Quoting Multiasset Equity Options in the Presence of Errors from Estimating Correlations

Abstract

Anyone using an option valuation model needs estimates of returns volatility. But volatility has been found to be hard to forecast accurately, partly because it varies randomly over time. Fortunately, the market provides a directly observable volatility estimate in the form of the implied volatility that can be backed out from an option’s market price. But for several increasingly popular types of options, the payoff distribution depends both on stock volatilities and also on the correlations among them. For such options, including basket options and options on the max or on the min, there are no dependable sources of implied correlations to use in pricing them. Correlations must be estimated from historical data, which leads to substantial estimation risk. In this article, Fengler and Schwendner describe a block bootstrap procedure that allows an investor to evaluate a multiasset option’s exposure to parameter risk from imperfectly estimated correlations. The results are translated into minimum bid-ask spreads that are required to account for this additional source of risk.