Risk Neutral vs Real World Valuation

[Numbers]

I have some questions on this subject and some are fairly technical. I am not sure this forum is really intended for this topic,so I thought I would float this post and see if there are people very familiar with these concepts who might be able to help me work through a couple of questions I have.

I think part of the issue I am having is I may be trapped in my own faulty logic or way of looking at things.

Sample question below:

Almost every book I have read has talked about RN valuation by calculating probs that make the expected return r. I haven't found a book that says you can get the same result by using Monte Carlo simulation and Brownian motion with an adjusted mean and variance. I have done this and replicated option values. Am I missing something?

If anyone has knowledge here I would appreciate the discussion.

[The Little Giants]

Numbers, I'm not sure if you are missing something. RN valuation was specifically derived with the intent of providing a dynamic hedge, which Brownian motion could not provide. Simply adusting the mean and variance will not allow you to use the Brownian motion to achieve similar results in all equations.

Having said that, it can work and was used for quite some time. However, The RN valuation method is a much better and a much more accurate method and that is why it is more widely used.

Now, the Monte Carlo options model can also be used, but they are usually too slow to be competitive. Stick with the risk neutral valuation and you will have more success.

[Numbers]

Thanks for the reply. Since I did get a reply I will work on restating my question with a little more detail and then hopefully you can show me the error in my thinking.

Thanks again, much appreciated.

[Numbers]

Very busy week at work, I have almost formulated the question, just thought I would post to let you know I am still interested in learning about this.