120105
For the 95th session of the Philosophical Foundations of Law and Finance, I will read from my unexpurgated and unpublished paper entitled, "Default Invariance." The thesis is that the intersecting discourses of law and finance, normally associated with the professional discourse of risk, can be translated into an UNIVERSAL ALGEBRA, {D, *}, where D stands for "human decisions" and * stands for any one of three isomorphisms, bilateral, translational or rotational. Beauty is thus a result of fundamental binary operations and incorporated into the firey belly of the equations. Since decisions are the objects and the three symmetries are the isomorphisms, the theory logically anticipates and therefore generously incorporates the traditional micro- to macro- economic equilibrium premises of Morgenstein, Von Neumann, Tversky, Kahneman, Debreu, Arrow. To illustrate this algebraic approach to law and finance, we critically examine the Arrow-Debreu-Sharpe model (1995) of a financial contract -- where Time 0 (T0) conditions point to an infinitely contingent states of the world and T1 points to the event of "pay". Theorists using ADS premises have an extremely biased view of financial contracts and have led to over-confidence and over-reliance in the prediction of pay events. For example, such theorists wrongly impute the value "1" for "payment" and "0" for "nonpayment." We correct this model by injecting the symmetric resultants of "pay or not-pay" to the interval between t0 and t1. What follows naturally is what is termed DEFAULT INVARIANCE. Thus, the values of "pay" and "not-pay" must be "0" and "1", respectively. This result has extraordinarily large implications for law and finance theory. For example, from this theory, a financial contract when paid exits from the infinitely contingent states of the world, i.e., (infinite-contingency) x 0 = 0, and thus, becomes a legal certainty of discharged obligations. And if unpaid, it remains as part of the infinitely contingent states of the world, i.e., (infinite contingency) x 1 = infinite contingency, and a continuing potential legal liability. One implication of this new theory is that another type of credit rating must exist in the real world (whether we like it or not). The current credit ratings in the world are based on the question of whether a legal entity can make good its financial obligations at T1. This is obviously based on an Arrow-Debreu model which sees "pay" as the only relevant event at T1. From this premise, the hierarchy of ratings AAA, AA, and so on unfolds. But this sort of credit rating obviously does not capture the continuing ("stretched out") event of non-payment except to nominate it at the bottom of ratings. From a "not-pay" event, an alternative credit rating agency would appropriate "XXX" to warn potential investors of the severity or intensity of default. (Think of warning labels on videos that are not appropriate to non-adults.) Some might argue that the XXX-rating is already incorporated in the AAA-rating system. But it is patently not since during times of credit crises, large institutional short-term traders asses the risk of AAA-instruments as "100% default probability."
Showing posts with label default invariance. Show all posts
Showing posts with label default invariance. Show all posts
Thursday, 5 January 2012
Saturday, 23 July 2011
Categorical Analysis of Selective Default -> The Morphism from [de facto] to [de jure]
1. Consider the achievement of yesterday's Euro Summit in Brussels where we find:
(a) €109 bn bailout funds from international lenders
(b) €37 bn in bondholders swapping or rolling over their bonds to new 30 year instruments
(c) European states to support Greece until it can re-enter the private markets.
See: http://www.ft.com/cms/s/0/952e0326-b3af-11e0-855b-00144feabdc0.html#axzz1Sq1THqaR
2. A category theory analysis as I have argued begins with the physical idea that Default Must Be, that is, that default is invariant in all possible market spaces where actors enter bilateral agreements called rather grandly, financial contracts. For definitions of financial contracts, Arrow and Debreu, who defined financial contracts in terms of two states of an infinitely contingent world, with the initial state as any particular state of the contingent world (t0), and the next state, (t1), as simply one change in the previous state, that is, as one of payment. It's important to keep in mind that t0 and t1 are two states of an infinitely complex and contingent world, but that the simple difference between the two is that the latter state involves payment. I have argued that this is not sufficiently realistic in terms of recognising the contingency of the world is embedded in the world itself (!) and therefore, cannot be logically eliminated from the contract without immediately contradicting Arrow and Debreu's first premise of that the world's universal property is contingency.
3. What does this mean in practical terms? In practical terms, default being invariant or default invariance means one needs to link any current valuation of any particular financial instrument to its placement in the Grand Cycle of Default, which we have previously divided into four logical spaces called phases:
(1) [I][I]
(2) [I][B]
(3) [B][B]
(4) [B][I]
where
I stands for "innovative financial instruments" in private markets, and
B means "bailout" in which government(s) using taxpayer funds partially or wholly replace market activities.
We have been seeing the rise of [B] since the U.S. Emergency Economic Stabilization Act of 2008, division A of Public Law 110-343. And a similar bailout for Greece and EU member states with the Euro Summit bailout agreement on July 22, 2011. See paragraph 1 above.
Therefore, we are definitely in the 3rd phase of [B][B].
4. Here's what is both INTERESTING and obvious when you translate the Great Cycle of Default into category theory notation:
(1) Every morphism between the bracketed objects is default, and
(2) Alternative paths and short cuts can be drawn between phases which are first order SOLUTIONS to typical intranet-phase problems, and
(3) Paths-on-paths can be drawn which can be thought of as higher dimensional solutions to various intra- and extra-phase problems.
(1) gives us the meaning of Default Invariance as a universal property in the form of an ambient morphism. In other words, to understand the STRUCTURE of law and finance in the context of global systemic risk, all we have to remember is that the reality of financial legal phenomena is mediated by default. And this is an observation of the de facto that continuously merges into the de iure. One can even characterise the transformative states in terms of differences in Hohfeldian legal relations before and after the default functor! this will be the topic of another discussion.
