Abstract
The dynamics of asset price processes in discrete time increments are typically described by two kinds of models: trees (lattices) and random walks. Arithmetic, geometric, and mean reverting random walks are examples of the latter type of models. When the time increment used to model the asset price dynamics becomes infinitely small, we talk about stochastic processes in continuous time. Models for asset price dynamics can incorporate different observed characteristics of an asset price process, such as a drift or a reversion to a mean, and are important building blocks for risk management and financial derivative pricing models.
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