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The purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance.

The authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums.

There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity.

Commodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced.

The empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.

This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.

This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.

The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.

The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.

This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

This study examines whether the variance risk is a priced risk factor in Korea using the over-the-counter variance swap quotes and realized variance data. We also study the term structure of variance risk premium. The empirical results show that the model with 2 stochastic variance risk factors with jumps in return is required to fit the variance swap and realized variance data. The analyses with the estimated models suggest that the variance risk premium in Korea are highly negative and the size of the premium increase with the maturities, meaning that risk averse investors in Korea are willing to pay a premium to hedge variance risk.

In asset management, what if clients want to purchase protection from risk factors, under the form of variance risk premia. This paper aims to address this topic by developing a portfolio optimization framework based on the criterion of the minimum variance risk premium (VRP) for any investor selecting stocks with an expected target return while minimizing the risk aversion associated to the portfolio according to “good” and “bad” times.

To accomplish this portfolio selection problem, the authors compute variance risk-premium as the difference from high-frequencies' realized volatility and options' implied volatility stemming from 19 stock markets, estimate a 2-state Markov-switching model on the variance risk-premia and optimize variance risk-premia portfolios across non-overlapping regions. The period goes from March 16, 2011, to March 28, 2018.

The authors find that optimized portfolios based on variance-covariance matrices stemming from VRP do not consistently outperform the benchmark based on daily returns. Several robustness checks are investigated by minimizing historical, realized or implicit variances, with/without regime switching. In a boundary case, accounting for the realized variance risk factor in portfolio decisions can be seen as a promising alternative from a portfolio performance perspective.

As a new management “style”, the realized volatility approach can, therefore, bring incremental value to construct the conditional covariance matrix estimates.

The authors assess the portfolio performance determined by the variance-covariance matrices that are derived by four models: “naive” (Markowitz returns benchmark), non-switching VRP, maximum likelihood regime-switching VRP and Bayesian regime switching VRP. The authors examine the best return-risk combination through the calculation of the Sharpe ratio. They also assess another different portfolio strategy: the risk parity approach.

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

The purpose of this paper is to consider that the model of volatility characteristics is more reasonable and the description of volatility is more explanatory.

This paper analyzes the basic characteristics of market yield volatility based on the five-minute trading data of the Chinese CSI300 stock index futures from 2012 to 2017 by Hurst index and GPH test, A-J and J-O Jumping test and Realized-EGARCH model, respectively. The results show that the yield fluctuation rate of CSI300 stock index futures market has obvious non-linear characteristics including long memory, jumpy and asymmetry.

This paper finds that the LHAR-RV-CJ model has a better prediction effect on the volatility of CSI300 stock index futures. The research shows that CSI300 stock index futures market is heterogeneous, means that long-term investors are focused on long-term market fluctuations rather than short-term fluctuations; the influence of the short-term jumping component on the market volatility is limited, and the long jump has a greater negative influence on market fluctuation; the negative impact of long-period yield is limited to short-term market fluctuation, while, with the period extending, the negative influence of long-period impact is gradually increased.

This paper has research limitations in variable measurement and data selection.

This study is based on the high-frequency data or the application number of financial modeling analysis, especially in the study of asset price volatility. It makes full use of all kinds of information contained in high-frequency data, compared to low-frequency data such as day, weekly or monthly data. High-frequency data can be more accurate, better guide financial asset pricing and risk management, and result in effective configuration.

The existing research on the futures market volatility of high frequency data, mainly focus on single feature analysis, and the comprehensive comparative analysis on the volatility characteristics of study is less, at the same time in setting up the model for the forecast of volatility, based on the model research on the basic characteristics is less, so the construction of a model is relatively subjective, in this paper, considering the fluctuation characteristics of the model is more reasonable, characterization of volatility will also be more explanatory power. The difference between this paper and the existing literature lies in that this paper establishes a prediction model based on the basic characteristics of market return volatility, and conducts a description and prediction study on volatility.

This paper aims to enhance a co-skew-based risk measurement methodology initially introduced in Polimenis, by extending it for the joint estimation of the jump betas for two stocks.

The authors introduce the possibility of idiosyncratic jumps and analyze the robustness of the estimated sensitivities when two stocks are jointly fit to the same set of latent jump factors. When individual stock skews substantially differ from those of the market, the requirement that the individual skew is exactly matched is placing a strain on the single stock estimation system.

The authors argue that, once the authors relax this restrictive requirement in an enhanced joint framework, the system calibrates to a more robust solution in terms of uncovering the true magnitude of the latent parameters of the model, at the same time revealing information about the level of idiosyncratic skews in individual stock return distributions.

Allowing for idiosyncratic skews relaxes the demands placed on the estimation system and hence improves its explanatory power by focusing on matching systematic skew that is more informational. Furthermore, allowing for stock-specific jumps that are not related to the market is a realistic assumption. There is now evidence that idiosyncratic risks are priced as well, and this has been a major drawback and criticism in using CAPM to assess risk premia.

Since jumps in stock prices incorporate the most valuable information, then quantifying a stock's exposure to jump events can have important practical implications for financial risk management, portfolio construction and option pricing.

This approach boosts the “signal-to-noise” ratio by utilizing co-skew moments, so that the diffusive component is filtered out through higher-order cumulants. Without making any distributional assumptions, the authors are able not only to capture the asymmetric sensitivity of a stock to latent upward and downward systematic jump risks, but also to uncover the magnitude of idiosyncratic stock skewness. Since cumulants in a Levy process evolve linearly in time, this approach is horizon independent and hence can be deployed at all frequencies.

The purpose of this paper is to investigate volatility spillovers across the interest rate swap markets of the G7 economies, and then the authors investigate whether spillovers of swap markets contain useful information to explain subsequent stock price movements.

This study uses the short- and long-term swap spread volatility of the G7 countries to explore the spillover effects of international swap markets, and then investigates the relationship between swap and stock markets. The authors use the generalized VAR approach suggested by Diebold and Yilmaz (2012) to study spillovers of international swap markets. The Granger-causality tests are employed to examine the linkage of interest rate swap and stock markets.

This paper shows that a moderate spillover effect exists for the short- and long-term swap markets. Moreover, the results show that the short- and long-term swap markets of France and Germany have a larger impact on other countries’ swap markets than that of other countries’ swap markets on the French and German swap markets. Finally, the results indicate that the total volatility spillovers for the long-term swap markets have a larger influence on the total volatility spillover index of stock markets and the global stock market volatility than that of the short-term swap markets.

Prior literature has used impulse response and variance decomposition analyses to investigate international swap markets linkages. However, the results depend on the ordering of variables. This study uses the framework of Diebold and Yilmaz (2012) to overcome the ordering issue, and thus the authors can compute directional spillovers. This paper is the first study to explore the linkage of the total volatility spillover of swap markets and the stock markets.