A typical quote in the derivatives market may be 2.00 bid at 2.50 ask with a size of say 100x100. How do practitioners go about choosing the size of the market (how many contracts) to quote? It seems to me that it should be proportional to their edge as well as their capital; a sort of Kelly criterion approach.
@chrisaycock raises a valid point about the process not being particular rigorous.
There are reasons why it is not a rigorous or optimized sizing mechanism.
1) most market makers are quoting many strikes & expirations, usually multiple underlying assets these days. Depending on venue there may be ways to limit the number of executions, eg, exchange side safeties or simply due to the fact that salespeople need to get the attention of the trader in some sort of order.
2) much of market making is setting prices in such a way as to either balance order flow or synthetically balance order flow by trading other options against fills (static hedging).
3) flows can be one way. most recently in bond options during March 2020. there was no realistic way to balance flows. it is very unusual but it does happen.
4) often there are external reasons for setting quote sizes. for instance, the matching engine might use a pro-rata process for allocation which encourages larger trading or on a bank desk there might be pressure to satisfy an important client.
5) re: 3, the big concern of a market maker is not the fill you just got, but the question "where are you now?" For example, I'll buy your 100, how are you now? and then all of sudden a 100 lot becomes a 700 lot and before the market maker has a chance to offset, there is a large loss and the position is very lopsided.
So the issue is that theoretical optimization is a lousy idea for market making. It works fine in an environment that a trader has significant control over, e.g., proprietary trading. Market making is an unknown that involves significant uncertainty about positions, order flow, asset price path, and even regulatory & event risk. Therefore it means that the correct answer will be significantly below an optimal calculation in order to stay solvent. How much so is a business decision.
Liquidity. If you are a market maker, you should be able to flip the order you just made as early as possible, with as much profit as you can. Volatility and Volume are the prime factors for market makers.
They establish their own internal rules and adhere to them. Say a company will only participate in buying options, in certain range of options/Equity, where their order volume is < 2% or 5% of market volume and has ~4 or 5 % vol. However when they are writing options, the opposite is true (for some, depending on their strategy).
Volume & the number of bids aid in identifying the size of the orders to be placed. For options, which are out the money, if the volume exists, you can write options with a higher price, than the actual value of the option.
The minimum size can be enforced on the market maker by the exchange or regulator. For example, some bond markets demand that market makers show a minimum size and spread for a certain period of the trading day. However, in personal experience the major drivers have always been liquidity and latency, with each working antagonistically to determine my quote size.