# Modelling risk when market making

Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest bid, and an ask that was slightly lower than the current lowest ask.

Whenever anyone bought or sold, that would mean that I would always be one of the people they bought/sold from/to. This would allow me to make a profit equal to the gap between the two.

The problem I'm having is in calculating the risks. As far as I can tell the variables involved are:

Variables out of my control

• Gap between highest bid and ask offered by others
• Average price paid for "pot" of BTC that I'm trading with
• Some measure of the volatility of prices over the preceding period (Risk)
• How much volume would move the market by a given amount higher or lower

Variables within my control

• Maximum exposure in terms of money
• Maximum difference in ratio between GBP reserve and BTC reserve
• Size of the gap between my bid/ask prices (out from the exact centre as percentage of total gap)

I'm struggling to figure out how to model this effectively though. I studied Computer Science and have a basic grasp of probability theory, but this is a bit beyond me. Any help, or pointers to the "proper" formula to model this would be greatly appreciated.

• I don't know much but perhaps the Black-Scholes model might suit your needs. – Sebastian Garrido Nov 30 '13 at 22:21
• The role you're thinking of playing is called a "market maker". The gap between the highest bid and the lowest offer is called the spread, and other traders can pay the spread to the market maker for the privilege of being able to buy if they want to buy or sell if they want to sell. The market maker receives the spread but can't choose which way the transaction goes. So he needs a lot of capital in case everybody wants to sell at once and he can't offload; the spread pays for this capital. Any ability to predict the market can reduce the capital needed, but at greater risk if it goes wrong. – HTFB Dec 1 '13 at 15:54
• Apart from anything else, if you are running this strategy, anybody who thinks they are richer than you can keep on selling you bitcoins, for as long as you are prepared to keep buying. When you run out of capital you will have to sell and sell hard, losing much more than the initial spread; at which point they can buy back their position having made money at your expense. So unless you are rich enough to take on absolutely anybody else in the market, it can be a very expensive game of poker. – HTFB Dec 1 '13 at 16:08
• This question requires some non-trivial work. I'll do it for a non-trivial bounty, preferably in bitcoins. – Anonymous - a group Dec 2 '13 at 1:59
• Another perspective: the market maker provides liquidity to the market, so from his perspective the instrument suddenly has reduced (or even negative?) liquidity. Since the bitcoin has no value apart from its liquidity, it must be a particularly uncomfortable place to trade. This suggests that the risk of the strategy is affected by the nature of the underlying instrument. It's not an easy modelling task! I'd be interested in any reference with a formal discussion of liquidity, as I've never seen it treated theoretically. – HTFB Dec 2 '13 at 9:17

Get your hands on some books on economics, econometrics, and financial engineering. Take a few years to understand them, and then model the bitcoin economy in terms of:

• the number of businesses actually taking bitcoin as payment (demand)
• the number of people actually paying businesses with bitcoin (supply)
• the rate of inflation due to mining (supply)

Speculation will dry up sooner or later, and we'll finally be left with a stable currency for doing business.

Also, your approach to modelling isn't so hot. Using variance of price as a metric of risk works okay in massive markets. Not so much in these tiny, highly volatile, shark infested markets.

As a limiting case, consider a market with exactly two participants. The model here is "negotiation", which is very different from the model for a large open market.

The point is: an effective model has to be driven by the economic considerations.

• Do you have any textbooks you can personally recommend? – Tom Busby Nov 30 '13 at 23:49
• It depends on how much you've already studied. A targeted, "complete" course might include things like: Krugman's "Microeconomics" and "Macroeconomics", Kellison's "Theory of Interest", Koops' "Bayesian Econometrics", Ruppert's "Statistics and Data Analysis for Financial Engineering". And the computer science stuff, which you probably have a better handle on than me. – nomen Dec 1 '13 at 0:02
• The question is about arbitrage/financial micro-structure. Micro or macro (or economic theory) are worthless. The other comments that addressed market-making are sound. – Sergio Parreiras Dec 5 '13 at 2:52
• That is nonsense. The macro-economics of bitcoin are extremely important to market making bitcoin. Ignore them at your own peril. Indeed, the comments you mention bring up scenarios where macro factors will ruin the market maker. – nomen Dec 6 '13 at 4:39
• @Tom: there have been recent advances, if you're still interested. In particular, there are now exchange traded bit coin options, so you can perform effective $\Delta$ hedging (you couldn't last year...) – nomen Dec 30 '14 at 22:12