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| {{freeessay|isda|tail events|}}{{d|Tail event||n|}} | | {{freeessay|isda|tail events|{{image|Tail event|jpg|}}}} |
| {{L1}}'''Statistics''': Of a range of possible independent events, one whose frequency is three or more [[Normal distribution|standard deviation]]s from the mean. An event with a low [[probability]]. <li>
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| '''Work life''': An unwanted outcome to which you weren’t paying attention, which you didn’t expect and, therefore, for which you don’t think you should be blamed.
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| </Ol>
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| We are, as the JC frequently complains, in a swoon to the [[Reductionism|reducibility]] of all things.
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| This usually involves converting all the things that we do and that happen to us into numerical [[data]] points.
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| But, “these that we do and that happen to us” things being the four dimensional social constructions that they are ineffable as they are, that conversion necessary involves a loss of information.
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| Data points, in themselves, are no more naturally [[effable]] than “odd things that happen to us” from which they are extruded, of course. But numbers have the quality of submitting easily to aggregation, symbolic manipulation and statistical techniques, in a way that “odd things that happen to us” do not.
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| What one has rendered as data, one can use in calculations. With these one can generate abstract mathematical properties: a mean, a median, a mode. One can calculate probabilities.
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| Applying a number to an artefact is a linguistic operation, like assigning a noun. The calculations we perform with that number tell us about the mathematical properties of the number. They do not tell us anything about the artefact it signifies. This is easy to see with an average. The average height of the passengers in this train carriage tell us nothing about any of the passengers. Yet so much of the modern world measures against the average!
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| We take harvest information from artefacts, convert it into data, generalised it, manipulate it mathematically, and then apply it back to the artefacts.
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| In the same way that one can calculate the probability of rolling consecutive sixes (1/36) so, it seems, one can calculate the probability of rain tomorrow, a cut in stamp duty in the spring, or a thirty-point intraday drop in the NASDAQ.
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| This is an invalid move, unless the artefacts were in the first place identical. The sides of a dice are (but for their label) identical. People are not identical.
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| But numbers are alluring. They are under our control. They ''behave''. They bend to the spreadsheet’s will. The spreadsheet’s will is our will.
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| Except, as [[David Viniar]]’s immortal words remind us, the events these numbers represent — the territory for which they are a map — are wont to have other ideas.
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| {{quote|{{viniarquote}}<ref>explaining why the [[vampire squid]]’s flagship hedge funds lost over a quarter of their value in a week, in 2008.</ref>}}
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| Rolling dice are not like the stock market.
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| ====The map and the territory====
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| Mr Viniar’s model, he hoped, would tell him something about the market’s behaviour. The model is the ''map'', the market is the ''territory''. We judge the success of a model by how close its prediction is to our subsequent [[lived experience]]. There is a natural dissonance: models are drawn from past experience, and that is singular, static and unalterable. It is dead. Our future experience is, as far as we know, none of these things.
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| You would not expect a “twenty-five sigma” day once in several lifetimes of the universe. Goldman’s model was in effect saying, this kind of event ''will not happen''.
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| This would be the equivalent of all the molecules in a cup of tea spontaneously jumping to the right at the same moment. The molecules are bouncing around randomly — Brownian motion, right? — and so conceptually they could all jump left at once<ref>it may be that, conceptually, they couldn't — Brownian motion depends on collisions. For all I know, this implies that half the molecules are jumping the other way.</ref> but the sheer odds of every single atom doing do at once are so infinitesimally small that it would never happen in several billion lives of the universe. Neither the cup or the tea in it would last that long, of course.
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| But that is the scale of likelihood of a twenty-five sigma event.
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| That Mr Viniar thought there were several such days ''in a row'' — in a market history measured in decades, not universe lifetimes — must mean the model was wrong.<ref>It was, for reasons we explore elsewhere.</ref>
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| Now here is the thing. When we calculate probabilities — when we roll dice — we are situations of known risk. That average means something. It is not just that on some some dice the probability is more like ⅐, on others now like ⅕, but on average the dice work out at all about ⅙. It must be true of every individual die..
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| Rolling dice to ''determine'' an outcome is is quite
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| different. We do not build a statistical model that predicts a ⅙ probability: we build the dice to yield the that outcome. The dice are what [[Nancy Cartwright]] calls a “[[nomological machine]]”: a carefully designed, constrained, hermetically-sealed device, designed to generate a specific theoretical outcome. If over time the dice don’t yield a ⅙ outcome we don't chuck out our statistical model: we chuck out the ''dice''.