(2) These alternative paths can be private as in new legal and financial methodologies that merely replicate many of the processes of a normal phase or they can be short cuts in which case, REAL ARBITRAGE emerge. I'm happy to freely talk about the former but I'd be a kind of naive sociopath if I gave away short cuts for free. Short cuts are the basis for genuine financial instrument patents.
(3) The higher dimensional stuff ("operads") are surprisingly normal operations in a complex society. So, for example, I've worked out how one might go from phase 2 back to phase 1 by combining a couple Dodd-Frank Act provisions in a private action against a couple banks posing a systemic risk to the U.S. economy. in this example, one could combine the Whistleblower Incentives and Protection provisions (which is an alternative path from phase 4 to phase 1) with the Orderly Liquidation Authority provisions (which is an alternative path from phase 2 to phase 3) in some type of private action litigation, and by setting PRECEDENT in that legal case, it is possible though highly improbable, that we could have a morphism from phase (2) to phase (1). If it does occur, it would be an example of the translational symmetry of the LAW.
5. Flight Path through Social Complexity
(a) Supposing default invariance and the great cycles of default, is justice a higher-order operad? Probably. But what dimension specifically? In other words, presuming justice is n-categorical, what n is it specifically? I'm guessing any and all social rules don't need any more than 3-category level translation. But this doesn't say much except to say there's an upper bound to the complexity of financial-social space. So what? Much more significant would be how to determine a flight path through the four phases.
(b) By the way, a selective default is not an alternative path from phase 2 to phase 1, and is strongly indicative of phase 3 behaviour. More apparent chaos cometh.
(a) €109 bn bailout funds from international lenders
(b) €37 bn in bondholders swapping or rolling over their bonds to new 30 year instruments
(c) European states to support Greece until it can re-enter the private markets.
See: http://www.ft.com/cms/s/0/952e0326-b3af-11e0-855b-00144feabdc0.html#axzz1Sq1THqaR
2. A category theory analysis as I have argued begins with the physical idea that Default Must Be, that is, that default is invariant in all possible market spaces where actors enter bilateral agreements called rather grandly, financial contracts. For definitions of financial contracts, Arrow and Debreu, who defined financial contracts in terms of two states of an infinitely contingent world, with the initial state as any particular state of the contingent world (t0), and the next state, (t1), as simply one change in the previous state, that is, as one of payment. It's important to keep in mind that t0 and t1 are two states of an infinitely complex and contingent world, but that the simple difference between the two is that the latter state involves payment. I have argued that this is not sufficiently realistic in terms of recognising the contingency of the world is embedded in the world itself (!) and therefore, cannot be logically eliminated from the contract without immediately contradicting Arrow and Debreu's first premise of that the world's universal property is contingency.
3. What does this mean in practical terms? In practical terms, default being invariant or default invariance means one needs to link any current valuation of any particular financial instrument to its placement in the Grand Cycle of Default, which we have previously divided into four logical spaces called phases:
(1) [I][I]
(2) [I][B]
(3) [B][B]
(4) [B][I]
where
I stands for "innovative financial instruments" in private markets, and
B means "bailout" in which government(s) using taxpayer funds partially or wholly replace market activities.
We have been seeing the rise of [B] since the U.S. Emergency Economic Stabilization Act of 2008, division A of Public Law 110-343. And a similar bailout for Greece and EU member states with the Euro Summit bailout agreement on July 22, 2011. See paragraph 1 above.
Therefore, we are definitely in the 3rd phase of [B][B].
4. Here's what is both INTERESTING and obvious when you translate the Great Cycle of Default into category theory notation:
(1) Every morphism between the bracketed objects is default, and
(2) Alternative paths and short cuts can be drawn between phases which are first order SOLUTIONS to typical intranet-phase problems, and
(3) Paths-on-paths can be drawn which can be thought of as higher dimensional solutions to various intra- and extra-phase problems.
(1) gives us the meaning of Default Invariance as a universal property in the form of an ambient morphism. In other words, to understand the STRUCTURE of law and finance in the context of global systemic risk, all we have to remember is that the reality of financial legal phenomena is mediated by default. And this is an observation of the de facto that continuously merges into the de iure. One can even characterise the transformative states in terms of differences in Hohfeldian legal relations before and after the default functor! this will be the topic of another discussion.
(2) These alternative paths can be private as in new legal and financial methodologies that merely replicate many of the processes of a normal phase or they can be short cuts in which case, REAL ARBITRAGE emerge. I'm happy to freely talk about the former but I'd be a kind of naive sociopath if I gave away short cuts for free. Short cuts are the basis for genuine financial instrument patents.
(3) The higher dimensional stuff ("operads") are surprisingly normal operations in a complex society. So, for example, I've worked out how one might go from phase 2 back to phase 1 by combining a couple Dodd-Frank Act provisions in a private action against a couple banks posing a systemic risk to the U.S. economy. in this example, one could combine the Whistleblower Incentives and Protection provisions (which is an alternative path from phase 4 to phase 1) with the Orderly Liquidation Authority provisions (which is an alternative path from phase 2 to phase 3) in some type of private action litigation, and by setting PRECEDENT in that legal case, it is possible though highly improbable, that we could have a morphism from phase (2) to phase (1). If it does occur, it would be an example of the translational symmetry of the LAW.
5. Flight Path through Social Complexity
(a) Supposing default invariance and the great cycles of default, is justice a higher-order operad? Probably. But what dimension specifically? In other words, presuming justice is n-categorical, what n is it specifically? I'm guessing any and all social rules don't need any more than 3-category level translation. But this doesn't say much except to say there's an upper bound to the complexity of financial-social space. So what? Much more significant would be how to determine a flight path through the four phases.
(b) By the way, a selective default is not an alternative path from phase 2 to phase 1, and is strongly indicative of phase 3 behaviour. More apparent chaos cometh.
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