Five’s company, six is a crowd

Simon Nursey at Digital Vega explores the optimum number of RFQs for FX options trades with a little game theory


In spot FX, various techniques for achieving best execution have been well examined and are backed by a wealth of research. But in the options world, analysis is more sparse, and often conflicting.

The FX options market is still mostly quoted manually and market impact times are measured in hours not milliseconds, so lag times and internaliser/externaliser models are less of a consideration.

But with so many combinations of strikes, dates, cuts, strategies, and an only partially observable interdealer market, price discovery is complicated.

An FX options execution strategy starts with a simple question: how many market-makers to ask. The FX options market is generally accessed on a request-for-quote (RFQ) basis. A customer asks multiple market-makers for a price, the market-makers respond and the customer can trade on one of those prices. Only the market-makers that have been RFQ’d see the interest and they cannot see each other’s prices. This is classically known as a blind auction.

The price uncertainty means that given a set of market-maker bid/ask prices, the best net price (highest bid, lowest ask) will always be narrower than the individual prices. How much narrower depends on the amount of price uncertainty and the number of market-makers asked.

On the Digital Vega venue, the ratio of spread to price deviation is around 3.5–4.0 and stable across pairs (see figure 1).



Taking a ratio of 4.0 and assuming a normal distribution of prices, figure 2 shows the relationship between average market-maker spread and the best net spread. With three market-makers the best net spread is 60% of the average individual spread and at five is it less than 50%. So why not ask as many market-makers as possible?



Option traders are acutely aware of the winner’s curse syndrome whereby the ‘winner’ of the trade, when in competition with too many other market-makers, loses money. The cost of getting it wrong can be significant and, due to the partial observability of the FX options market, may not be apparent for hours or even days.

To counter this, market-makers will widen their spreads based on how many market-makers they perceive are being asked. This has the effect of limiting the benefit of adding more participants to an RFQ. But how much?

We can model exactly how much a market-maker should widen their price by treating this as an n-person game of competing market-makers and making the following assumptions:

- market-makers act independently to maximise their own revenue.
- revenue is measured against a single clearing price which is not known with certainty and follows a normal distribution.
- all market-makers follow the same strategy and know how many other market-makers are being asked.

We simulate this game with a given number of participants, each time finding the Nash equilibrium. This is the point where each market-maker would make less revenue if they adjusted their strategy (i.e. their spread) while all others left theirs unchanged.

Varying the number of participants and solving each time, we get the relationship in figure 3 showing the optimal spread they should take as a multiple of the clearing price uncertainty (standard deviation).



It’s perhaps surprising that two market-makers acting independently and in strict competition will still settle on a wide spread, while three market-makers in competition will individually quote the tightest price. Above three and the forces of adverse selection oblige market-makers to widen their spreads. A market-maker competing in a panel of 10 will quote almost 20% wider than a market-maker acting in a panel of three.

However, the tightest individual spread does not mean the tightest aggregate spread. To see this, we must combine both results i.e. the spread compression from aggregating multiple prices, and the widening market-makers employ to avoid adverse selection.



In this very simple model, it is apparent there is considerable advantage to RFQ multiple market-makers. However that advantage diminishes rapidly with only marginal improvements in execution cost above five and quickly swallowed by other factors like information leakage (to be covered in a future article). At Digital Vega, we hold the view that five market-makers is the best panel size for our customers’ execution.

Note that an important aspect of this simulation is that each market-maker knows how many other market-makers they are competing with. In the real world, takers are clearly incentivised to make that look as small as possible and market-makers must take a view on this number.

We are also assuming that market-makers aim to maximise only their revenue rather than broader relationship-driven metrics. Hopefully, though, this article provides a firmer base for the discussion of how many market-makers is optimal.

Simon Nursey is head of Asia-Pacific at Digital Vega, and previously an FX options trading head at Standard Chartered and BNP Paribas.

Digital Vega is a multi-bank aggregator with a customer base covering asset managers, hedge funds, private banks and regional banks, with liquidity provided by 19 major FX banks. 

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