A question often asked is the best way to deal with modelling dependencies in risk models. The topic is in fact incredibly rich; in this post, we just recap some of the basic elements that apply in many simple cases.
Where two items vary in similar ways due to an external (non-modelled) factor, the use of correlation (correlated sampling) is a common method. This generally allows the relationship between multiple items to be captured, where each varies partially according to some exogenous factor (e.g. the inflation rate may affect several items, even if inflation were not explicitly modelled).
Another form of dependency is parametric dependency, for example where a stochastic variable (call it V2) is partially determined from the value of another stochastic variable (call it V1). This can be thought of as a one-way partial causality. For example, V2 could be a heads/tails process, whose probabilities depend on the outcome of V1, with the parameter (probability of a head) for V2, such as P(Heads for V2)=0.7 if V1=heads, 0.2 if V1 = tails; P(Tails for V2)=1-P(Heads for V2) in each case). Another example could be that the oil price (V1) is random, but the value of a processed industrial chemical (V2) is a random process whose average or most likely value depends on V1 e.g. V2 could be a normal distribution N(mu, sigma), where sigma is its volatility, but is average (mu) is determined (at each iteration of a simulation) from the sampled value of V1.
Similar examples are discussed in more detail in the book Business Risk and Simulation Modelling using Excel, VBA and @RISK. Chapter 7 of the book also discusses dependency modelling using scenarios, categories, and variations of these.
In addition to these basic methods, there are of course many other possibilities. For example, copulas are essentially a more generalised form of correlation (as they determined how distributions are jointly sampled), with co-integration and time series models being other variations. These latter approaches are all more challenging (than correlation or parameter dependency) from an intuitive/pragmatic (and mathematical) perspective, but of course add to the accuracy of some types of models.