I am trying to explain the concept of a solution to SDE being the model for the evolution of a price process. How would you do this to someone who doesn't have a financial engineering background?
Consider the following SDE: with the condition $X_0=1$,
My question is about the layperson intuition behind the usual language:
The dynamic evolution of a price process is modeled as a solution of a stochastic differential equation of the above form.
Some of the questions I have to answer in a very easy language is:
- What is SDE?
What is a solution to SDE?
What is the evolution of a price process?
Why are we modeling the evolution as a solution to SDE?
What makes such modeling a legitimate one compared to a chimpanzee throwing a dart to predict the evolutionary path of a stock?
p.s. The explanation is not to involve BM, Girsanov type tranformation, equivalent martingale measure, etc FYI. Just for a layperson.