Scapegoats or Systems - What Hinders Effective Risk Management

We can read: we only learn from turbulences (caused by many things including failures) … but if it comes to real failures, management theory is often forgotten.

Risk management is about helping optimize risk - in terms of economic value. There are different types: market risk, credit risk, liquidity risk, …

Often operational risk is included, but IMO, it is not a risk, it is a danger - that does not mean it cannot be managed. In its core it is the danger that a "system" behaves unexpected and with unintended consequences.

Failure: models and management

What management does in an organization when something goes wrong?

Quant finance work is characterized by the interplay of users with technologies. Consequently the model of an error causation can be person- or system-oriented.

A bad reaction is to hunt for a scapegoat - trace back to team members, who might have caused the failure and blame them. However, the person approach seem to remain the dominate tradition. Blaming individuals seem to be emotionally more satisfying?

The better approach is to take the systemic view and analyze what can be done to avoid them.

Antifragility again

Remember, an antifragile becomes stronger with added stress. In a systemic view failures are seen as consequences rather than causes. It is wrong to assume we cannot change conditions under which humans work.

One of the systemic dangers in quant risk management are model and method traps - and their avoidance cannot always be automated by verification and validation processes.

System defences are very difficult and often fragile themselves.

But there is a better way

Knowhow Men

The is the title of a commentary about UnRisk in the July, 2014 issue of the Wilmott Magazine. Its editor, Dan Tudball, interviewed Andreas Binder and Michael Aichinger.

In the usual scheme of things, when a solution provider has developed a successful set of applications atop a proprietary engine, the layers of obfuscation and opacity over how that engine does what it does generally become thicker and thicker as time goes by. As a firm makes its mark and carves out a market niche for itself, marketing speak multiplies in inverse proportion to openness ...

the article starts.

Why we made the decision for an open information policy is the essence of this three page article. In short, transparency is indispensable, it is fun, and it pays back.

In our understanding, we think for you is outdated. For the better way, we have established the UnRisk Academy. For the system approach of failure management and more.

This post is inspired by this post of Eight to Late.

Implied Black Volatility continued

Last week, in When Uncertainty is Good, I wrote on the difficulties of identifying an implied volatility, when vega is close to zero. I recapitulate the results we obtained by solving for the implied volatility from noisy data were quite poor when far away from the money.

The noisy call prices we used were as follows


Noisy call price as function of the strike price
 

This looks OK, but when we zoom in at the right end, we see what happened:


Noise dominates signal

Our eyes (and the brains behind) see clearly, what the "true" call price curve should be.


Does Pre-Smoothing Help?
A naive approach would be to take averages of noisy data, specifically we take the averages of the point itsellf and its 4 left neighbours and its 4 right neighbours. The averagred prices are drawn in the following plot

Averaging leads to smaller variance levels

 

Taking these as inputs we obtain



Implied volatilities from pre-smoothed noisy data

These are already much better results. They could be further improved by applying, say, a Gaussian filter instead of naive averaging and by choosing the filter bandwith depending on the level of vega.

Why Quants Should Tell More Stories

Simplified, a story is a problem solution description. Stories have a character that has a problem trying to solve it.

Most of our time we live in stories - novels, movies, interactive games, .... Even dreams are stories. Pointedly speaking, storytelling makes us different. But storytelling is different in the sciences and the humanities - maybe even more, storytelling has the power to close the gap between the two cultures, but scientists think, stories belong to the other territory and the humanities reject scientific method?

The tension between the two cultures is old and ongoing.

You can write stories in the language of mathematics 

Think of portfolio-across-scenarios analysis. You can check the "normal" and "pathologic" cases to understand extreme situations and shift things to the borders of your working space, as well as the usual (expected) behavior. The mathematical story, like others, has a problem, a crisis, a dilemma and a solution.

Such stories work as kind of financial reality simulators. You can write them in the language of mathematical finance but burn the mathematics if you tell them to market participants?

Do the difficult things

Quants are good at many things: financial engineering, risk management, statistics, stochastic calculus, numerics, programming, … but it is really hard work to explain what they found and achieved to market participants who do not fully understand the complexity of financial concepts.

But, who else can do something so difficult that others cannot even imagine doing it?

It's a black box - white box principle

To simulate you can start with black boxes, but understanding a behavior and compose a story describing it in the theater of your mind, you need to know all the details.

