Appendix D Chapter 6
Technical Topic: Stock
Price Dynamics
Appendix D Chapter 6
Technical Topic: Stock
Price Dynamics
D.1 Stock Price
Dynamics: Certainty Model
Assume
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.