Asset prices integral

The standard Wiener process is a close approximation of the behaviour of asset prices but does not account for some specific aspects of market behaviour. In the first instance, the prices of financial assets do not start at zero, and their price increments have positive mean. The variance of asset price moves is also not always unity. Therefore, the standard Wiener process is replaced by the generalised Wiener process, which describes a variable that may start at something other than zero, and also has incremental changes that have a mean other than zero as well as variances that are not unity. The mean and variance are still constant in a generalised process, which is the same as the standard process, and a different description must be used to describe processes that have variances that differ over time these are known as stochastic integrals (Figure 2.3). 

By applying Ito calculus, i.e., Ito s lemma, (4.17) can be transformed to solve for the price of an asset. Taking the integral of expression (4.17) results in equation (4.18), which derives the forward rate,... 

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