A framework for robust measurement of implied correlation

Abstract

In this paper we consider the problem of deriving correlation estimates from observed option data. An implied correlation estimate arises when we match the observed index option price with a corresponding model price. The underlying model assumes that stock prices can be described using a lognormal distribution, while a Gaussian copula describes the dependence structure. Within this multivariate stock price model, the index option price is not given in a closed form and has to be approximated. Different methods exist and each choice leads to another implied correlation estimate.We show that the traditional approach for determining implied correlations is a member of our more general framework. It turns out that the traditional implied correlation underestimates the real correlation. This error is more pronounced when some stock volatilities are large compared to the other volatility levels. We propose a new approach to measure implied correlation which does not have this drawback. However, our numerical illustrations show that determining implied correlations with the traditional approach may be justified for strike prices which are close to the at-the-money strike price.We also show that implied correlation estimates can be used to define an index, called the Implied Correlation Index (ICX), which reflects the market’s perception about future (short-term) co-movement between stock prices. Using a volatility index together with the ICX gives an accurate description of the current level of market fear.