It would take me at least 3 seconds to modify an existing order. When stock price rises or falls quickly, how do buyers and sellers change their prices so quickly?
Do they really calculate option value using Delta/Gamma/Vega/Theta before they adjust their bid/ask?
If option premium value changes based on stock price and the Greeks, where do they reflect?
In an illiquid market, the market maker sets the prices. His computerized programs will automatically adjust the options price when the underlying changes enough to warrant a change in the price of the option (delta of option times the underlying's price change).
In a liquid market where market participants are the market, there are various types of algorithmic orders in play. Similarly, they automatically adjust order price as well. Some of these might be:
Conditional orders
Volatility orders
Various pegged orders
One type of pegged order would be the Pegged-to-Stock Order. Like the market maker explanation above, it continuously adjusts the price of the option order by the product of a user defined delta and the change of the option's underlying stock price.
Your broker must offer such order algorithms in order to be able to utilize them.