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| The “map” and territory ” are transposed: the dice are the map, the theoretical ⅙ probability is the territory. The map is, as far as engineering permits, ''identical'' to the territory. We could, indeed, generate the outcome we wanted without dice, by running the model with a random number generator.
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| The machined dice, the flat, constrained surface — these are a representation of the reality, which is the hypothetical model, and not the other way around. A loaded die is a ''flawed'' machine. You don't chuck out the theory: you chuck out the equipment.
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| Likewise, if, inside your nomological machine there is a mischievous imp who catches and places the die as it sees fit, the conditions for your probabilistic calculation do not prevail. There is an interfering causal agent.
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| “Nomological machines” are highly constrained, artificial environments. If all their conditions are not satisfied, we can expect the world to behave differently without validating the machine. This is how, as [[Nancy Cartwright]] put it “the laws of physics lie”.
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| In any case, these are the circumstances in which the rules of probability prevail. Should the universe “misbehave” then the conditions required for the nomological machine cannot be present.
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| Boy did I get sidetracked.
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| Normal distributions standard deviations, and confident probabilities require a complete nomological machine where all potential events are known, are independent, and there is no intervening agency that can upset the observed behaviour of the system. If you have all that all risks can be calculated and probabilities assigned.
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| Markets, in the abstract, look just like such a machine. There is a bounded environment, a finite trading day and a limited number of market participants and financial instruments which one can buy or sell. In the modern days of computerised trading everything is very clean, tidy observable, unitary and discrete.
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| ====Derivatives trading====
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| In the context of trading derivatives, things that (a) you didn't reasonably expect and that . (b) bugger up your contract.
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| =====Credit defaults=====
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| A swap being a private, bilateral affair, the most obvious category of tail events is “things which mean your counterparty cannot, or will not, or has not, performed its end of the deal”.
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| Straight out refusal to — repudiation — is rare, at least without the cloak of some kind of dispute as to whether the party was under such an obligation in the first place.
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| Inability is the main player here: generally captured by insolvency, and correlative defaults under other agreements.
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| Much of financial services being a play on [[leverage]] — the name of the game being to earn more, with other people’s money, than it costs you to borrow it — many market participants flirt with various formulations of [[insolvency]] as a basic business model, so there tend to be some pushback on the parameters of these correlative failures and “ostensible inabilities” to perform. Much of a [[negotiator]]’s life is spent haggling about them.
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| Where refusal or inability to perform cannot be proven, actual failure to pay or deliver ends all arguments. If you ''actually'' haven’t performed, it no longer matters ''why''.
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| There is therefore a sort of hierarchy of these events. Actual default is the safest, and most common, default trigger. Bankruptcy is the next — though there is more looseness around some of its limbs, an administrator actually being appointed, or a petition actually being filmed is clean, public and unlikely to prompt many arguments. Default Under Specified Transaction — that transaction being one to which you are directly a party,
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| The remaining events are sketchy and unpopular, depending as they do on private information you most likely won't have about thresholds you can't easily calculate. We may argue till we are hoarse about Cross Default. We will not invoke it.
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| =====Externalities=====
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| There are a category of events which make it impossible even for a solvent counterparty to perform. Change in law, for example — it is not beyond possibility that certain kinds of swaps might be restricted or outlawed altogether<ref>Not long ago the European Union proposed restricting the carbon market to “end users” to discouraged financial speculation, for example. This would have rendered certain forward contracts in {{euaprov|Allowances}} involving delivery to non-users illegal.</ref> or Tax events that make the transaction uneconomic as originally envisaged.
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| Secondary events of this kind — things that limit a delaer’s ability to hedge, or materially increase its costs of doing so, tend not to be Termination Events partly this reflects a fact not often stated, but nonetheless true: there is a price at which the parties will agree to terminate any swap. Just because a party doesn't have an economic option to terminate the trade doesn't mean it can't terminate the trade. It always has an “at market” option. In liquid markets during times of fair weather this is a source of great comfort; in illiquid markets and at times of stress, less so. A dealer will say, “I will always show you a price. You just might not mind the price, is all.”
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| Customers have less incentive to break trades if it means realising
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| {{sa}}
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| *[[The map and the territory]]
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