Chapter 1: Financial Models
1.1 Introduction
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 ...
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