Background: For a dissertation I have a multi-agent stock market model that I am using to assess different mechanisms for producing particular dynamic regimes. A key point is assessing how closely it reflects the real world, this will be done by comparing it with historical price data of 5 large-caps in 5 different sectorsn where the model simulates trading for 1 month.
I would like to be able to say "this is x% accurate/good" etc. I hope to do this using a measure of volatility ("the standard deviation of the instrument's yearly logarithmic returns.")
My question is what should the function I use consist of? I believe an 'excellent' model produces prices that are no more or less volatile than the stock is, but they shouldn't go in opposite directions to the 'real' prices. So clearly the model needs to produce prices that are in line with the actual prices, with it expected to have greater deviations 30 days into the simulation compared to 1.
So I believe the function for the 'fitness' of the model needs to use volatility and an exponential average or somesuch? How best do I combine these two... or perhaps there are better ways of doing this?
Any help most appreciated!