Jun 28

Vasicek is a simple, handy one-factor model for interest rate process

by David Harper, CFA, FRM, CIPM

FRM |

iStock_000004837000XSmall

  • FRM AIM: "Identify and explain the steps of using a Monte Carlo simulation engine to model potential future exposure to a counterparty, and discuss considerations for applying such a model to various market instruments"

Monte Carlo simulation is the preferred way to estimate counterparty risk. This owes to differences between lending and counterparty risk (i.e., bilateral contract, unknown future exposure, netting arrangements) that make counterparty risk, in a nutshell, more complex. Monte Carlo is powerful but susceptible to serious model risk. Specifically, what "engine" will be used to model the future behavior of an instrument?

Canabarro (in the FRM assigned Measuring and marking counterparty risk) lists common stochastic processes for various instruments:

mcs_sim_engines

These are not specific, just vague categories. For equities, from Hull, we know geometric Brownian motion (GBM) is popular, which gives normal periodic returns and therefore lognormal price levels. For interest rates, there are at least three one-factor models:

  • Rendleman & Bartter: the same as GBM for stock prices. Not advisable. The key difference between equities and interest rates is mean reversion: we anticipate mean reversion in the level of rates. GBM does not do this for us.
  • Vasicek: similar to R&B above but adds mean reversion. For this reason (i.e., relatively simple but also mean-reverting), this is a handy model
  • Cox, Ingersoll, and Ross: similar to Vasicek but avoids negative rates, which aren't realistic but still possible in Vasicek.

The EditGrid below simulates Vasicek process: ten Monte Carlo trials (one per column across) and 120 time steps in the rows going down (10 years x 12 months = 120 discrete steps). The inputs in yellow; note the ‘equilibrium rate' and the ‘strength of mean reversion' conspire to pull the rate gravitationally toward 6%:

  • Initial interest rate: 6%
  • Time: 10 years
  • Strength of mean reversion: 0.10
  • Equilibrium rate: 6%
  • Volatility: 1%

Editgrid:

Comments

  1. Jayson 07 Jul 2008

    This post is helpful. Thanks for the sample.

Leave a Comment