4 May 2012/9 Comments

Twelve years ago, in ‘Inventing Money’ I explained the principles of option pricing to a general audience. Although the maths looked complicated, the financial market that Fischer Black, Robert Merton and Myron Scholes modeled in the early 1970s was really quite simple. You bought and sold derivatives, such as options or forward contracts, and traded between the underlying assets, and a liquid cash account.

The cost of replicating the derivative was equal to its price, because otherwise traders would arbitrage the discrepancy away. With that Nobel prize-winning concept in place, bankers and regulators thought you could safely trade and hedge as many derivatives as you wanted – and that’s exactly what people did from the 1980s onwards, creating a multi-trillion dollar market.

The ‘law of one price’, enforced by replication and arbitrage , resembled a financial law of nature. It made derivative pricing particularly attractive to people from a physics background. One of the greatest achievements of twentieth century physics was Quantum Electrodynamics which described the behavior of particles like electrons and photons. QED was ‘perturbative’ in the sense that complex interactions between particles were less important than simple ones.

In the 1970s model of financial markets, complex interactions between traders involving liquidity or counterparty default were also minor corrections to derivative pricing that in practice were ignored. Once you defined the instrument – a barrier option or an interest rate swap – its price was the same for everybody in the market.

Today, the kind of market that Black, Scholes and Merton modeled in the 1970s seems quaint in the wake of the financial crisis. At a conference in Barcelona’s Hotel Arts in April, I watched quants grappling with a new landscape of counterparty risk, collateral and clearing houses, that has turned the old world upside down.

Consider the old framework of derivative pricing in which counterparties enter into derivatives contracts with one another, while buying and selling the underlying asset to hedge themselves, dipping in and out of cash accounts. The starting point today is counterparty risk, collateral and cash.

Before you take on counterparty exposure, you need to think about these counterparties’ credit spreads. How volatile are they? What’s the ‘jump-to-default risk’? That drives a crucial parameter, the credit valuation adjustment. Of course, you might default before they do, and the possibility that you might not pay out on a derivative becomes valuable as your own credit spreads widen. Enter the debit valuation adjustment. These two quantities, CVAs and DVAs, make derivative trading books at major banks lurch around like aircraft in a thunderstorm.

Then there’s the cash and collateral aspects of derivatives. For banks everywhere nowadays, cash is precious: if holding a derivative requires a cash account for its hedging strategy, that means borrowing money somewhere to fund that. Can you pledge the derivative as collateral? Can you lock in a deterioration in your own creditworthiness by using the cash to buy back bonds? That leads to another correction, the funding credit adjustment, that also needs to be added in.

One answer to the problem was supposed to be the posting of collateral to cover swings in the mark-to-market value of a derivative. That was fine when there was an unlimited supply of highly-rated bonds that everyone assumed were interchangeable – Treasury bills, Italian bonds, collateralized debt obligations. This is no longer the case as safe assets become increasingly contested, and the safest thing of all – cash – is like blood.

Along with CVAs, DVAs and FCAs, the credit support annexes that govern the posting of collateral have now become equally crucial parts of a derivative contract. What kind of collateral can you post, and in what currency? Can you re-pledge or hypothecate it? How do you discount the value of that collateral? And if a counterparty defaults suddenly at a time when markets are highly volatile (which isn’t implausible), even a CSA won’t necessarily protect you.

In today’s world, the derivative that used to be the same for everybody sits on top of these new components, like a decoration on a wedding cake. Pricing has become context dependent, as CVAs and CSAs throw out different numbers depending on what positions a bank already has, and what collateral it owns, and how the market perceives its default risk. A keynote speaker at the Barcelona conference, BTG Pactual’s Tom Hyer, suggested a new paradigm for derivatives was necessary.

I would go back to a physics analogy. In particle physics, the euphoria over the success of QED wore off when the theory was adapted to account for the behavior of unseen particles trapped within atomic nuclei – quarks and gluons. That theory, Quantum Chromodynamics, was ‘non-perturbative’, in other words, the more complex interactions dominated the simpler ones. That made the physics much harder.

Derivatives today are like that. Complex interactions between banks and within portfolios dominate the pricing of derivatives, as opposed to the behavior of the assets the contracts are supposedly ‘derived’ from. Maybe that’s nature’s way of telling us to make the banks, and the market simpler.

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I dagene da fysikk o[…] Nick Dunbar has a good column today on how derivatives have followed physics from being clean to being messy. Once upon a time, both physics and derivatives had beautiful, simple models: quantum electrodynamics and Black-Scholes, respectively. But nowadays they’re both vastly more complex. […]

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Tim JohnsonIMHO economics should stop relying on analogies from physics, it hasn’t solved anything in 200+ years of trying.

Physicists focus on B-S and the PDE because it is familiar. Mathematicians use the Fundamental Theorem:

1. A market is arbitrage free iff a martingale measure exists

2. A market is arbitrage free and complete iff a unique martingale measure exists

Statement (2) is forget an idealised world, you can’t price uniquely. Statement (1) can be seen as a version of the statement that “fair exchange is based on equality”, and was the foundation of the development of mathematical probability from Cardano to Bernoulli. The more popular frequentist approach only came to dominate after Montmort and De Moivre claimed to have defeated chance in the 1710s.

A new paradigm (actually an old one): price assets in a market on the basis of fair exchange, not on utility maximisation

Chaos, Derivatives,[…] be made any more clear than with a recent revelation given by ex-physicist and author, Nick Dunbar, in describing a new level of complexity facing banks and derivatives. Ironically, Thurdsay […]

Chaos, Derivatives,[…] be made any more clear than with a recent revelation given by ex-physicist and author,Â Nick Dunbar, in describing a new level of complexity facing banks and derivatives. Ironically, Thurdsay […]

Chaos, Derivatives a[…] be made any more clear than with a recent revelation given by ex-physicist and author,Â Nick Dunbar, in describing a new level of complexity facing banks and derivatives. Ironically, Thurdsay […]