Dupire or Not Dupire? Is this a Question?

The concept of local volatility certainly has its merits, and Bruno Dupire is the name attached to local volatility. With his analytic inversion formula published in RISK (1994), he made it possible to calculate the local volatility surface easily.

But is it also a numerically sound method to identify local vol? To answer this question, we performed the following naive experiment.Let the local volatility to be identified be in fact a flat volatility of 30%. This, of course, leads also to implied volatilities (the sysnthetic market data) of 30% for all strike prices and all expiries of options. We now add some noise so that the quoted implied volatilities are in the interval (29.99%, 30.01%).

We now assume the spot price is 100 and that these implied volatilities are quoted for strike prices (50, 52, 54, ..., 146, 148, 150) and for expiries (5 weeks, 10 weeks, ... 245 weeks, 250 weeks).

See here what Dupire's formula delivers.

What happened here? Numerical differentiation of noisy data is instable, dividing by something instable close to zero even more.

Chapter 15 of "A Workout in Computational Finance" gives insight into parameter identification problems, stable methods for treating them and how Egger and Engl obtained the following smooth (almost boring) volatility surface from the same noisy data. 

 

Scenarios - Stories About Possible Futures

for todays decision. Our UnRisk FACTORY is, in its core, an untiringly working factory that does instrument group-across-scenarario-groups analytics. Fast. Accurate. Automated.

It often performs millions of full valuations to provide insight supporting risk-controlled decision making. Scenario planning and analytics can change financial strategies.

Make Possible Opportunities Plausible, Not Probable -  scenarios cannot predict the future, but comprehensive what-if analysis can provide a deeper foundation of knowledge

Understand What is Relevant and What is Challenging - scenario analysis spans a "cube" of information helping to understand risk-factor-dependent sensitivities and trade-offs between returns and values

Scenarios Tell Memorable Stories - post processing, say, by producing movies based on dynamic visualization of the vast variety of results across certain factors, possible behavior is brought to live. Reports that are programs keep them evident

All Numbers are Evident - every single valuation over the complete history with the financial objects, models, data, prices and risk spectra is stored and managed in the data base to understand what happened in a period and what would have happened, if ...

Scenarios Open Doors - if used to explain and discuss complex financial concepts in financial engagements

Manage Critical Views as an Asset - a great value of scenarios is that they create a culture  where  critical questions can be asked based on insight

One could even say scenarios build a framework that fits into a broader financial management system and become a source of dynamism based on risk-controlled decision support and constructive learning.

With UnRisk FACTORY Capital Manager we are driving this approach even further, discussing with CEOs of small and medium sized capital management firms about their risk-informed decision making.

How to Avoid Functional Stupidity

A communication and promotion expert would warn me to publish two posts a day in one blog. But I do not post for maximizing visits ...

Interested in machine learning I read about Andrew Ng and the one algorithm hypothesis and it came to my ming that I myself found in one or the other project that local intelligence and single programs could make clever decisions where we failed using more complex algorithms with special functions ....

I remember in the early 90s we managed to detect certain segments of images (full tone, half tone, edges, "watercolor", ..) from analyzing 9 pixels by a few fuzzy rules ...

However, what might be a breakthrough in machine learning making artificial units intelligent should not be applied to organizations?

Functional stupidity and stupidity management

And quite in parallelI I read A Stupidity-Based Theory of Organizations. It is about functional stupidity a term that might have some direct vector into the no-problem problem of risk management.

In general, it is reflected in an approach of organizations who do not consider solutions that are outside of a boundary, maybe derived from strategies, business principles and tactics. Intrinsic in  business-as-usual and the-one-successful-approach-we-do-here-for-years scenarios. Functional stupidity is not only a negative thing - it maintains harmony and certainty. But negative consequences include the killing of innovativeness.

The authors use the term stupidity management describing actions discouraging, say, teams and individuals in the organization from thinking themselves. It may be called corporate identity .... often backed by hierarchies and bureaucratic rules.

How to avoid?

Good risk management does not work to fulfill the requirements of regulatory bodies. They know that might give them the false comfort of having optimized their risk. Red-blooded risk managers are reflexive use substantive reasoning and justify their actions.

And avoid systems that do not support multi-strategy, multi-model and multi-method approaches.

One-algorithm approaches might be great for a single robot, but not for an organization.

8 Reasons, Why Econophysics Research Matters

No, I am not an economist. But interested in complex system research, I read about complexity economy an especially about Brian Arthur's work - obviously, as a technology provider, "The Nature of Technology". This is also one of the reasons why I read, and refer to, frequently Mark Buchanan's "The Physics of economy" blog - this weeks post what has "econophysics" achieved?