We at UnRisk, are highly committed to help quants to do the hardest things. With products, leading edge technologies and uncompromising transparency.

UnRisk for Quants, UnRisk Financial Language, UnRisk Engines, UnRisk FACTORY Data Framework, UnRisk Deployment Services, …

Check them out. Get a proof by trial installations or online access. We serve our trial users, like clients.

This post has been inspired by Jonathan Gottschall's post in Edge: The Way We Live our Lives in Stories.

Team UnRisk at the Beach Finals continued

Last Friday we took part in the Business Cup at the Beach Finals in Perg, Upper Austria. First of all I have to say that the event itself was great! Everything was well organized, there was free food and drink for all the teams and the overall atmosphere was amazing.

But I am sure you are already impatiently waiting to hear how our team performed, so I won't keep you in suspense any longer: Team UnRisk took the 5th place! We are very happy about this result, since the only two matches we lost were against the teams that later played in the finale. 

We had a lot of fun playing and we really enjoyed the whole competition (although to be honest we were a bit intimidated when we first met the other teams). I think I can speak for all the team members when I say that this event has reignited our interest in beach volleyball. 

We already agreed to take part in the Business Cup again next year and with a bit more training there are no limits to what we can achieve!

A Comparison of the Schrödinger and the Black-Scholes Hamiltonian

In last physic's friday blog post A Black-Scholes Schrödinger equation we introduced a Black Scholes Hamiltonian. And as announced we will compare the properties of this equation with the properties of the Schrödinger equation. To have some comparison I write both Hamiltonians:

Time independent Schrödinger Hamiltonian

Black-Scholes Hamiltonian

Viewed as a quantum mechanical system, the Black–Scholes equation has one degree of freedom, namely x, with volatility being the analog of the inverse of mass, the drift term a (velocity-dependent) potential, and with the price of the option C being the analog of the Schrodinger state function. The Black–Scholes Hamiltonian is non-Hermitian due to the drift term.
We can also formulate the Black-Scholes equation using Dirac's notation:

Next week we will introduce stochastic volatility into our Quantum-Finance framework ...

Multi Curve Modelling - Dealing with uncomfortable stochastic integrals

Today I'd like to put the focus on the multi curve modelling framework. The delevopement of financial markets after the credit crunch requires a new methodology for the valuation and modeling of financial instruments, since the basis spreads have increased and can no longer be neglected as it was done in the standard approach before.
These market adaptions require a multi curve modeling approach, where different curves for the calculation of discount and forward rates are used. From the UnRisk developer team, I was selected to analyze the latest innovations in multi curve modelling and to incorporate a new multi curve model to our UnRisk software product.
As the new model, we decided to extend the one factor Hull & White model to a multi curve interest rate model, having the form

where rd is the short interest rate process used for discounting, and rf  is the short rate interest rate process used for the calculation of the forward rates.
Using this model, one of the problems I encountered was the derivation of analytic formulas for the instruments used for the calibration process, i.e. zero coupon bonds, caps and swaptions. Therefore I had to solve some time consuming stochastic integrals. I don't want to go into details here, but to get an impression, here is a little out-take of the pricing formulas, which were computed by hand in flipchart format A1, since there was not enough space for a clear illustration of the formulas in an A4 format...

We Are Going Before We Are Asked

A few days ago at the Lake Attersee. It was very hot during the day - in the late afternoon a thunderstorm  came from the west and within a few minutes the wind changed from doldrums to a storm and the water began to swirl. The flashing lights of storm warning were switched on …

This is not a so rare event, but again (small) sailing boats have been surprised and needed to be pulled ashore by the water rescue.

I completely save held my breath for a moment and it came to my mind that everything is easy when things go smooth - it's a no-problem-problem.

We know this situations in finance and this is the reason why we often answer questions and go to visit our clients before asked.

When the flashing lights of regulatory storms turn on it may be late …. this was true when (a naive belief in) VaR became questionable and it is now indispensable with xVA - especially for small and medium sized market participants, who are confronted not only with exposure modeling but centralized collateral management ….

When Uncertainty is Good

As announced last week, I will look at model calibration from different angles in the posts to come.

To start with an elementary example, we want to identify a flat (Black-Scholes) volatility from prices of call options with different strikes. To be more specific, let the spot price S be 100, the flat interest rate r = 0.02 (continuous compounding), expiry T= 0.5 (years), and the true annualized volatility sigma =0.25.

