Wednesday, 11 April 2012

The IMA Conference on Mathematics in Finance

Since John Maynard Keynes rescued a collection of Newton's private papers and declared that "Newton was not the first of the age of reason. He was the last of the magicians" the popular imagination has looked at the influence of esoteric arts on the emergence of Western' science. What is often forgotten is that in almost the same breath, Keynes declared Newton as "one of the greatest and most efficient of our civil servants", in recognition of his work as Master and Warden of the Mint, positions that he held longer than his Chair at Cambridge.

The significance of the relationship between mathematics and finance is often overlooked when considering the development of science. Probability is, to both Poincare and Russell, the foundation of all science, emerged out of the analysis of financial contracts and Bernoulli first identified the number e in the context of interest payments. On a more profound level, historians such as Richard Hadden, Joel Kaye and Alfred Crosby have provided compelling arguments that the uniquely European 'mathematisation' of science came out of a synthesis of commercial practice, following Fibonacci, and scholastic analysis. Copernicus wrote on money before he wrote on planets.

While equity options trading dominated the 1980s, today, the Black-Scholes-Merton pricing formula is used more as a gauge of market volatility than to price traded contracts and the problems of finance have moved on to managing the complex interactions of many agents in the economy. It is in recognition of this evolution that the financial world has changed, not just in the last four years but over the past 25 years, that the Institute of Mathematics and its Applications (the British equivalent of SIAM) is sponsoring its first conference on mathematics in finance, to take place in Edinburgh in  2013.

Algorithmic trading is currently the focus of financial innovation. Investors, such as pension funds, will use algorithms implemented on electronic trading systems to , hopefully, optimise their market transactions. Market makers, and speculators, will use algorithms to search the markets for profit opportunities, often executing transactions in milliseconds in high frequency trading. Algorithmic trading is typically light on mathematics, using simple trend following or mean reverting criteria, and relies more on computational developments.

Since the recent Financial Crises society has realised that financial innovation, like any technological development, is not always a good thing. The Quant and Mammon report of 1998 called for academics to support banks in innovation, today the emphasis has shifted and the consensus is that academics should be trying to understand the financial system and support society's eyes and ears, the Regulators, as much as the Banks. In response to this, the IMA have invited the Bank of England to help organise the conference and provide guidance on what the Regulators' key concerns are.

The Bank of England believes that recent developments in financial mathematics have focused on microeconomic issues, such as pricing derivatives. Their concern is whether there is the mathematics to support macroeconomic risk analysis, how the whole system works. While probability theory has an important role to play in addressing these questions, other mathematical disciplines, not usually associated with finance, could prove useful. For example, the Bank's interest in complexity in networks and dynamical systems has been well documented.

The initial outline of the conference is that it will have three parallel sessions, covering developments in algorithmic trading, the concerns of the Bank of England and contemporary issues in mainstream financial mathematics. For example, in the algorithmic trading stream topics could include data mining, pre-trade analysis, risk management and agent based modelling. As well as the Bank of England’s interest in models of market failure and systemic risk, more esoteric topics such as non-ergodic dynamical systems and models of learning in markets would be interesting. Topics associated with mainstream financial mathematics could include control in the presence of liquidity constraints, Knightian uncertainty and behavioural issues and credit modelling. 

In addition to the main mathematics Conference organised by the IMA, the Scottish Financial Risk Academy is planning to organise an "Industry Day" at the end of the Conference. 

Applied mathematics is developed as a consequence of solving problems. While it is easy to criticise the world's bankers, it is harder to come up with solutions to the complex issues they face. It is always worth remembering that the laws of physics (almost surely) do not change, but finance is constantly transforming itself. Ever since the time that Newton left Cambridge for the City, the UK has built its prosperity on financial innovation, funding the wars with France and the Industrial and Agricultural Revolutions. today financial services account for some 10% of the UK's GDP and it is only fitting that applied mathematicians consider whether they can provide solutions to the difficult problems the sector faces.

The IMA Conference on Mathematics in Finance, scheduled for early April 2013, aims to provide a forum for mathematicians to become more involved in the industry and for industry to become more involved in mathematics, and we would invite any mathematician, academic or practitioner, to attend.

If you would like to register your interest in attending the conference, please contact the IMA.

Wednesday, 4 April 2012

Creation myths

There is currently a debate being carried out on the internet between Steve Keen  and Paul Krugman on the nature of money. For those (like myself) who do not have a formal training in the discipline, economists will consider money to be either endogenous or exogenous to the economy. Endogenous theories posit that money is created by the economy, exogenous theories place money as a ‘tool’ outside of the ‘real’ economy.

