Monte Carlo Process Simulator

Overview

Credit Monte Carlo computes the risk due to default for a set of instruments by Simulating the default of those instruments a large number of times and measuring the resulting distribution.

Simulation Runner

The monte carlo in this section utilizes the following simulation runner.

def simulate(iterations, items, simulate_item, dates = None, process=None, context=None): if process == None: process = lambda x,y:x for i in range(iterations): citems = [item.copy() for item in items] iteration = [] contexts = [] idates = [{}] idates = dates if dates != None else [{}] for date in idates: date_simulation = [] if context!= None: context1 = context(date, contexts) if context1 != None: contexts.append(context1) for index, item in enumerate(citems): sim = simulate_item(item, contexts, date) if sim != None and isinstance(date, str): date_simulation.append({"simulation":sim, "item":item, "date":date}) elif sim != None: date_simulation.append({"simulation":sim, "item":item}) pass iteration.append(process(date_simulation, contexts)) pass yield iteration pass pass

The runner iterates through the number of iterations. For each date in the list of dates (this doesnt have to actually be a date, it can be any id for the given period), and for each item in the inputted items (for the credit application, each item is a loan record) it calls the simulate_itemmethod. The simulate_item method should run a single simulation for the inputted item and return a result. If the result is not None, then it is collected in an array, and that array is passed to the next call to simulate_item for that item.

Simulate One Period

When the simulate_item method is called, it is passed four arguments.

  • item - the record of the item (loan) being simulated
  • simulation - for each item, a list of simulation results is retained. It collects the results of each call to simulate_item. This list is passed to each call to simulate_item. This means that each simulation can maintain a history for each item, so that the simulation can have path dependencies
  • date - the id of the period being simulated
  • contexts - if a context function is passed into the simulation, the for each date in the iteration, the context function is called and the results saved in a contextts list. This list is then passed to simulate_item method and can be used in the simulation.

    Contexts are simulated objects that may affect an outcome, but is not specific to a particular loan. So for instance, you can simulate the interest rate curve, and this could a context that is passed into the simulate_item method for each loan, which may determine its probability of default based on the current curve.

Process Function

After each simulation, the process function is called to process the simulation before adding the results to the simulation. This is just a utility function that is used to extract the pertinent information that needs to be saved from each simulation, without having to change the function doing the simulating.

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