Spread options and risk management

Lognormal versus normal distribution approach

Abstract

We provide better tools for managing the downside risk related to the spread between the asset portfolio and corresponding liabilities. These tools are particularly applicable for individual investors. We investigate the spread option valuation model where both underlying instruments follow geometric Brownian motion, and one where both underlying instruments are assumed to follow arithmetic Brownian motion. We show that the risk parameters are often materially different. These results are important in practical applications of risk management for individual investors as well as financial institutions. For most personal financial planning applications, one can safely use the simpler arithmetic Brownian motion model.