Dynamic Financial Models

A dynamic financial model can be of two types:
Discrete where time advances by chunks
        Synchronous where time advances by a fixed increment such as day or a year
        Asynchronous where time advances by a specific event therefore uneven increments of time such as buying stock or selling stock
Continuous Where changes occur over time

Introduction

In general, an option gives the holder a right, not an obligation, to sell or
buy a prescribed asset (the underlying asset) at a price determined by the
contract (the exercise or strike price). For example if you own a call option on
shares of IBM with expiry date Oct. 20, 2000 and exercise price $120, then
on October 20, 2000 you have the right to purchase a fixed number , say 100
shares of IBM at the price $120. If IBM is selling for $130 on that date, then
your option is worth $10 per share on expiry. If IBM is selling for $120 or less,
then your option is worthless.

in finance, the recognition that for all practical purposes, the prices of equities in an efficient market are random variables.
while they may show some dependence on fiscal and economic processes and policies, they have a component of randomness that makes them unpredictable.

in the simple toss of a fair coin, the result is predetermined by the force applied to the coin during and after it is tossed. In spite of this, we model it as a random variable because we have insufficient information on these forces to make a more accurate prediction of the outcome.

a precise estimate of the price of an asset one year from today is clearly impossible

This is the basic argument necessitating stochastic (Random) models in finance.

In constructing a simulation, you should be conscious of a number of distinct
steps;
1. Formulate the problem at hand. Why do we need to use simulation?
2. Set the objectives as specifically as possible. This should include what
measures on the process are of most interest.
3. Suggest candidate models. Which of these are closest to the real-world?
Which are fairly easy to write computer code for? What parameter values
are of interest?
4. If possible, collect real data and identify which of the above models is
most appropriate. Which does the best job of generating the general characteristics of the real data?
5. Implement the model. Write computer code to run simulations.
6. Verify (debug) the model. Using simple special cases, insure that the code
is doing what you think it is doing.
7. Validate the model. Ensure that it generates data with the characteristics
of the real data.
8. Determine simulation design parameters. How many simulations are to
be run and what alternatives are to be simulated?
9. Run the simulation. Collect and analyse the output.
10. Are there surprises? Do we need to change the model or the parameters?
Do we need more runs?
11. Finally we document the results and conclusions in the light of the simulation
results. Tables of numbers are to be avoided. Well-chosen graphs are
often better ways of gleaning qualitative information from a simulation.