Article Detail

Naïve Monte Carlo

Journal 36: Global Finance and Regulation

The Basel II regulatory framework has created incentives for banks to invest into their counterparty risk management infrastructure in order to obtain the internal model method (IMM) waiver from their regulators. IMM banks have the right to use expected exposure profiles produced by their Monte Carlo-based risk engines to calculate risk weighted assets (RWAs) and, therefore, regulatory capital requirements. It is generally believed that regulatory capital calculations using an IMM approach can reduce capital requirements by as much as 50% as compared to the more basic current exposure method (CEM), under which RWAs are derived from (conservative) regulatory add-ons. Basel III provided further incentives with the introduction of the new CVA capital charge [BCBS (2010)].

This explains why banks have invested resources in either building inhouse or buying ready-made Monte Carlo risk engines. However, in the pursuit of a capital saving objective, it is essential that institutions focus on in-depth model validation, particularly when third party products are involved, which tend to come as essentially black boxes with welldefined inputs and outputs but not-too-transparent internal processes. This paper focuses on just one aspect of the risk factors simulation that serves as a good illustrative example and, surprisingly, is sometimes completely neglected: quanto adjustments.

Quanto adjustment
Everyone knows what a quanto adjustment is, right? Wrong. Very often when we deal with Monte Carlo risk engines we find quanto adjustments applied to the pricing of quanto options, which you can read about in a textbook. However, we do not always find it in the place where it matters the most – in the risk factors simulation. And there is no textbook on this topic yet.

What should be done?
How does a quanto adjustment appear in risk factors simulation? Monte Carlo scenarios should be mutually consistent. Another way to say this is to demand that the probabilities assigned to all possible future market scenarios should be mutually consistent. We can achieve this by choosing a particular probability measure and simulating all risk factors under this measure.

We have a wide range of possible probability measures to choose from (actually, infinitely many) but by far the most convenient measure is the spot risk neutral measure in the base currency. The choice of measure is equivalent to the choice of numeraire, and the choice of the base currency spot risk neutral measure is equivalent to choosing the base currency money market account as a numeraire. This means that in the traditional spot risk neutral world, the prices of all traded instruments at time t divided by the base currency money market account at time t are martingales.

What are the implications for specifying risk factors’ dynamics in different currencies? Let us consider the simplest case of an asset whose price dynamics are modeled using geometric Brownian motion (GBM). Assume that the base currency is USD and the asset price, S(t), is measured in the foreign currency, e.g., EUR.