Monte carlo methods

[welsh_owen]

Hi All,

In chapter 10 of the notes different Numerical methods are considered for valuing derivatives.

For the section which looks at Monte Carlo simulation I wondered why it is necessary to build a quadratic function to estimate Vi (the present value of the derivative assuming this is not exercised)?

I think I might have missed something but to my mind would it not be easier to evaluate the actual difference between Vi and the intrinsic value of the derivative assuming it were exercised at this point?

Cheers
Owen

 

[David Hopkins]

Hi Owen

The problem is that you don't know the actual value of Vi at each point in the future. All you know is that for this particular run the final payoff was some amount, but this includes a large random component depending on how the asset price moved after this point in this particular run.

So the idea of the LS method is that you can try to average out some of this random component by fitting a least-squares formula to all the discounted payoffs at that time point and then assume that this will be close enough to the true value.

If you look at the solution to Sep09 Q5 in ASET, you can see how the method works.

David

 

[welsh_owen]

Thanks David,

That's great. I (think I) understand how to calculate this method. Just wanted to clarify why it was needed. The need to reduce the randomness associated with each run makes sense.

Thank-you for clarifying
O.