Chapter 1: Financial Models
The movement of financial assets and products generally displays some type of expected return, even over a short period. This expected return trends at a predictable rate that may be positive, indicating growth; negative, indicating a decline; or zero. Additionally, there are random movements that are individually unpredictable; however, the general distribution of these fluctuations is predictable based on historical movements. The common approach to model randomness is to assume a single- or multi-component Gaussian process. The generalized format to describe a time-dependent stochastic process is
where the drift and volatility are functions of time and asset price , and is a Wiener process. If the drift and volatility are constants, then ...