The most common application being researched for machine learning is optimal execution. When large trades are executed in the market, it could potentially push prices in an unfavourable direction, so it makes sense that traders are keen on optimising this cost.
So far, most of the interest in applying machine learning technology to reduce trading costs has been from the buy side.
However, recent research by quants from Standard Chartered shows this may be about to change.
In this month’s first technical, Evolutionary algos for optimising MVA, Alexei Kondratyev, a managing director at Standard Chartered in London, and George Giorgidze a senior quantitative developer in the strats team within the same bank, propose machine learning techniques to optimise initial margin costs through trade selection.
Since September 2016, an increasing number of large dealers have been required to post initial margin on new non-cleared trades with other in-scope counterparties. The initial margin has to be funded, which creates material costs as more and more counterparties become involved. This cost is typically priced into trades in the form of a margin valuation adjustment (MVA).
Market participants have estimated initial margin funding requirements under the regime to be close to $1 trillion. As a result, a number of margin compression and risk optimisation solutions have popped up to reduce margin funding costs, each promising more significant margin reductions than the last.
In their paper, Kondratyev and Giorgidze, apply two machine learning algorithms – a genetic algorithm and a particle swarm optimisation (PSO) – to reduce margin costs over the life of the portfolio, while keeping the market risk exposure of the portfolio the same.
This is not easy. Because there are many parameters that evolve over time, the problem becomes heavily non-linear – that is, traditional optimisation methods do not work in simulating and reducing MVA.
This is where the benefits of machine learning come in, says Kondratyev.
From generation to generation, our calculation becomes better and better, until finally we evolve to a population of solutions that converges to a global minimum of our objective functionAlexei Kondratyev, Standard Chartered
Both algorithms used by the quants belong to the class of so-called evolutionary algorithms that run multiple iterations of chromosomes, tweaking one or two genes at a time, to find the most beneficial mutation. The StanChart quants apply the same principle to MVA.
Here the objective function, which defines the quantity to be maximised or minimised, is incremental MVA on a portfolio of trades. The chromosomes represent individual trades and the genes are trade details such as direction, notional size and currency.
“The algorithm works by finding such values in our solution, which is a trade or pair of offsetting trades that would minimise our objective function, and our objective function is incremental MVA, so we try to find the most negative incremental MVA,” says Kondratyev.
The algorithm randomly generates trades by tweaking one or two trade details each time, and keeps those that reduce MVA and discards those that increase MVA – similar to how evolution works. The genetic algorithm is used when trade details are discrete or categorical, such as currency for example. In this case all variables need to be discretised – for instance tenor, can be discretised by month. PSO is used when they are continuous – notional size, for instance, is a continuous variable.
“From generation to generation, our calculation becomes better and better, until finally we evolve to a population of solutions that converges to a global minimum of our objective function,” adds Kondratyev.
One could take a snapshot, look at portfolios, as of say, end of day, and then one would see that if a couple of trades are added into the portfolios, the Simm initial margin profiles would be flattened out and MVA would be reducedAlexei Kondratyev, Standard Chartered
The resulting set of optimal trades could then be used to guide traders on what sort of trades and counterparties would help reduce their margin costs under the industry’s standard initial margin model.
“One could take a snapshot, look at portfolios, as of say, end of day, and then one would see that if a couple of trades are added into the portfolios, the Simm initial margin profiles would be flattened out and MVA would be reduced. Then, a proposal can be made to the trading function and it’s up to them to decide whether to go ahead and execute these trades,” says Kondratyev.
The techniques have been in use in Standard Chartered since the beginning of the year. The quants did not reveal what their MVA savings were, but they said it would be significant enough to justify the cost of development of the technique, also factoring in future increases in MVA as more counterparties come in scope of the margin rules.
In the race to survive the rising costs of the derivatives business, it is not surprising that quants have started to use evolutionary algorithms to reduce what is likely to be one of their biggest costs – the funding initial margin.
Derivatives valuation adjustments, in general, are complex to model. So optimising them requires more innovative techniques.
While buy-side quants have done most of the early exploring of machine learning, Kondratyev and Giorgidze’s paper is a step in the right direction towards encouraging more sell-siders to explore the technique as well – which may become crucial as MVA becomes more substantial over time.