Mainstream, ‘neo-classical’ economics is based on exogenous theories and  describes money emerging as a tool to facilitate exchange. First there was barter,  but then the problem of a “double coincidence of wants” lead the rational caveman to introduce money. This description has no basis in fact. Just as astrophysicists use telescopes to look back in time, anthropologists visit isolated communities to see how society evolved, and the evidence of this research is summarised by Caroline Humphrey
Barter is at once a cornerstone of modern economic theory and
an ancient subject of debate about political justice, from Plato
and Aristotle onwards. In both discourses, which are distinct
though related, barter provides the imagined preconditions for the
emergence of money …[however] No example of a barter economy,
pure and simple, has ever been described, let alone the emergence
from it of money; all available ethnography suggests that there
never has been such a thing.1
The barter money story originates in Plato and Aristotle and, unlike much of Aristotle’s physics, became integrated into modern science.

An earlier Greek writer, Herodotus, the first Greek historian writing some 150 years before Aristotle, recorded that the Lydians, from modern Turkey, invented games and money, implying that they were the first gamblers. The earliest tokens used as ‘money’ were not specific weights of a certain metal but roughly cut pieces of metal with an official stamp on them2.

 Coins, tokens with a specific weight of a precious metal, emerged in the  Mediterranean and Near East at around the same time as states started employing mercenary armies. States paid soldiers in gold to conquer some community, the soldiers then spent the gold in the colonised lands and the state  recovered the gold by taxing the colonised merchants and innkeepers that the soldiers had paid for food and lodgings. Greek and Roman citizens never paid tax, only the conquered paid for the privilege and were bound to the conqueror by having to exchange their resources for the Imperial currency. The model would survive, known as the the State Theory of Money, and drive colonialism in the modern age. For example, in the 1920s the British taxed Kenya at a rate of about 75% of wages and forcing the colonised to grow cash-crops to be consumed by the colonisers. The Belgians did not tax the Congo – they relied on forced, rather than ‘free’ wage labour3.   These observations are sometimes used to support the theory that markets are created by governments, they are a consequence, not a pre-cursor, of civilisation.

As well as Herodotus’ historical account of the introduction of money, the  Greeks had a mythological account. Athena was the goddess of wisdom, just war, the domestic crafts and agriculture. In summary, the Greeks associated Athena with the skills and characteristics of civilisation, and the image associated with this blog is from a mosaic of Athena (as Minerva) in the Library of Congress. She was born out of the union between the Titans Zeus and Metis, the goddess of prudence and cunning. However, Zeus had been warned that Metis would give birth to children who would challenge him, and so immediately after they had slept together, Zeus swallowed Metis whole, but too late to prevent Athena’s conception, and Metis’s pregnancy took place in Zeus’s belly. Sometime later, Zeus was struck down by a terrible headache and asked Hephaestus, the god of fire, metal working, and technology, if he could do anything about it. Hephaestus split open Zeus’s head and Athena emerged, fully formed and wearing armour.

Athens was named in her honour after she and Poseidon competed to become the city’s patron god by offering gifts to the citizens. Poseidon gave the city a brackish spring, which was the basis of the city’s sea power and prosperity through trade. Athena won the competition by giving the city the olive tree, which gave the city wood, oil and food. She is sometimes known as Athena Parthenos, indicating her virginity, and the Parthenon is her temple on the Acropolis, Athens’ citadel.

Hephaestus, who was the most loyal of the gods, had an arranged marriage with Aphrodite, but the goddess of love and beauty resented being married to the lame and ugly blacksmith and so spent her time with Ares. When Athena visited Hephaestus to have some weapons made, the frustrated blacksmith attempted to rape the virgin. She resisted and was able to escape, but not before Hephaestus ejaculated on her thigh. She wiped the semen of her leg  and onto the ground where it fertilised Gaia, the goddess of the earth. The result of the union was the mortal, Erichthonius, who was raised by Athena in the Parthenon and became King of Athens. The Greek tradition is that this king gave the citizens of Athens, the plough, the four-horse  chariot, he had inherited his father’s lameness and needed transport, and money.

This is a more absorbing story than the standard economic narrative that out of barter emerged money, the medium of exchange. As well as being more interesting it is possibly more meaningful, suggesting money is a consequence of a synthesis of civilisation, technology and agriculture with the influence of the war in the background. Money is central to society.

Athena and Hephaestus play another role in the development of economic theory, as characters in what is considered the first Greek text that addresses economics, written by the poet Hesiod4 who probably lived around 750 BCE, an approximate contemporary of Homer.  Archaeologists identify the period around 800 BCE as the transition between the Bronze Age and the Iron Age, and while traditionally this was seen as a time of positive technological progress, the archaeological record paints a more disturbing picture. The transition from the Bronze to Iron Age in North Western Europe took place during a mini-ice-age between 850 and 760 BCE and is now associated with a switch from interconnected communities active in regional trade to isolated communities centred on Iron Age forts. The impact of the change was food shortages, conflict replaced trade and communities moved into the hilltop forts that are still features of the British landscape. The archaeological record for the Aegean at the time also suggests that climate change led to a long running famine and there was migration from the main city-states into new areas for farming. Hesiod’s father had been a farmer and merchant in north-western Anatolia, but the recession had forced him to move to Boeotia, a barren region about 100 kilometres north-west of Athens. When he died he left his estate to his two sons, Hesiod and Perses. The oldest of Hesiod’s poems, that still exists, Works and Days, is essentially the story of how Perses, a lazy good-for-nothing, bribed the local judges and obtained most of the father’s legacy, which he then squandered. Hesiod overcame the loss of his inheritance through hard work and ended up happier and richer than his brother.

