Template:M intro isda tail events: Difference between revisions

Not having to deal with rust, water damage, and manufacturing defect simplifies the business of investing. The ''effects'' of these events are supposed to play out in the information layer, and translate efficiently into the prices at which related instruments trade. If an oil company’s tanker is wrecked, its share price declines.  

From this price information we can ''derive'' a relationship between transactions — price went up, price stayed the same, price went down — and a ''trend''. A trend is a stab at extracting a signal from the noise.

The [[Signal-to-noise ratio|signal]] depends on a theory of the game: otherwise the “relationship” between the two discrete transactions is arbitrary.

 

Without a theory, ''everything is noise''.  

If events are truly “independent” then any “trend” we draw between them beyond their distribution is, more or less, meaningless.  In a first order sense, market events are independent: the participants in the later trade do not know who or where the participants in the earlier even are, let alone what their motivations for trading were. All we have is a theory and some mathematics. But we draw the line all the same. We make assumptions: the market is homogeneous; all participants have similar price information; all are propelled by the same rationale. No trader sells things she expects to do well, or buys things she expects to do badly.  

Given these assumptions, individual investors’ private motivations, opinions, theories and idiosyncrasies cancel each other out, so we can disregard them. They are like the [[Brownian motion]] of molecules in a [[nice hot cup of tea]]: reversions to the [[entropy|entropic mean]]; baseline white noise. This is just as well, because otherwise our models would not work. We can ignore individual sentiments because they don’t matter. Until they do.

Put another way: although the “interconnectedness” of similar transactions means they do ''not'' have the quality of independence that a [[normal distribution]] requires, most of the time they ''pretty much'' do: information is chaotic in the immediate term, here the dissimilarities between trader motivations are most pronounced, but over a large aggregation of trades and a longer period a “signal” emerges. This is what [[Black-Scholes option pricing model|Black-Scholes]], volatility and convexity models track: as long as all traders all use the same aggregated market information — and the market works hard to ensure they do — a “normal” probabilistic model works fairly well. It’s not a bad ''model''.  

So we treat professional market participants as a largely homogenous group from which emerges, over time, a [[signal]]. Almost like, you know, like an ''invisible hand'' is guiding the market. This gets our model out of the gate. If investors were not broadly homogeneous, our models would not work. “The average height of every item in this shed” is not a particularly useful calculation. Which way the causal arrow flows — whether signal drives theory or theory determines what counts as a signal — is an open question.