The call price for K=S=100 is then C=7.517

We calculate the true call prices for a wide range of strike prices (distributed around the spot price), and perturb the true call prices with a normally distributed error with mean 0 and standard deviation 0.03. Then, we determine the implied volatilities from the perturbed prices and obtain

Image Source: A Workout in Computational Finance, Chapter 15.

We observe that we get a reasonable recovery at the money and that the quality gets worse the deeper in the money or out of the money the option ist. Why?

The reason behind this phenomenon lies in the Implicit Function Theorem from basic calculus. Assume, for a fixed strike K, we want to determine the volatilitysigma leading to the quoted (perturbed) price p, where C_K is the operator that calculates the call price for K and sigma.

Differentiating with respect to p (and obeying the chain rule), we obtain

and finally

This is also the amplifier of noise. When the call price does not change much as a function of the volatility (vega is small, the option is deep in the money or deep out of the money), then the implied volatility cannot be recovered reasonably.

How does this relate to the headline of my post? When the price contains vega risk (the price changes significantly with volatility), then we can expect to recover implied volatilities, and the implied function theorem gives us error estimates.

The Battle of Austrian Economics

In … Fit the Battle of Econo, Econo, Econo  I wrote about the misunderstanding between economists and "econophysicists".  It is related to complexity.

Here I link to a pointed blog post of Noah Smith Austrianism, wrong? Inconceivable showing that there is another battle going on - the battle of the Austrian School of Economy.

It's about the use of maths and statistics in economics

As Austrians, we should be interested, just because of the term Austrianism? No, we are not.

We are interested, because it is about the use of mathematics and statistics in economy. And it seems that Austrian economists are averse to use them. Maybe even more, Austrian economics lacks of scientific rigor and rejects scientific methods and the use of data in modeling behavior.

In our understanding any theory needs models (in my understanding of axiomatic mathematics a theorem can only be explained in a model world.  Only a model gives operational semantics to a theorem expressed in the language of mathematics - provocatively speaking: there is no such thing as an abstract mathematical program).

And a model is only as good as it backtests. On real data.

Analytic AND data-driven methods

With What Can We Recover from Data Andreas has started a series of posts dealing with parameter identification - the task to transfer a model into a real working space.

I am looking forward to this posts myself.

If humans use models their behavior will change.

IMO, there is a need for a quantitative meso-layer between the micro layer of concrete financial/economic transformations and the macro layer of the development of a complete economy. 

Consequently, I am not fighting at the side of the Austrian economists. You cannot predict future, but quants help to build it.

Team UnRisk at the Beach Finals

This weekend the Beach Finals, the regional championship in beach volleyball, are taking place in Perg, Upper Austria. The final match will be on Sunday and the kickoff for the event is on Friday, where the qualifications are taking place. There will also be a Warm Up Party and, new this year, a Business Cup. In this cup eight company-teams are competing against each other. And one of these teams will be Team UnRisk!

We are definitely not the most experienced beach volleyball players but we are highly motivated! And competing as a team is something we all enjoy. I am very happy to be part of this team, where team spirit and having a good time together are the main focus. To be well prepared we have a training session this week, where we will develop our winning strategy.

We will keep you updated about the outcome of the match and the performance of our team.

Picture from the men's finals 2013

A Black-Scholes-Schrödinger Equation

In Quantum Physics and Options I promised to discuss the essentials of quantum mechanics that are relevant for option pricing. In classical mechanics Newton's law of motion determines the position of a particle at a given time by a deterministic function. So classical mechanics can be seen as the (deterministic) evolution of a stock price with zero volatility. In contrast, in quantum mechanics the particle's evolution is random, like it is the case for a stock price with non zero volatility. In the one dimensional case the random numbers indicating the position of the particle can be all points on the real line. At some fixed time the probability of finding the quantum particle at position x  is given by the product of the wave function times its conjugate complex.

