What Is Stochastic Modeling? Stochastic modeling is one of the widely used models in quantitative finance. As it helps forecast the probability of various outcomes under different scenarios where randomness or uncertainty exists. There are two very important concepts that help understand the stochastic models and they are Markov Chain and Brownian Motion.
The Markov Chain is a fundamental part of a stochastic process. One in which the Markov property must be satisfied. This means that the future state only depends on the current state and is independent of the past. And this is a very useful reduction of the various parameters in stochastic modeling.
In addition, the other very important concept is Brownian Motion, which is a continuous stochastic process for random behavior, and mostly used in pricing an asset in which the volatility is inherent. Furthermore, geometric Brownian Motion is the foundation when modeling stock prices in the Black-Scholes model.
The opposite of the stochastic model is the deterministic model. One where it would provide the exact same result even with numerous computations. In order to satisfy the conditions of the deterministic model. As a result, the variables cannot be random. But must be known, and thus the uncertain factors are excluded from the model. Unlike the deterministic models, stochastic models account for uncertain factors in the model. And the model produces numerous outcomes under various scenarios.
Thus, stochastic models, widely used in the financial industry to manage assets and liabilities with lots of uncertainties. And to optimize their portfolios with random variation of future payments or cash flows. For instance, an investment bank or an asset management firm might have interest in the analysis of how a portfolio performs during a certain period of market when there is a high volatility.
Using a stochastic model can be useful to predict probabilities of each outcome under such circumstances. In fact, in the real world of investing, it would be impossible to eradicate any random variables that come with great uncertainty.
However, a stochastic model is useful in a way that it allows for randomness in the model to estimate the probability of various outcomes. Further study of stochastic modeling is the Monte Carlo simulation. Where it can simulate how a portfolio may perform based on the probability distributions of individual stock returns.