Valuation of Variance Forecast with Simulated Option Markets

An appropriate metric for the success of an algorithm to forecast the variance of the rate of return on a capital asset could be the incremental profit from substituting it for the next best alternative. We propose a framework to assess incremental profits for competing algorithms to forecast the variance of a prespecified asset. The test is based on the return history of the asset in question. A hypothetical insurance market is set up, where competing forecasting algorithms are used. One algorithm is used by each hypothetical agent in an "ex post ante" forecasting exercise, using the available history of the asset returns. The profit differentials across agents (in various groupings) reflect incremental values of the forecasting algorithms.

The technique is demonstrated with the NYSE portfolio, over the period of July 22, 1966 to December 31, 1985. For the limited set of alternative specifications, we find that GARCH(1,1) yields better profits than the 3 competing specifications. The profit from pricing one-day options on the NYSE portfolio significant. The evidence also suggests that using a limited estimation period may be preferable to estimating specification parameters from all available observations. Finally, the hedging activity that requires a variance determined hedge ratio is an important component of the success of a variance forecast-algorithm.