How do derivative prices react so quickly to changes in underlying prices?

Question

Just trying to understand something with the market pricing and how it works. There are literally thousands, if not millions of derivatives tied to say an index fund (which in turn are composed of a basket of underlying stocks). So say an index moves up 1 point. How is it that instantaneously all those derivatives (thousands of option chains, strike prices, calls, puts, etc, bid/ask/price change at the very second to account for that tick up). It's done so accurately within under a second that is astounding. so the question is: these are normal people adjusting their bids/asks according to that move in the underlying. First off, they can never do it that accurately and that timely, considering the complex equations and time-component which are behind Options prices, and all under a second. Are prices bid/ask updated by computers and placed there? But aren't individuals who set the bid/ask manually on those? Also what if in some obscure out of the money option strike, no one is interested in trading at all. Who then updates the bid/ask for those to reflect market efficiency?

Just trying to understand how millions of prices get changed to match the underlying in such a short sub-second time frame whether there are any interest even in some strikes or not. Is this what a Market-Maker is for? Even if all this is computerized, it would have to work at supremely fast speeds to make those calculations and update all those prices at sub-par seconds, every second. How does this all work?

Answer 1

The market makers in various options operate their own or third-party pricing and valuation systems which will take the price of the underlying into account. These valuation models will run on server farms in data-centers with good connectivity to the exchange(s) on which the market maker operates.

If the price of the stock moves, then so will the price of the options. This creates a burden on the market maker to update thousands of quotes near-instantly, which is why throughput to the exchange systems is important. Many options exchanges offer 'bulk quoting' API interfaces so that market makers can update a 'page' of quotes in a single computer message, as well as 'mass cancel' mechanisms where a single message can be transmitted to an exchange to request that all quotes belonging to a particular market maker or a particular underlying be cancelled. These features improve the efficiency of the systems for market makers.

Rounding also plays a part, in that many options are only priced to the nearest 5 cents, so a $0.05 move in the underlying will be required to move the price of the option by one tick.

The adjustment of the price of the option based on the price of the underlying is simple arithmetic (underlying price - strike price) so can generally be updated quickly by a computer algorithm.

In the case of the index moving, generally options market makers will only look at the price of the underlying security for that option rather than the index overall.

A market maker is a specific type of exchange member who in practice is a registered broker dealer trading its own capital (i.e. proprietary trading). Historically, and on some exchanges still today, the market maker is also called a specialist.

Answer 2

I doubt that there are millions of derivatives tied to an index fund. Perhaps tens of thousands in something like the SPY. Even so, that's a separate issue. All options must update as their underlying price changes.

The market and its derivatives is an intertwined being. Market makers and professional traders are constantly evaluating derivative prices and adjusting accordingly. Professional traders and experienced traders use algorithmic orders that can adjust price accordingly, if so desired. Normal people just place an order and if they are not actively monitoring and adjusting order prices, their orders get filled.

Regarding your obscure OTM option, they do not change second by second for every tick change in the price of the underlying. If a deep OTM 5 delta option trades in 5 cent increments it's going to move up 5 cents if the underlying moves up $1. Some time in the time it takes to move up that $1 the option, the option's price will tick up (the market maker adjusts his quote), assuming that buyers and sellers haven't become active in that option.

Overall, the answer is obvious. You see derivatives adjust in price every second when underlying price is moving, you know that humans can't process such changes that quickly so it's the computerization.

Answer 3

The answer is that it's not done manually.

Institutions have access to massive amounts of computation power and are consistently running algorithms that establish prices of derivative securities in a matter of milliseconds, according to well-established laws such as Black-Scholes, as well as conduct high-frequency trading of them as well. I'm not sure if recalculations are time-triggered, event-triggered, or both. But they happen often.

Incidentally, this is one of the reasons why telecommunications companies are valued so much, and why high-speed glass fiber communications, including transcontinental cables, are relevant to trading - they can send data at some large percentage of the speed of light, across oceans on the order of ~30ms.

Also remember that theoretically the price of the option increases or decreases in response to movement of the underlying in a mathematically predictable direction. Called delta. It's the partial derivative of the option with respect to a variation in the price of the underlying. These estimates provide guidance to institutions and professionals as what they should expect the price ideally does in response to market movements, and if we ignore theta decay and implied volatility for sake of simplicity, are, in response to these movements, a good approximation of what actually ends up happening to option prices.