Why are manual market makers still predominant in options markets? Why haven't algorithms replaced these market makers, as they have for liquid stocks for example?
You need to differentiate between OTC and listed options in order to appreciate the fact market makers are still active and relevant in either segment:
Listed Options: Actually most listed options market making is governed by market making algorithms, however, most such algorithms are implemented with manual overlays. Something very similar goes on in the eFX world, where most quoting engines are fully systematized, however, spread tightening and widening can and is in fact overridden by humans who analyzed counter party profitability, trading actitivity such as frequency and such forth. This may not fully translate into listed options markets but the reason in general for listed options is that too much can go wrong when stocks, for instance, move by 10%+ within minutes post market-impacting events. Now that is true for stock markets as well but please keep in mind that most hft participants do not have an obligation to show prices, whereas options market makers are bound to stricter liquidity provision requirements, subject to each exchange on which such options are listed. So, while most all listed options contract market making is in some way or the other automated, there still are manual overrides at force.
OTC options markets: On the rates side, please appreciate that 90%+ of underlying notional traded goes through the OTC rather than listed markets. On the equities side that is somewhat lower but still significant, especially on the index side of things. With full customizability goes aboard the ability to fully automate. Now, everything in life can be automated, given a sufficient budget and no time constraints. But in a sense what chrisaycock pointed out is actually right: Car dealers, travel agents, and a host other middle men fight hard to stay in place and try to remain indispensable. Same with most OTC options markets: Fact is that which counterparty requests quotes, at what time, in what size, and especially the chatter surrounding an OTC trade is hugely important in brokering a deal, something that would be very expensive and time consuming to automate. For example, a keen understanding whether the requested size by a client is all that client is intending to trade or whether there is more that he/she possibly attempts to deal with other counterparties is part of the core job description of any trader, as it can hugely influence expected profit and loss for the market maker.
I am sure we will get there in the future, but for now most OTC market participants are not too interested in pushing into this direction simply because it also means they would cut their own fingers.
I used to work in OTC, many of the deals would be so individual I can't imagine an algorithm being able to cope. In addition there were some extra factors like how we feel towards a counterparty and sometimes the broker over whether we would step in or not.
I now work in exchange traded futures and options (listed options), and I can say the number one reason there is not more market-making by algos is Risk. By risk I mean risk of a error, risk of an event happening when you might have quotes in hundreds of instruments and liquidity risk. It's one thing to quote a couple of liquid markets, and the underlying's for the options might well be very liquid, but there's much more risk of an expensive mistake in exopts with the number of quotes one would have to have in the market. Whether we like it or not algos do go wrong, we fail to foresee all the possible outcomes, situations change.
Finally it's worth considering what we're risking for, you could quote all day in some illiquid strikes and not see any business. In fact by quoting, especially if the market is really illiquid, all you're really doing is giving pricing information away for free.
Because it still is profitable. Nowadays most of the market making is somehow based or backed by algorithms. It is similar to the chess player example: If a human plays vs. a machine, the machine will win. But if a human plays together with a machine vs. another machine, the human team will win.
Trading algorithms have plenty of parameters which need to be calibrated or adjusted at all times. For example a simple market making algorithm needs inventory limits and position targets. These need to be updated all the time. While a configuration might work for some hours, it might not work for others.