Markov Chain Monte Carlo

Markov Chain Monte Carlo is a class of algorithms used for sampling from probability distributions when direct sampling is difficult. In quantitative finance, it is extensively used to estimate the parameters of complex models, such as those involving regime switching or non-linear dependencies.

By constructing a Markov chain that has the desired distribution as its equilibrium distribution, the algorithm allows researchers to simulate and understand the behavior of financial models. This is critical for Bayesian inference in risk management, where one needs to estimate the probability distribution of future asset returns given current market conditions.

It enables the evaluation of high-dimensional models that would otherwise be computationally intractable. For crypto derivatives, it helps in pricing complex instruments where closed-form solutions do not exist.

It is a cornerstone of modern computational finance and risk modeling.