The wave function more generally spoken the state vector of the quantum system is an element of a linear vector space. In quantum mechanics physically measurable quantities such as energy, position and so on are represented by Hermitian operators that map the linear vector space on itself. The Hamilton operator evolves the system in time. Whereas the Hamilton operator in quantum mechanics is hermitian (Schrödinger equation) in finance it is in general not. Let us take a look at the Black Scholes equation (used for example for option pricing with constant volatility)

Changing of the variable

leads us to a  "Black-Scholes-Schrödinger" equation

with the Black Scholes Hamiltonian given by

Seen as a quantum mechanical system, the Black-Scholes equation has one degree of freedom (x). Next week we will compare properties of the Schrödinger equation with properties of our Black-Scholes Schrödinger equation.

CATWOE and the UnRisk Universe

Business is innovation and marketing. Marketing (as we understand it) is about focussing on market segments, purpose-driven positioning, connecting to engaged market participants and developing the right things the right way.

Make things that matter for those who care

We don't do much market analytics on (big) data but we structure the results of our thinking-feeling-doing process. And this is it:

Clients - banks, investment and capital management firms, asset management of insurances, financial services providers, financial advisors and auditors.

Actors - quants, investment- and risk professionals.

Transformation - computational knowledge into know-how packages for better investment and risk management. In our opinion a know-how package consists of a solution that is a development environment in one combined with learning arrangements from courses to intimate workouts that explain in full detail what is behind (the curtain) - "operational risk" is not a risk that can be optimized it is a danger.

Weltanschauung - Arming David. Making big systems for the small sounds crazy, because big means high in cost and small means low in price. But, in a market of Goliaths able to justify huge spend on risk management how are the numerous risk management teams at small market participants to overcome the regulatory tsunami whilst remaining cost effective?  It needs to be done.

We are highly committed to do it and help quants to leverage their work.

Ownership - we offer comprehensive licenses on a yearly fee base. They include premium services.

Environment - great opportunities in a competitive arena.

The UnRisk Universe

In more than 12 years we have developed a quant finance universe combining technologies -  UnRisk Financial Language, UnRisk Engine, UnRisk Data Framework and UnRisk Web Deployment Services - the UnRisk Academy, this Blog and the UnRisk Magazine (coming soon). We also co-design and co-buid solutions.

It's the technology suite and knowledge that empowers us to deliver the big systems for the small - carefully choosing the maths, mapping every practical detail and tying it together to a solution and development system environment in one.

What can we recover from the data?

At the UnRisk Academy events, there is typaically at least one session on parameter identification, just as it has been at the Frankfurt and Zurich events.

From my understanding, the typical workflow in quant work is

1. Choose a model for the underlying
2. Given prices of liquid instruments, calibrate the parameters of this model
3. Use the parameters to valuate something more complex than the vanilla things.

The second step is a classical inverse problem, and we should ask ourselves questions about existence, uniqueness and stability.

In a sequence of forthcoming posts, I will cover some examples from finance.

We, at MathConsult and UnRisk, have been working on a wide range of inverse problems in the past. Some examples are:

• Identification of cooling strategies in continuous casting of steel
• Tomography of the atmosphere for astronomical applications
• How thick is the wall of a blast furnace?

The Culinary Provenance Paradox

I took 3 days off and drove to the south-east corner of Austria, close to the Slovenian border.

My destination: Neumeister - wine makers running the outstanding restaurant Saziani Stubn and the "Schlafgut" with 7 spacious apartments that breathe the spirit of the landscape.

My objective: relax by hiking, reading, eating and drinking fine things.

Talents are rare

About four years ago, Albert Neumeister, the patron, hired Harald Irka (then 18) direct from school. Harald Irka is now a celebrated chef, who creates superb dishes in perfectly composed menus with seven servings and a fantastic series of amuse gueules (I had both the green and the earthy menu - adapted to the season).

IMO, he is the best chef in Austria and one of the most talented chefs world-wide. He created his own style, but if I want to draw a line, I'd say it's inspired by the new Scandinavian way (Noma, Faviken Magasinet, ..) of looking into the landscape and delve into its ingredients …. And this corner of Austria has wonderful ingredients.

Saziani Stubn also offers a great wine list with outstanding national and international entries, but in interaction with the menus I prefer the Neumeister Grand Cru wines, the Pinot Gris "Saziani", the Sauvignon Blanc or Morillon (Chardonnay) "Moarfeitl" that are available back to 2001.

