Various model of stock price

[timlee]

1. I was wonderingwhat kinds of stock price can be modeled as a Geometric Brownian motion as in Black Schole model?
2. Can the above model be used to model jump?
3. I also very much appreciate some references that discuss various models of stock prices and in which cases to use which model.

Thanks in advance!

 

[Darou]

Hi timlee,

the most important stock price processes for option pricing are Geometric Brownian Motion, Jump Diffusion which can model jumps and Heston, which has a time dependent process for volatility. For risk management, people often use GARCH, a process which can meet the statistical properties of historical stock prices very well. But, GARCH cannot easily be used for option valuation.

I hope, this helps!

-- Darou

 

[amanda.jayne]

1. I was wonderingwhat kinds of stock price can be modeled as a Geometric Brownian motion as in Black Schole model?

On a long horizon timescale with reasonable accuracy, none that come to mind.

You could try a broad market index or ETF, perhaps?

The stock market is significantly more irrational than options or fixed income markets whose instruments have a more deterministic price that they tend to trade towards.

1. Can the above model be used to model jump?

Doubtful. Fundamental analysis may serve you better for this purpose

1. I also very much appreciate some references that discuss various models of stock prices and in which cases to use which model.

There are a number of papers written about (and arguments posed regarding) using such techniques on stocks.