Works and Days is split into two parts; the first explains how evil, the source of strife, first came about through the Myth of Pandora’s Box. The story of Pandora starts with the theft from Zeus of the secret of fire and from Hephaestus and Athena the crafts, by the Titan, Prometheus (‘forethought’). Prometheus had created mankind and passed these secrets on to humans. Zeus, not satisfied with punishing Prometheus for the theft by chaining him to a rock and having his liver eaten each day, decided to punish the mortals as well. He asked  Hephaestus to create a the first woman, Pandora, ‘all gifts’ who was given such characteristics as beauty by Aphrodite, cunning by Hermes and the skill to spin thread by Athena. Zeus ensured she was also lazy and

Pandora was sent to Earth to seduce Prometheus’s dim-witted brother, Epimetheus (‘afterthought’), with a single possession a jar which had been given to her under the strict instruction never to open it. However, Pandora had been given the gift of curiosity, by Zeus’s long-suffering wife Hera, and so one day she opened the jar, which contained all the evils that afflict mankind; disease, strife, war and the need to work, and these all escaped into the world. Realising her mistake, Pandora put the lid on the jar, trapping the last thing left in there – hope. Hesiod is saying that work is necessary as a consequence of Zeus’s punishment of mankind, and the story bears a remarkable resemblance to that in Genesis.

The second part of the poem then goes on to say that people can free themselves from poverty and misfortune through hard work
Both gods and men are angry with a man who lives idle; but let it
be your care to order your work properly, that in the right season
your barns may be full of victual. Through work, men grow rich
in flocks and substance, and working they are much better loved
by the gods.
The final part of the poem is a practical advice on how to run a household, the word  ‘economics’ comes from the Greek for ‘household management’, and farming. The reason why this poem is considered an early economic work, rather than a straightforward myth, is that it identifies the role that scarcity has in determining  human behaviour. The gods make life a struggle for mankind, and so we have to work hard.

The Greeks recognised the significance of the relationship between Pandora  and Athena and the story of Pandora’s birth was featured on the base of Athena’s statue in the Acropolis. Just as with the myth of the origin of money, the Pandora myth might lack literal truth but it is rich in meaning. It highlights a causal relationship between understanding technology and a greater complexity in life that results in strife.

Today, many scientists, in particular social scientists, regard knowledge as  ‘shared belief’, not necessarily ‘justified belief’, science is less about ‘truth’ and more about ‘consensus’. Deirdre McCloskey, who is simultaneously a professor of economics, history and English at the University of Chicago, recommends an Italian definition of science
the speculative, agreed–upon inquiry which recognizes and distinguishes,
defines and interprets reality and its various aspects and parts, on
the basis of theoretical principles, models and methods rigorously
Science is speculative, not certain, and agreed–upon, not secret. It is on this basis  that society can begin to understand the value of science.

This definition of science allows economics to base itself on an unjustified myth  that barter evolves into money. However, it could alternatively allow economics to build itself on the Pandora myth, a myth that is remarkably similar to the story of the Fall in the Bible. It might be argued that the barter-money myth is un-scientific, since it is not supported by evidence, just as the Biblical myth is not supported by evidence. However, the barter-money myth endures because it conforms to two key characteristics of mainstream contemporary science. The myth is progressive, it describes a linear process where by the system evolves from a primitive beginning to the complex end we experience, and it is material, its explanations, involving people, goods and metal tokens, do not rely on metaphysical concepts such as society, trust or

Physicists will argue that, while social sciences can be built on such shaky foundations, the certainty of physics is not. This overlooks the fact that physicists are constantly disregarding old theories and building new ones. Physics is the  ultimate science because it is so eager to evolve. This makes it difficult to contradict, because it will embrace its contradictions, indubitable but not


1 Humphrey [1985, p 48]
2 Ingham [2004, p 98]
3 Ingham [2004, p 76]
5 McCloskey [1995, p 6]


B. Gordon. Aristotle and Hesiod: The economic problem in Greek
thought. Review of Social Economy, 63(3), 2005.

C. Humphrey. Barter and economic disintegration. Man, 20(1), 1985.

G. Ingham. The Nature of Money. Polity Press, 2004.

D. McCloskey. The limits of scientific knowledge. In R.F. Goodman
and W. R. Fisher, editors, Rethinking Knowledge, Reflections Across
Disciplines. State University of New York Press, 1995.