Market Making Requires Inventory Control and Market Structure Knowledge

# Quantitative Math required for Market-making?


# Quantitative Math required for Market-making?












I understand there is an awful lot of Quantitative Math required for statistical arbitrage/algorithmic trading. However, would someone "in the know" be able to tell me whether there is less quantitative requirement for being a market-maker?

My (simplistic) viewpoint on market making is you simply want to keep quoting, collect the exchange rebates and if you get hit on one side of the bidask spread you need to hedge that trade. Using this (admitedly simplistic) viewpoint, I got the impression there was far less PhD-level mathematics involved than stat arb/algo trading?

I ask because myself and a group of friends are low-latency programmers and we are pondering whether we could realistically start up a small market-making business and utilise our low-latency experience. However, with our speciality on the technical side and no PhD mathematicians, we weren't sure how plausible it was.

Assuming it was plausible would you suggest beginning with a smaller exchange/market? Straight equities vs index futures/options, does it matter?

Any useful advice would be most welcome.

## Answer by user2763361 (score 16, accepted)

https://quant.stackexchange.com/a/12768

Successful strategies in both areas can have the same math requirement. It just depends on the algorithm. PhD level mathematics is not a requirement in either area, despite the impression you may get from academic papers (note that a lot of these papers use math to build a sim market, which is completely dislocated from what a researcher needs to do). I feel that, if anyone is bogged down in esoteric math in either area, their strategy is about to break down.

What you primarily need to be good at is data analysis and statistical modelling, and being able to come up with good ideas.

Why do you guys think you will be successful without a research background? I have spoken to a few low-latency software engineers who hadn't had research exposure yet and I can give a 100% guarantee that they would not have made a cent if they were out on their own and had to build strategies. Trading is an actual profession and an actual skillset that is not as simple as "adjusting your quotes around the inside levels". Academic papers aren't going to help with strategy either (I haven't read something that would make money yet).

In summary, you should not be concerned about a lack of math ability (my position still applies if half you guys are math PhDs), you should be concerned about a lack of trading ability.

## Answer by lehalle (score 26)

https://quant.stackexchange.com/a/12769

The primary quant skill needed to make the market is optimal control (a typical paper is Guéant, O., L, and J. Fernandez-Tapia (2013, September). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics 4 (7), 477-507), because you need to control your inventory and adjust your quotes accordingly:

- be more aggressive on your long leg

- and less on your short one.

But it has to be done with respect to your cost function (how do you valuate the risk of having a position, the cost of your short inventory, the fees, what are you assumptions on the price moves, etc). In reality if you do that for a large institution the risk of your inventory would probably be measured on the whole book of the firm (it adds questions about correlations --thus Epps effect--, etc).

Moreover, you will need to hedge your inventory: if you make the market on derivatives, you will need to understand the marginal variations of their value with respect to changes in their underlying (i.e. the "greeks" stuff, see Stoikov, S. and M. Saglam (2009). Option market making under inventory risk.).

Of course you need to have some knowledge in microstructure: Kyle (Kyle, A. P. (1985). Continuous auctions and insider trading. Econometrica 53 (6), 1315-1335.) and Glosten-Milgrom (Glosten, L. R. and P. R. Milgrom (1985, March). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics 14 (1), 71-100.) like literature: adverse selection, market impact, etc. And since the devil is in the detail; you need to know order types, trading rules, etc.

By the way, I have a (long) list of papers on quant market making on my citeulike account which is also stored here

## Answer by madilyn (score 15)

https://quant.stackexchange.com/a/12779

Unfortunately, the ability and tools to develop a low latency trading system are extremely commoditized and will be insufficient for you to make a living in this field. An overwhelming majority of electronic market makers are staffed 100% by PhDs because trading experience and research compose their primary differentiators, e.g.:

- SIG EMM - 100% PhD.

- DRW EMM - Almost 100% PhD.

- Chopper EMM - Only 1 non-PhD.

- Two Sigma EMM - About 80% PhD.

The list goes on. There are a few shops that hire mainly among those with B.Sc-level mathematics background, but these shops were also all started by former veterans of floor trading and/or early adopters of electronic trading, e.g.:

- Optiver

- Tower Research Capital

- Virtu Financial

- GETCO

- IMC Financial Markets

...or late adopters who were former veterans from Citadel, Tower Research, SIG etc. and spun off, e.g.:

- Hudson River Trading

- Jane Street

- Headlands Technologies

One will be very mistaken if he expects to take @lehalle's list of papers and some coding ability across the profitability hurdle. I wouldn't dream of doing so alone even though I wrote an entire custom UDP/TCP layer against reduced architecture in the early stages of my firm. You could downvote and ignore this advice, but I welcome you to inject a few dollars into the market.

## Answer by Pam (score 3)

https://quant.stackexchange.com/a/12933

No. All you need is to be naturally smart, and not lack common sense.

Well, clearly, a bare minimum of education (the 4 operations should suffice) ;-)

Also sometimes, too much specialized education may really be detrimental (it's common the case of Physics PhDs, who have an harmful tendency towards predictive models).

Usually, and generally speaking, a Statistics background is the best (clearly, most it's up to the individual. You will surely find clueless statisticians too, no doubt).

## Answer by nimbus3000 (score 2)

https://quant.stackexchange.com/a/70092

I think a lot of people look for PhDs are not only for their mathematical or quantitative skills, but also for their research mindset. It takes a lot of iterations, trying a lot of ideas most of which would not work to come up with a profitable trading strategy. Having a PhD becomes a sort of testament to the fact that you have the perseverance required to work on open problems and take it to conclusion. I not saying that mathematical skills are not required, but that it takes far more than mathematical skills.