Narrow Results

We propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index.

This paper examines the predicting power of the volatility indexes of VIX and VHSI on the future volatilities (or called realized volatility, ${\sigma }_{30,r})$ of their respective underlying indexes of S&P500 Index, SPX and Hang Seng Index, HSI. It is found that volatilities indexes of VIX and VHSI, on average, are numerically greater than the realized volatilities of SPX and HSI, respectively. Further analysis indicates that realized volatility, if used for pricing options, would, on some occasions, result in greatest losses of 2.21% and 1.91% of the spot price of SPX and HSI, respectively while the greatest profits are 2.56% and 2.93% of the spot price of SPX and HSI, respectively, making it not an ideal benchmark for validating volatility forecasting techniques in relation to option pricing. Hence, a new benchmark (fair volatility, ${\sigma }_f)$ that considers the premium of option and the cost of dynamic hedging the position is proposed accordingly. It reveals that, on average, options priced by volatility indexes contain a risk premium demanded by the option sellers. However, the options could, on some occasions, result in greatest losses of 4.85% and 3.60% of the spot price of SPX and HSI, respectively while the greatest profits are 4.60% and 5.49% of the spot price of SPX and HSI, respectively. Nevertheless, it can still be a valuable tool for risk management. $z$-values of various significance levels for value-at-risk and conditional value-at-value have been statistically determined for US, Hong Kong, Australia, India, Japan and Korea markets.

This paper proposes a method that uses volatility index of US and six other markets of Pacific Basin, namely Hong Kong, Australia, India, Japan, Korea, and China, to provide value-at-risk (VaR) and expected shortfall (ES) forecasts. Empirical constants that are used to multiply the levels of volatility indexes for estimating VaR and ES of various significance levels for 1–22 days ahead, one by one, for seven market indexes have been statistically determined using daily data spanning from 4.75 to 16 years. It is because it would be inappropriate to simply scale up the one-day volatility by multiplying the square root of time (or the number of days) ahead to determine the risk over a longer horizon of $i$ days. Results show that the shift to ES approach generally increases the regulatory capital requirements from 2.09% of India market to 8.56% of Korea market except for the China market where ES approach yields an unexpected decrease of 3.21% of capital requirement.

The aim of this paper is to comprehensively compare option-based measures of volatility, with the ultimate plan of devising a new volatility index for the Italian stock market. The performance of the different implied volatility measures in forecasting future volatility is evaluated both in a statistical and in an economic setting. The properties of the implied volatility measures are also explored, by looking at both the contemporaneous relationship between implied volatility changes and market returns and the usefulness of the proposed index in forecasting future market returns.

The results of the paper are of practical importance for both policy-makers and investors. The volatility index, based on corridor measures, could be used to forecast market volatility, for value at risk purposes, in order to determine trading strategies on the underlying index and as an early warning for future market conditions.

This paper focuses on the 2008–2020 period during which two major crises, affecting the economy and the financial markets, occurred. Between 2008 and 2020, there were less extreme tail events, including the lingering Eurozone and Greece crises. In particular, after extremely high stock market volatility and volatility of volatility (VoV) during 2008, the long-run average volatility declined to about 20% and the VoV to around 100%. This paper analyzes this period through the lens of risk and ambiguity (uncertainty). It aims to address the question: what are the financial markets that trade risk — the volatility derivatives markets — telling us? To this end, this paper uses several measures of uncertainty. It reviews the history of volatility and uncertainty measures and discusses their informativeness. It then discusses the information derived from volatility derivatives.

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial "dynamically purified" price process that in theory allows to eliminate the impact of the stock price movements. The complete elimination would be possible if the option prices were available for continuous sets of strike prices and expiration times. In practice, we have to use only finite sets of available prices. We discuss the construction of this process from the available option prices using different methods. In order to overcome the incompleteness of the available option prices, we suggests several interpolation approaches, including the first order Taylor series extrapolation and quadratic interpolation. We examine the potential of the implied volatility derived from this proposed process for forecasting of the future volatility, in comparison with the traditional implied volatility process such as the volatility index VIX.