Markov Processes

A Markov process is a stochastic process where the future state of a system depends only on its current state and not on the sequence of events that preceded it. This property, known as the Markov property, simplifies the modeling of financial time series by assuming that past price data does not influence future probabilities.

Many derivative pricing models rely on this assumption to facilitate calculations of future expected values. However, some market participants argue that financial markets exhibit memory, suggesting that Markovian assumptions may not always hold true.

Understanding this concept is essential for building models that predict price transitions in order books and liquidity pools.