A Bidimensional Markov-Modulated Poisson Process is a stochastic model utilized for describing event occurrences in two distinct, yet correlated, dimensions, where the underlying rates of these events are modulated by an unobservable, finite-state Markov chain. This model finds application in accurately capturing complex dynamics within crypto market data streams.
Mechanism
The process operates by transitioning between a discrete set of states, dictated by the Markov chain’s probabilities. Each state corresponds to specific intensity parameters for two independent Poisson processes, which then generate events like trade arrivals or order book changes. This structure allows for a time-varying, state-dependent modeling of event rates.
Methodology
Implementing this model requires employing advanced statistical inference techniques, such as the Expectation-Maximization algorithm, to estimate the hidden Markov chain parameters and the associated Poisson rates from observed bivariate data. This analytical framework enables a more nuanced understanding of correlated event clusters and their impact on liquidity and volatility in crypto institutional options trading.
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