**Appendix D Chapter 6
Technical Topic:** **Stock
Price Dynamics**

**D.1 Stock Price
Dynamics: Certainty Model
**

A |

ssume that the
stock price *S* grows at the
continuously compounded rate *r* in a market with no uncertainty.
The equation describing this growth has the following form:

If
you differentiate this with respect to *t*,
you get

Thus,
the certainty model assumes that the rate of change of the stock price through
time is a constant proportion of the current stock price.

This
expression describes the **dynamic stock
price process** in a world with certainty.
Multiplying both sides by dt and rearranging,
we can rewrite the equation as:

In this form, the *instantaneous
rate of return* on the stock is *r*. Here, *r* is also
called the *drift rate* of the stock
price process. In the
technical topic __Ito Processes__, the dynamic
stock price process presented in this current topic is extended to a world with
uncertainty. In this extension, a
constant volatility term is added so that the price process is assumed to follow
a specific type of diffusion process.