Performance of Asset Martingale Tests: Bond Portfolios and Equity Indices
Document ID: 2008-96 (previously S2007/008)
Published on: 1st July 2008
Author: Colin Holmes, David Roseburgh
The concept of the 'risk-neutral' world is a useful tool in the no-arbitrage pricing of assets. In this world, investors require no compensation for risk - loosely speaking, the (expected) return of any asset must equal the risk free rate. A more rigorous definition is that the stochastic process followed by any asset value, divided by the risk-free cash account (or "roll-up"), must be a martingale in the risk-neutral world - its expected value at any point in the future is equal to its present value. All models used within the B&H ESG are arbitrage free and accordingly all modelled assets should pass the martingale test. However, in nearly all cases approximations are made in the implementation of the models, and this note examines the effect of these approximations on tests of the martingale property for bond and equity assets.
