Capturing implied correlation skew from options prices via multiscale stochastic volatility models

The aim of this paper is to derive a second-order asymptotic expansion for the price of European options written on two underlying assets, whose dynamics are described by multiscale stochastic volatility models. In particular, the second-order expansion of option prices can be translated into a corresponding expansion in implied correlation units. The resulting approximation for the implied correlation curve turns out to be quadratic in the log-moneyness, capturing the convexity of the implied correlation skew. Finally, we describe a calibration procedure where the model parameters can be estimated using option prices on individual underlying assets.

Implied Correlation Index: An Application to Economic Sectors of Commodity Futures and Stock Markets

An implied correlation index (ICI) measures the average correlation between all constituents of the portfolio. The concept of the index is similar to that of the S&P500 implied correlation index, but it is based on volatility estimation instead of option-implied volatility. The objective of the study is to examine the dynamics and properties of the implied correlation estimates within various economic sectors of the stock and commodity markets. We explore three commodity futures markets: metals, energy, agriculture, and five stock markets: basic materials, financials, industrials, oil & gas and technology over the period of 2006–2017. In order to capture the dynamic character of the implied correlation we propose to take into account the GARCH type approaches to calculate volatility and Value at Risk estimates of considered assets and use them in implied correlation estimates. We also found statistical properties of the implied correlation indices. The implied correlation for most sectors is both time-varying and market-state-dependent. Assets in stock sectors are on average much more dependent than assets in commodity sectors. The implied correlation exhibits clustering properties, long memory, asymmetry and co-movement with volatility. Using the Granger causality test we showed that the impact of ICI on volatility is highly statistically significant. These results provide some useful practical implications for investors and financial institution how to estimate and control time-varying dependence between the assets in the investment portfolio.

Asymmetric Volatility Risk: Evidence from Option Markets*

Asymmetric volatility concerns the relation of returns to future expected volatility. Much is known from option prices about the marginal risk-neutral distributions (RNDs) of S&P 500 returns and of relative changes in future expected volatility (VIX). While the bivariate RND cannot be inferred from the marginals, we propose a novel identification based on long-dated index options. We estimate the risk-neutral asymmetric volatility implied correlation (AVIC) and find it to be significantly lower than its realized counterpart. We interpret the economics of the asymmetric volatility correlation risk premium and use AVIC to predict returns, volatility, and risk-neutral quantities.