The Wider Scope of BICs

Why BICs matter so much

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This article further expands on putting the concept of BICs introduced earlier in a wider context.It is intended to reinforce the statement of the benefits of BICs.

"The theory of probabilities is fundamentally an imposture"
Rene Thom (1995)

Laws of Nature – 3 – BICs

 

This article further expands on putting the concept of BICs introduced earlier in a wider context.It is intended to reinforce the statement of the benefits of BICs.

Clearing Potential Misconceptions

  Prediction is very difficult, especially about the future.
- Niels Bohr

  • BICs are not a predictive model of market dynamics or system dynamics, they do not attempt to forecast or detect a pattern of what is going to happen or how things are likely to evolve. BICs do not assume a particular model or dynamic for underlyings

  • Rather, BICs are an expressive structural framework. They are a coherent and robust structural framework in which predictive information can be seamlessly and efficiently encapsulated for a variety of purposes related to decision making.

In financial derivatives risk management, our identification of the BICs and the characteristics of each one of them can be likened to the identification of the gene as the basic unit of heredity in a living organism as well as the inventory of all possible genes. Here the value is not the identification of an individual gene, but rather the general structure of this type of compound and the role they play in the human body.

As such, as a philosophical theory of decision sciences under uncertainty and risk management, BICs represent a description of uncertainty that parallels the philosophical atomism inquiry that focuses more on physical matter.

In order to understand why it matters so much, consider the number π . If we only had integers to estimate it, we ‘d face an obviously impossible task. If we have only rational numbers, one would easily spend one’s life trying to estimate it without success. However, defining real numbers as class of equivalence of Cauchy sequences of rational numbers makes everything whole.


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And we can go on and on with examples.

BICs as a novel and useful theoretical concept

BICs as More Effective Generalizing Proto-Probabilistic Concept or Generalized Theory of Probabilities

From a theoretical mathematical perspective, as described in BICs 4 Derivatives Volume I: Theory, BICs are a proto-probabilistic concept or a more generalized notion of probabilities and conditional probability in the sense that they generalize and extend the concept of probability and stochastic processes as commonly understood, in a way that is more responsive to economic and financial analysis needs.

a) Under narrowing assumptions such as no transaction costs, infinite liquidity, they reduce – under no arbitrage restrictions to – in a one to one (i.e. isomorphic) correspondence to:

– a probability measure modulo the discount factor;

– a set of conditional probability measures modulo the term structure of discount factors that then extend to the specification of a stochastic process;

b) When transaction costs are assumed, a Yin and Yang dichotomy emerges:

i) When transaction costs are assumed but market instruments prices are viewed from a Price taker’s standpoint (Chapter VI pp. 125-158), arbitrage free BICs lead to an isomorphic correspondence with two positive real numbered measures that can then be more practically handled with a positive Complex measure.

ii) When transaction costs are assumed and market instruments prices are viewed from a Market maker’s standpoint (Chapter VII pp. 159-184), arbitrage free BICs lead to an isomorphic correspondence with two filtrations of positive real numbered measures that can then be more practically handled with a a filtration of positive Complex measure. The filtrations here being indexed on the notional of contracts.

A Rejection of Continuous time/ Continuous Space as dominant Paradigm in Derivatives analysis

Understood from an epistemology of science viewpoint, just as Gregor Mendel, by noticing that biological variations are inherited from parent organisms as specific, discrete traits put geneticist on a path that culminated with the identification of DNA as the genetic material, the BICs analysis start with a refutation of the Continuous time/ Continuous Space setting as ultimate appropriate framework for derivatives analysis.
The continuous time/continuous space standard would be best if there the unit basis points of underlyings kept shrinking or if trading time increments did. Clearly this is not the case. To understand this argument, consider this:

If you are trying to compute a real number, since it is the class of equivalence of Cauchy sequences of rational numbers, using any such sequence to a high enough order could be a reasonable approximation of the real number. However, if the number sought is precisely the n-th number of a specific sequence, it could be seriously erroneous to take any given term of an equivavalent sequence as a reasonable proxy.

