CP1 - Stochastic Models

[RedCoat]

Hello! I think I must be misunderstanding something about stochastic models/variables in the context of CP1. It seems that in multiple places throughout the notes it is said that stochastic models with more than one stochastic variable are impractical, e.g.

Chapter 28 page 9
"the run times that result from having more than one, or possibly two, variables simulated by stochastic methods become impractical with even the most modern computing power."

Chapter 28 page 21
"As discussed in the earlier chapter on Modelling, a stochastic model with more than two stochastic variables will be impractical to run."

I work in capital modelling and it is common for our models to have multiple variables that I would consider to be stochastic, e.g. losses being drawn from distributions for multiple lines of business (distributions with fixed parameters, is that where I'm getting confused?), currency risk severities being sampled from a distribution, similar for claims inflation etc. etc. These models are pretty standard across the industry and certainly don't take long to run even without "the most modern computing power". So I feel like I must be getting confused about what the core reading is referring to, any help is much appreciated!

 

[Dar_Shan0209]

Hi,
I guess what the course notes is saying that from an insurer perspective (or even company!), the less number of stochastic variables you use, the faster and easier it becomes to model. For example, consider a simple asset model that you would want to construct. There are various features that you would need to take into consideration:

• Time horizon used for projecting cashflows
• Time-frequency used for projecting cashflows
• Number of runs required for the purpose
• The frequency with which the model is run

Now, you would need to model the asset prices, returns, setting capital requirements and several other parameters (inflation and so on). You might realise that you prefer to model returns using a stochastic distribution rather than making all parameters stochastic such as say, inflation.

The overarching principle is that a balance to be struck between realism (and hence complexity) and simplicity (for ease of application, verification and interpretation of results). The greater the functionality required by the model, the more complex it becomes which conflicts with objectives of parsimony, the model will be harder to use and maintain and the results will be more complex to interpret and communicate.

Say, if you are to run, say 10 000 simulations for this model, you would agree that some time is required assuming a full-fledged asset model. The more variables that you would model stochastically, the more time it will take and not to forget the capacity of the computer, power considerations all that comes into play (bearing into mind that not everyone will be able to afford all those)...

Hope this helps!

 

[RedCoat]

Thanks very much for the detailed response Darshan. I think I am comfortable with the concept of more stochastic variables leading to more complexity, longer running times etc. Just not sure why the Core Reading seems to think so strongly that anything more than 1 or 2 variables is completely impractical! I think I'll just have to accept it though.