Time Diffussion

[MUSIC]

Welcome.

This is a

background

class on stochastic differential

equations, continuous time mathematics.

This is very useful in asset pricing.

It's a branch

of math that seems formidable.

But, in fact, the basic tools you need are

pretty simple.

And that's what we'll go over.

I assume that you've read the notes.

And many of the derivations are in the

notes.

If you feel like you're not following the

algebra.

Stop, go over how the algebra works.

Diffusion models, that's what we call the

kind of model we're looking at.

Why?

This is what a stock price typically looks

like.

Stock prices go up and down and they

jiggle a lot.

They're random.

We don't know what they're going to be.

We need a convenient mathematical model

for something that's random, that

we don't know exactly where it's going to

go in the future.

I'm going to base this off of discrete

time.

So I assume you're familiar with discrete

time difference equations.

So let me remind you the kinds of things

you know how to do.

In discrete time, we build up processes

for something like a stock price.

We start with a building block, epsilon,

iid.

I'll make them normal, they don't have to

be,

will be in continuous time, mean zero unit

variance.

That's our building block.

It's