As such, BICs from a theoretical standpoint is relevant as a mathematical theory of probabilities, as a mathematical finance theory, as a  finance theory, as a general equilibrium and disequilibrium theory.

For more, read this.

BICs as Practical Tool of immediate transformative applicability

BICs have substantive transformative applications for Derivatives Pricing and Exchange Systems or for Derivatives Risk Management in General. US Patent No. 7,933,824 is one of its applications.

BICs for Derivatives Pricing

BICs are presented as the most effective and efficient derivatives pricing method seamlessly and efficiently
capable of encompassing all possible payoff structures and underlyings dynamics profile.

The underlying may be as simple as a call or put option or more complex such as Asian options and ever more exotic structures.

The underlying dynamic may be as simple as a geometric brownian motion to the more complex structure anyone can imagine.

A compelling example can be seen in our article “Estimating Asset Costs for TARP in a Market Making Framework & BICs“.

BICs as a pricing method in the traditional derivatives pricing framework present themselves as a better alternative to Binomial and Trinomial Tree pricing methods; These tree methods are used in a narrow scope and are too stringent on the possible state space and thus suffer from logical incoherence evident in negative node probabilities that appear when one tries to calibrate to observed market prices of traded derivatives.

BICs as a pricing method in the traditional derivatives pricing framework present themselves as a better alternative to the Monte Carlo method.

BICs reduce computational cost primarily through efficient pricing input representation (i.e entropy minimizing representation – See BICs 4 Derivatives Volume I: Theory Chapter XI pp. 255-285) while basic Monte Carlo through sampling and averaging is inefficiently computer intensive and only approximating in general.

Furthermore all the speed/accuracy improvement methods used for more advanced Monte Carlo algorithms such as Low-discrepancy sequences can be readily translated in the BICs pricing framework for even greater speed and accuracy gains. (See BICs 4 Derivatives Volume I: Theory Chapter XII pp.

287-296.)

As a means of incorporating refined information about anticipated dynamics, the level of refinement of BICs exceed that of the various concepts of local volatilities currently used for derivatives pricing.

BICs Markets and Derivatives Trading Systems

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The development of BICs markets and its attendant pricing and hedging methods represent the most efficient and effective means of control and allocation of risks in properly functioning markets.

As a result, trading or exchange markets can advantageously provide superior risk management products by being establishing a derivatives trading or exchange systems whereby :

  • a user or price taker may specify any desired derivatives contract to suit their risk management needs and specify its payout as function of the realized values of chosen underlying from contract agreement up until payout payment time;

  • Using the BICs backward replicative sequence, the payout may then be broken into BICs units with functional notionals.

  • Market makers would submit bid/offers on those BICs units without knowing what contract they would be used to compose.

  • The trading system would then select among the market makers quotes, the most competitive BICs prices and use them to compute the price of the derivatives contract requested by the price taker.

Fig. 1 below further illustrates the operation of such a system.

More information can be found at: http://www.wipo.int/pctdb/en/wo.jsp?wo=2003107137
or here

BICs and the Financial and Financial Crisis of Sept-Oct 2008


Systemic Risks Avoidance

In BICs 4 Derivatives Volume I: Theory, the systematic analysis put in place helped make obvious that an “optimally informationally efficient” (p. 192-195) market is a market with a central counterparty. This analysis showed that had such a system been in place with a government backed entity acting as central counterparty, the markets would not have frozen in September 2008 as heightened fears of counterparty risk paralyzed market participants after the fall of Lehman Brothers. Such a prescription remains the most effective for transparent markets in which regulators are fully aware of the credit risk of all participants and can take corrective measures in a timely manner.

The systemic risk overseeing entity should act as central counterparty of reference on all trades whose default may pose a systemic risk or act as a regulator and guarantor of last resort to private entities (exchanges, clearing houses,…) who play such a role.

