## QUANT: Important Stochastic Processes

#### Geometric Brownian Motion

- It’s SDE is:
or also as

- Solution:

#### Ornstein-Uhlenbeck Process (aka Vasicek Model)

- It is a Mean-Reverting Process, although random, shows a pronounced tendency toward an equilibrium value.
- It’s SDE is:
– long term mean/equilibrium value/mean value

– volatility to model random shocks

– rate by which the shocks dissipate and variable returns towards equilibrium mean - Solution for this SDE is:
- Useful for modeling interest rates, currency exchange rates, and commodity prices

#### Bessel Process

- Stochastic Differential Equation:

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