I bullet list the 8 points he selected: Physicists have

• helped to establish empirical facts about financial markets - that the probability of large market returns decreases in accordance with an inverse cubic power law, ... patterns like the elf-similar structure of market returns, .....
• identified links between markets and natural phenomena - like post market crash shocks similar to earthquake aftershocks ...
• helped to develop more realistic models of markets - like computational models of heterogeneous adaptive interactive agents
• - through the study of the minority game - revealed quality features of markets; for example that the key determinant of market dynamics is the diversity of market participant's strategic behavior
• that a key variable of driving booms and busts is the amount of leverage used by financial institutions
• shown, that too much risk sharing in a network of institutions can decrease stability
• shown, that completeness brings with it inherent instability 
• developed a network measure called DebtRank which aims to cut through network complexity and expose the real riskiness of any particular institution. I wrote about this in Analogies, Metaphors and Big Problems

In general, and this is why I write this here, innovation is often the result of a technology transfer - a transfer of knowledge from one sector to another.

And the other aspect, we are interested in: you look into a model and see something that is counterintuitive. Like the toxicity of the most complex credit derivatives - in the best sense their introduction ignored Innovation Risk.

A Short Letter From A SteelTown

Not so few of us UnRiskers are born into the fire and heat feeling of a steel town. The steel maker is voestalpine.

Not surprisingly we enjoy a long-lived partnership with them - focussing on quantitative methods for process simulation and automation, quality management ... where the models need to be solved fast, accurate and robust.

But this is not the main reason why the book cover let you feel the heat.

Expose traps practitioners fall into

Quantitative skills are a prerequisite for everyone in quant finance. A thorough grounding in advanced numerical techniques necessary, as the ability to assess their adequateness, qualities and limitations. This is what the book is about - a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into.

The book is the result of cross-sectoral mathematics experience. Numerical schemes transferred from complex technical systems to finance are presented, referenced with practical examples. They include schemes that are not so common in financial circles.

Making hig-quality steel is not so easy 

To control fire-and-heat processes you usually need to model various phenomena, flows of solids and liquids, chemical reactions or metallurgical transformations, .. thermodynamic processes and what have you. If you are faster than the real process you create a lot of benefit.

And you need to control risk. If the iron breaks through the shell of a blast furnace or a continuous casting plants all being around better run quickly away.

So, being a coal-faced mathematician in finance is being lucky ....

We've Got the Proof

OK, this was misleading. To be honest, we’ve got the proofs. We, that is Michael Aichinger and myself, and the proofs are the proofs of our book “A Workout in Computational Finance”, which should appear with Wiley Finance in July 2013.

Pre-order at Amazon

The appearance date approaches quickly which makes us quite happy. We have been working on the book for almost two years, and, from our point of view, we cover a wide range of numerical techniques useful for practitioners in quantitative finance.

In the course of the next weeks, we will spotlight selected sample sections. Hence, stay tuned.

Do We Work to Get Picked?

Yes, I took quite a high ink factor explaining not only what we do, or how our offerings work, but also why we do it. And why we question ourselves quite often, whether this is right. And what would independent experts think about what we do.

Like in Is There Optimal Competence?, Is This The Best I Can Do? or earlier Create More Value Than You Can Capture.

Selecting a platform, it matters who you are working with

When I select a platform, I want to know who I am working with, where to find them and how they "think". It was 1990, when I personally met Stephen Wolfram the first time. In Linz (still our headquarter). I organized one of the First European Tour events, where Stephen presented Mathematica. I managed to attract an audience of 400 people, a press conference and an interview at the Austrian TV... and had enough time to talk to Stephen about motivations, principles and approaches.

And I made a quick decision. Mathematica will be the computational platform for our innovations - to extend it or work atop it. And this happened since then with Mathematica: Stephen Wolfram talking about the Computational Future.

To get picked or choose yourself? 

selected .... this is what you often read in a press info. And to be honest, we also used that phrase. But looking a bit deeper the question arose: Do we need to being picked or do we choose ourselves ...?

Seth Godin had two amazing blog posts (Getting picked .. and  But I don't want to do this ...) about this in the last few days. And I could not agree more: to do what you find important, it helps if you get picked. But this is not the only way. If you choose yourself you set the pace now and then and maybe create a new context - probably only in a segment. Opening a path that does not require to get picked to succeed.

After the experience it is easy to say

As a marketer, I should not admit, but it was rationale and intuition to decide working towards long lasting partnerships with our users. Especially at the beginning it is frightening to choose yourself. But, at the other hand to work for the mainstream creates (only) mainstream ...

We have 100+ customers now. But more important: a significant part of them became partners and innovators. And they require that we do not only choose, but prove ourselves. And this also means that we need to change quite often.

Especially in quant finance - new difficulties may be ahead.