Gault Millau rated the Saziani Stubn (only) 17/20 (3 Toques) - this is great for a chef of the age of 22+. But if he were in one of the regions celebrated as "culinary centers", they were top rated by Michelin, GM, …

The only way to add value in an exotic provenance

It was just by chance that I wrote about The Prvonance Paradox, when Harald Irka started. He's, BTW,  from Linz, like most of us UnRiskers.

The Neumeister-working-style seems not so different from ours - innovation and cooperation, with a heart for young talents. And like us they are not doing everything to get picked - they choose themselves. They do the difficult work for those who care.

A place really worthy of a visit …

Cloud Call

Last week, Mathematica 10 was released. The two major new features (at least from my point of view) are the Wolfram Programming Cloud and Finite Elements. Luckily, when there are new gadgets around to play with, the blog provides a perfect excuse  :)

To be able to toy around with both new features, I set out to solve a simple PDE (the Black-Scholes equation, of course), and deploy the whole calculation as small web application in the Wolfram Cloud.

Part I of this endeavour proved to be extremely simple: It's really just a matter of writing down the differential equation, the boundary and initial conditions and calling NDSolveValue with that (see screenshot)

The above example shows the value of a European Call as a function of time to maturity (tau=0...20) and price of the underlying (0..10). The strike of the call was K=5.0 in this example, the risk-free rate r=0.02 and the volatility was time dependent, with a value of 0.2 for tau=10, and a value of 0.8 for times tau > 10.

Part II proved to be a bit trickier: The FEM solution calculated on the cloud server is often different from the solution delivered by my local Mathematica 10. For constant volatility, my local Mathematica always obtains a solution that is indistinguishable from the analytic solution, while the results obtained in the cloud often (but not always) differ. Well, I guess that's why it is called a "beta"

Anyway - if you want to try the cloud solution, the link is here.

(in the form, "strike" is the strike of the option, vola1, tjump and vola2 are the constant volatility for times smaller or greater than tjump, rate is the risk-free rate and maxtime the maximum time to maturity to calculate)

Quantsourcing - Managing the Polarity of Risk Management

Let me start with the dilemma of enterprise risk management. Is it a cost for securing business or a strategic asset? Shall it be centralized or autonomous? Shall it be system driven or business driven?

Managing Polarity

This are the poles of the dilemma of (enterprise-wide) risk management: predictability vs adaptability, control vs agility on the positive side and bureaucracy vs lack of control on the negative side. Organizations tend to oscillate between poles.

The shock of the crisis has given the pole of cost, centralization and system magnetic power. Regulators want tightly coupled systems.

But what about optimizing risk?

Managing polarity is listening to supporters and detractors of the poles and view the positives and negatives of each pole, create awareness of them and try to avoid the negatives. Optimizing risk needs learning from turbulences, adaptability and agility.

Make or buy? One size fits all? Is it enough to being good in not being bad?

Quants would usually have an important role in understanding the the right oscillation trajectory through a pole map (oscillation is inevitable - antifragility needs fragility).

Quantsourcing?

Let me jump to the roles. When we say to a (large) group: everybody-does-this, than it is easy to let someone else do it. Everybody doesn't make things, they may use things.

It's a bit like with crowdsourcing and crowdfunding. Crowds don't make things. It's people, who make things.

Ann, Paul, .. make it. Individual quants make things that diffuse into valuation and risk management - it's Annsourcing and Paulfunding. One person, one contribution, urgent, necessary and indispensable.

Our quantsourcing promise is two-sided - because we believe in quant-powered innovation, we offer quant work for small market participants who do not have quant teams and we serve quants with our technologies enabling them doing things better and swifter.

Expanded Curation

The consequence of unleashing the programming power behind UnRisk, is transparency,. We deliver know-how packages, not black boxes. To optimize the knowledge transfer we always look for new formats. Hybrid learning arrangements between lectures and live presentations. Events that bridge science and usage.

A crowd of quants is not a crowd, but rather a number of individuals gathered in a space, not listening, like in an opera, but interacting.

We want to perfect such formats and try new ways, like this one. In response we hope quants will embed the event experiences into their products and services.

We want quants understanding their role in managing the polarization. Modern risk management needs innovators, not only administrators of black boxes.

The Zurich Workout in Computational Finance

On July 3, Michael Aichinger and myself  conducted the Zurich Workout in Computational Finance, which had been very conveniently organized by our partner Nube AG.

