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In the Realm of Volatility

I went to see John McEnroe: In the Realm of Perfection, which really was a movie about what it’s like to be transcendently in the realm of the senses, playing with expert intuition combining body and mind. It wasn’t Oshima’s In the Realm of the Senses but it could have been just as good a title.

In the middle of the movie the narrator stated that tennis is about the invention of time. Unlike football or most other games which end at a finite time, a tennis game goes on until someone is up by two points and has won at least four points. And, before the era of tiebreakers, something similar applied to the number of games in a match. The players themselves determine how long the game goes on.

An imperfect analogy:

Tennis: The tennis ball moves back and forth across the net, in a sort of (not quite) three-dimensional random walk, punctuated by shots (returns, actually, after the initial service). The time between shots is not constant; sometimes a shot comes sooner, sometimes later. The game ends when the ball is mishit or missed. There might have been one shot (an ace) ,or two shots (a winning return) or three shots (a serve and volley), or a long rally. The faster the returns occur in sequence, the more one is in the realm of the senses, of feeling and intuition, of playing without conscious reason.

Stock prices: move up and down in a sort of random walk, punctuated by trades (that define returns) that occur at random times. The number of steps taken for a stock to move from 100 to 110 could be small or large, dependent on volatility. There are stock options that expire not when a certain amount of time passes, but when a certain amount of stock volatility has been experienced. (Early versions of LOR’s Portfolio Insurance scheme that supposedly caused the ’87 crash gave clients protection against market declines not for a certain time but for a guaranteed amount of experienced variance.) What may matter for stock price modeling and market impact is market sentiment, related to the number of trades that occur in a fixed time. The faster the trading occurs (the greater the trading frequency), the greater one is in the realm of the senses, the greater the sentiment/sensual component of the trade.

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