the hasidic jews in new york. they operate a cash-based transactional system. they stroll their babies in designer strollers and yet receive government benefits. they dig tunnels in new york. they own billions in real estate. they skirt the law easily. but they are not lawless people; they practice faith dilligently.
it is an entirely different way of living. one different and yet so similar to our own. i do not know whether to praise or criticize them. do they live optimally? is it more optimally than our own? how do we even compare apples to oranges? we can price abstract derivative markets to a tee but we cannot figure out how to live our lives.
it is entirely fascinating. and a little horrifying. but the real point i want to make is that i do not like how we have not allocated our intelligence correctly. it cannot, it must not be that our smartest and brightest work on minute changes in financial models or advertisement matching. the google of old was responsible for gmail, gmaps, google earth. they innovated transcontinental wires just to send data faster. they invented the basis of chatgpt a decade ago. now they just shutter products and haven’t innovated in years. it’s like they’ve given up. it’s like they sold out and called it quits, citing stakeholder value as a crutch. it is utterly pathetic.
in another sense, i do not know where to go from here. the world continues on. innovation still thrives. maybe this is the right way.
it’s not like i’m any different. i follow the traditional route; i am not nearly prodigious enough to find the optimal one.
another addendum is that black, scholes, and merton discovered their legendary equation in the 1970s. they proceeded to have a 20% year. a 40% year. and then another riveting 40% year. and then they lost $5B in one summer. we had to lose a fund for the others to thrive.
so maybe, we all just do have one life to live and we do not have the luxury of blowing it up. carpe diem.