As there was no FIFA world cup football match in the evening, there was less time pressure, and we succeeded to have an after-seminar beer with some of the participants. These were highly qualified quants from various institutions and I really enjoyed the intellectual resistance and the lively discussions.

And I also enjoyed to have an evening shopping at Globus gourmet store (Thanks for the recommendation from our former colleague, Robert, who works at a large Swiss bank now.). This time, it was black pepper from Malabar.

Beyond Goats, Wolves … a Comparison of Programming Languages - in Modern Macroeco

Sascha posted the distribution of programming languages in UnRisk yesterday. Use the language that fits best for purpose. The objective leads to hybrid programming - inevitably. Performance is one criterion.

A paper of the National Bureau of Economic Research

We solve the stochastic neoclassical growth model, the workhorse of modern macroeconomics, using C++11, Fortran 2008, Java, Julia, Python, Matlab, Mathematica, and R. We implement the same algorithm, value function iteration with grid search, in each of the languages. We report the execution times of the codes in a Mac and in a Windows computer and comment on the strength and weakness of each language.

This are their summarized results

C++ and Fortran are still considerably faster than any other alternative, although one needs to be careful with the choice of compiler

C++ compilers have advanced enough that, contrary to the situation in the 1990s and some folk wisdom, C++ code runs slightly faster (5-7 percent) than Fortran code.

Julia, with its just-in-time compiler, delivers outstanding performance. Execution speed is only between 2.64 and 2.70 times the execution speed of the best C++ compiler 

Baseline Python was slow. Using the Pypy implementation, it runs around 44 times slower than in C++. Using the default CPython interpreter, the code runs between 155 and 269 times slower than in C++. 

However, a relatively small rewriting of the code and the use of Numba (a just-in-time compiler for Python that uses decorators) dramatically improves Pythonís performance: the decorated code runs only between 1.57 and 1.62 times slower than the best C++ executable. 

Matlab is between 9 to 11 times slower than the best C++ executable. When combined with Mex Öles, though, the di§erence is only 1.24 to 1.64 times. 

R runs between 500 to 700 times slower than C++. If the code is compiled, the code is between 240 to 340 times slower. 

Mathematica can deliver excellent speed, about four times slower than C++, but only after a considerable rewriting of the code to take advantage of the peculiarities of the language. The baseline version our algorithm in Mathematica is much slower, even after taking advantage of Mathematica compilation. 

This is the paper (I found googling).

Mathematica (Wolfram Language)? Based on a presentation of Sascha, I wrote this post about Idealism vs Realism in Programming.

Deciding for hybrid programming was a great choice. We were able to make blazingly fast engines, platform agnostic and widely accessible - with unbelievable low efforts.

Have a Cake and Eat It

The TIOBE Programming Community index is an indicator of the popularity of programming languages on a global level. According to the index, the programming languages C and Java have been the most popular programming languages for more than a decade now. It seems worthwhile to compare the TIOBE index to the popularity of programming languages that we use for the implementation of our products UnRisk-Q and UnRisk FACTORY.
We’ll measure the popularity of the different programming languages used by counting lines of code. The LOC counts for the languages were computed with the tool CLOC.

UnRisk-Q

The UnRisk-Q code base consists of 700,000 lines of code. The distribution of programming languages used for its implementation is shown in the pie chart below.

C++ takes the major piece of the cake. This is not surprising. In quant finance, where delivering results as fast as possible is of paramount importance, there is no viable alternative to C++ for implementing the low level numerical code.
The rest of the code base mostly consists of Mathematica code, because the UnRisk Financial Language we use as the high-level interface for modeling the financial problem domain is based on the Wolfram Language. The “Others” portion of the pie consists of shell scripts, CMake files and DOS batch files, which make up the build system of UnRisk-Q.

UnRisk FACTORY

The UnRisk FACTORY lets a user access the functionality of UnRisk-Q through a web based graphical user interface and uses a database for persistent storage. The UnRisk FACTORY code base consists of around a million lines of code. These are distributed among different programming languages in the following way:

The pie chart shows that the code base is roughly equally distributed between the programming languages SQL, Java, JSP (JavaServer Pages) and Mathematica. XML is used throughout the whole code base for configuration purposes and for the Maven based build system.

Solving Society's Problems from the Bottom Up

We, at UnRisk, like programming the bottom up fashion. And it seems from-the-bottom-up is the right approach to solve society's problems too.

