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