# A three-point turn in derivative design

## Citibank quant’s triangle method allows information geometry to be applied to hedge structuring

The artwork for Pink Floyd’s The Dark Side of the Moon is every bit as celebrated as the album’s music. A design classic, it depicts a white beam shining on to a glass triangle before diffracting into the constituent colours of the spectrum.

Now Andrei Soklakov, the Asia-Pacific head of prime and delta-one quantitative analytics at Citibank in Hong Kong, has come up with what he hopes will be his own design classic. And, like the cover of Floyd’s magnum opus, it has a triangle at its core.

In 2008, Soklakov introduced the concept of information derivatives, with which he intended to improve the design of volatility products by helping structurers customise the exposure to volatility risk. It became apparent to him that all types of derivative could benefit from a similarly flexible design approach.

Although the work he published over the following years concerned the design of investment products, Soklakov has now extended his theory to include hedging products. In his latest paper, Information geometry of risks and returns, he shows how derivatives can be viewed through a new perspective and portrays their risk structure as a triangle.

In his derivatives structuring framework, information is the product’s underlying asset and takes the form of probability distributions. A product’s value will depend on the difference between the probability distribution implied by the market and the probability distribution built on the investor’s view. In the case of hedging products, a scenario distribution that comprises market risk factors enters the picture. These three distributions are identified by three points in a multidimensional space and those three points form a triangle.

##### Andrei Soklakov, Citibank

The co-ordinates of the three points hold the information about the three probability distributions, and each co-ordinate corresponds to a statistic. They might indicate the average, the volatility or the parameters of the implied volatility surface. Those points are, in a more algebraic sense, vectors of information.

Such representation is useful because it can be dealt with by applying information geometry, a branch of mathematics developed to analyse probability distributions and their relationships – for example, by measuring their distance.

Handling all the information required to design a product in a simple triangle facilitates the design and, according to Soklakov, allows for an optimal allocation of resources while adhering to the investor’s views. “As I see it, finance is all about optimal resource allocation,” he says. “Information derivatives can be viewed as the result of optimal resource allocation within the scope of a single product.”

### And all that you deal…

“It’s an intriguing work,” says Francois Buet-Golfouse, head of decision science at JPMorgan Chase’s UK consumer business. “Not many people have tried to connect information geometry and quant finance. The difficult part is identifying the correct payoff structure, conditional to the client’s needs and preferences. But once one has it, this approach allows us to work out a derivative structure that replicates it.”

A client might, for example, express a positive view on a particular asset and believe that volatility will decrease. It therefore wants a long position on the asset and a short position on volatility. This client might also be a pension fund that is required to limit its exposure by adding a capital protection feature to the structure. The first idea a structurer would typically come up with in such a case would be a call option. However, this type of option would be long volatility, while the client would want to be short volatility.

Soklakov’s framework enables a structurer to build a hypothetical product based, in part, on the client’s view, but also incorporating the market view as derived from observable data. The framework provides the tools to combine the three probability distributions and translate into a payoff function that includes the client’s requirements. In the example above, the payoff function would be replicated with a basket of vanilla calls and puts, which could be bundled into a single product.

“This theory becomes especially useful when clients want to combine various types of views,” says Soklakov. “Combining such views optimally in a single product is very easy within this theory.”

Because the structurer can measure the distance between distributions, including those that are model-generated, Soklakov says the framework enables model risk to be quantified in an easy and intuitive way, such that the assessment of model risk can be automated and monitored.

The framework’s intuitive advantages go beyond the tractability of the geometric representation. It translates risk in terms of returns, which Soklakov reckons are easier to understand. “This is certainly true about model risk and might even help with standard sensitivities,” he says. “Within the paper there’s a formula that helps [in] expressing risks like delta and vega as simple spreads in expected returns.”

With regard to the immediate implementation of Soklakov’s framework, Buet-Golfouse is cautiously optimistic. “This new framework has some of the right ingredients to become popular,” he says, “although it’s still early days and we are still at the proof-of-concept phase.”

Soklakov himself is confident that time will prove him right. “In the space of ideas, information derivatives are probably a niche topic,” he says. “But in the space of financial solutions, this will be a very useful tool. It is guaranteed to be useful.”

To assist with that, he wants to adapt his framework so it can be plugged into existing systems. “I’m planning to write another paper showing how to use the approach for making small improvements in existing products as opposed to replacing them outright with brand new designs. This could open a safer evolutionary approach of incremental improvements in product design.”

Time will tell whether the framework has the staying power of a classic album cover or whether it might even eclipse standard approaches to structuring.

Editing by Daniel Blackburn

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