See Complexity and the Art of Public Policy, Colander, Kupers.

I just found it and will read it. 

It seems a fresh view of policy, based neither on free market ideology nor on heavy government control. We should see economy as complex system (complexity economy) that cannot be controlled but guided towards wanted outcomes.

If it is "complex enough, it can be programmed. Programs that can produce innovation while maintaining robustness (antifragility?).

Riemann and Large Numbers

Every now and then, I read in Ian Stewarts Hoard of Mathematical Treasures (to be more specific: in its German translation Professor Stewarts mathematische Schätze. Recently, I fell across Skewes' number.

From wikipedia:
In number theory, Skewes' number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which
pi(x) > li(x),
where pi is the prime-counting function and li is the logarithmic integral function

(Note that the integrand has a singularity at t=1, and the integral must be evaluated as a Cauchy principal value).
It was already conjectured by Gauss that pi(x) behaves asymptotatically like li(x). This conjecture was provedy by Hadamard in 1896 (the same Hadamard who broought up the formulation of well-posedness of mathematical problems.

Anyway, for small numbers (small in a strange academic sense), pi(x) is smaller than li(x).

li(x) (red), pi(x) (blue)

Littlewood proved in 1914 that there exists a number (albeit huge) for which pi(x) li(x), and Skewes showed in 1933 that there exists such a number with
x < 10^ (10^ (10^34)).
For this proof, Skewes needed the validity of Riemann's hypothesis (which is still not proved.)
Without the assumption of Riemann's hypothesis, Skewes succeeded to prove the existence of an x with
x< 10^ (10^ (10^963)) in 1955.

The estimates for smaller Skewes numbers have been reduced significantly. It seems that 10^316 is now a relevant order of magnitude.

Don't Get Shorty!

Picture from Wikipedia

The first what I learned, when I entered the field of quant finance (15 Years ago): arbitrageurs, hedgers and speculators live in co-evolution. They need each other as counter party.

Then I needed to learn the "secret language" - short sellers and long buyers …. Quite often, I am a short seller of my cash and a long buyer of goods I do not need at that moment.

Shorting

"Short selling (shorting, going short)" means the sale of a security the seller does not own - motivated by the belief its price will decline opening a profit opportunity when buying it at a lower price later. Short sellers usually borrow the security and a number of rules restrict which securities might be shorted how (without borrowing it is "naked short selling").

Its risk is theoretically infinite - it should be used by hard-boiled traders only? Whilst put options another bearish strategy have another risk-reward profile. But both can be used for speculation or hedging long exposure….

The benefits of shorting to the market

Expressing their opinions short sellers play an important role in the efficient matching of buyers and sellers. They run counter to the market's natural bias. Their opinion expresses in a way: the market is overpriced. They help to keep markets in balance.

If we see short sellers as "rational investors" (arbitrageurs) they contribute to close arbitrage.

But

Shorting has extra cost

First, the risk of high fees - dealers who lend the securities may drive the fees high before the short position is closed. Second, the dealers have the right to recall the security loan.

Short selling risk

This is the abstract of the paper of Engelberg, Reed, Ringenberg

Short sellers face a number of unique risks, such as the risk that stock loans become expensive and the risk that stock loans are recalled. We show that these short selling risks affect prices among the cross-section of stocks. Stocks with more short selling risk have lower returns, less price efficiency, and less short selling. Overall, short selling risk adds to the limits of arbitrage and may help explain the low short-interest puzzle 

Don't ban short selling 

There has been a lot of discussion about short selling. Many blamed the "shorts" whenever stocks went down. Why bans have unintended consequences can be read here. It is like shooting down ideas, opinions, …

Don't Get Shorty

Get Shorty is a novel and film about the milieu in which a loan shark, Chili, in love of movies, who wanted to help dealing with a script, a B-movie producer, Zimm, wanted to buy - thinking this is Academy Award worthy. The problems: Zimm does not own the script and needs other "deals" to get the money to buy it … Finally they made a film about themselves.

Shorts are not bad

We should help them to do their jobs. How to avoid exploding fees may be subject to regulation, but the risk of (multiple) callability as well as mean reverting can be modeled.

Treating multiple callability correctly is essential from valuation to exposure modeling. We put a lot of efforts to do it right in UnRisk.

This post has been inspired by Noahpinion's post.