Mixture of Models: A Simple Recipe for a ... Hangover?

Abstract:     
The idea of using a weighted average of derivative security prices computed using di?erent "simple" models (the so-called "mixture of models", or "ensemble of models", approach) has been put forth recently by a number of authors. Some view it as a simple way to add stochastic volatility to virtually any model, and others advocate it on the grounds that it provides a simple and tractable method for capturing certain market characteristics, most importantly volatility smile. Ease of calibration to market prices of vanilla and exotic instruments is also cited as the approach's redeeming quality. While not disputing the fact that such "models" are easy to calibrate, we explain that these models are under-specified (leading to multiple possible prices of derivatives). We also demonstrate that the "weighted average" valuation formula, the main selling point of the "mixture of models" approach, is self-inconsistent and cannot be used for valuation.

Keywords: Mixtures of models, model ensembles, stochastic volatility, lognormal mixture

Working Paper Series