As a guarantor of last resort, this entity may be best within FDIC; As guarantor of credibility through the power to print money, this entity may be best within the Central Bank authority. What is most important in my view is that its function be articulated as proposed above.

This analysis can be replicated globally and the information shared through an entity such as the Bank for International Settlements.

Trding Restrictions, Liquidity Dry-ups, Short Sale Bans, Currency Trading Restrictions

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BICs, in the functional nature of notionals they admit are a product of the lessons of the 1997-1998 crises.

In order to address the perversions of dynamic hedging built on the Panglossian view of a world where markets have infinite liquidity, no transaction costs exists and trade is done continuously as risk management strategy, BICs as trading instruments where designed to achieve hedging effectiveness shielded from liquidity dry-ups that happen in times of economic stress which often lead to damaging sudden regulatory  changes such as short selling bans on equities which occurend in September October 2008 or currency control measures as occurred during the 1997 Asian Financial Crisis.
 
Furthermore the synthetic nature of BICs allows hedging activity without impact on the underlying itself. Therefore in times of crisis derivatives contracts hedgers using BICs can remain effective even with short
selling bans

BICs and Distributional Linkage – More Suitable Alternative to Copulas

  • I provided a robust response to this problem in BICs 4 Derivatives Volume I: Theory Chapter IX pp.203-232. My unease with the concept of Copulas as was being used in the credit derivatives industry stemmed from the extemporaneous circumstances of their use.

BICs & PPIF

The structural mind frame of BICs has led to writing two articles on how to best dispose of toxic assets while restoring liquidity in the financial markets that neither implies nationalizations as argued by liberal/progressive economists or a Public Private Investment Partnership PPIF as advocated by the administration.

Aside from the cultural barriers to the idea of nationalization and the dampening effect on private enterprise brought  by uncertainty of a government heavy handed intervention, it is unclear what such a plan would entail except that proponents say it would be on the Swedish model or the the Resolution Trust Corporation (RTC) model that was charged with liquidating assets of bankrupt savings and loan associations in the S&L crisis of the 1980s.

The biggest flaw in the PPIF is that it forces the government subsidize investors and to buy Toxic assets at a premium while the market making approach demonstrably lead to the assets being bought at a discount. The argument made by the administration to justify paying the premium is that otherwise banks would not sell the asset and investors otherwise would not be willing to co-invest. Our argument here would be that after setting up a market making operation, the government could simply then just setup new banks with a mandate to lend directly to lend to consumers and business. Such institutions would then later be privatized.
 

Origin & Credibility

Following my experience on a currency derivatives trading desk witnessing the 1997-1998 East Asian and Russian crises where liquidity on those currency dried up and convertibility was interrupted, I sought to develop more robust hedging strategies immune to these types of stress events.
I laid down the foundational structures of BICs in early 2001. I filed for a patent in 2002. The international preliminary examination examination report issued on Oct 1, 2004 by the world international property organization substantively backed all the 273 claims made. See: http://www.wipo.int/pctdb/en/wo.jsp?wo=2003107137.  The patents are at various levels of prosecution in different jurisdiction.

Under the pen name of Obi-Wan Yoda, I published a book BICs 4 Derivatives Volume I: Theory
that further expands on the theoretical scope and motivations for BICs and the mathematical, economic and financial results they lead to.

My pen name Obi-Wan Yoda was indeed inspired by Star Wars’ Episode I: The Phantom Menace and Yoda’s prescience in seeing in young Anakin Skywalker the onset of a future Darth Vader. While working on BICs, the deep architectural or structural imbalances noticed in the derivatives market led me to fear  – when very few  suspected otherwise, that the whole edifice of derivatives trading might crumble causing damage to the whole economic system.

Add to that the fact that I come from far away…

What Are We Looking For?

We are looking for partners for the next step in this journey. Contact me if you have ideas about what we could do together to bring this project to fruition.

This knol’s tiny URL: http://tinyurl.com/cfapm5

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