Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

Change-point inference on volatility in noisy Itô semimartingales

This work is concerned with tests on structural breaks in the spot volatility process of a general Itô semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up on infill asymptotic results for certain functionals of spectral spot volatility estimates. A weak limit theorem is established under the null hypothesis relying on extreme value theory. We prove consistency of the test and of an associated estimator for the change point. A simulation study illustrates the finite-sample performance of the method and efficiency gains compared to a skip-sampling approach.     

Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence

Commodity futures have long been used to facilitate risk management and inventory stabilization. The study of commodity futures prices has attracted much attention in the literature because they are highly volatile and because commodities represent a large proportion of the export value in many developing countries. Previous research has found apparently contradictory findings about the presence of long memory or more generally, long-range dependence. This note investigates the nature of long-range dependence in the volatility of 14 energy and agricultural commodity futures price series using the improved Hurst coefficient (H) estimator of Abry, Teyssière and Veitch. This estimator is motivated by the ability of wavelets to detect self-similarity and also enables a test for the stability of H. The results show evidence of long-range dependence for all 14 commodities and of a non-stationary H for 9 of 14 commodities.     

Intraday volatility and network topological properties in the Korean stock market

We examine whether the relationship between market volatility and network properties in the low-frequency level can be applied to the high-frequency level. For the analysis, we use the minimum spanning tree (MST) method constructed from intraday Korean stock market data. The results show that the higher the market volatility is, the denser the MST of stocks becomes. The normalized tree length shows a strong negative relationship with market volatility, indicating that the distances between nodes are shorter when the market volatility is high. The mean occupation layer shows the tendency of having a smaller value in a higher volatility market. The maximum number of links becomes larger when the market volatility increases. All these network properties support the network being dense and shrinking in high market volatility conditions; that is, the degree of co-movement in financial market is reinforced in the intraday high-frequency level.     

Universal scaling behaviors of meteorological variables’ volatility and relations with original records

Volatility series (defined as the magnitude of the increments between successive elements) of five different meteorological variables over China are analyzed by means of detrended fluctuation analysis (DFA for short). Universal scaling behaviors are found in all volatility records, whose scaling exponents take similar distributions with similar mean values and standard deviations. To reconfirm the relation between long-range correlations in volatility and nonlinearity in original series, DFA is also applied to the magnitude records (defined as the absolute values of the original records). The results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series.     

Quasi-maximum likelihood estimation for multiple volatility shifts

We propose the Gaussian quasi-maximum likelihood estimator (QMLE) to detect and locate multiple volatility shifts. Our Gaussian QMLE is shown to be consistent under suitable conditions and the rate of convergence is provided. It is also shown that the binary segmentation procedure provides a consistent estimation for the number of volatility shifts.     

Forecasting the volatility of crude oil futures using intraday data

We use the information in intraday data to forecast the volatility of crude oil at a horizon of 1–66 days using a variety of models relying on the decomposition of realized variance in its positive or negative (semivariances) part and its continuous or discontinuous part (jumps). We show the importance of these decompositions in predictive (in-sample) regressions using a number of specifications. Nevertheless, an important empirical finding comes from an out-of-sample analysis which unambiguously shows the limited interest of considering these components. Overall, our results indicates that a simple autoregressive specification mimicking long memory and using past realized variances as predictors does not perform significantly worse than more sophisticated models which include the various components of realized variance.     

Stock price dynamics and option valuations under volatility feedback effect

According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price–dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.     

Modeling natural gas market volatility using GARCH with different distributions

In this paper, we model natural gas market volatility using GARCH-class models with long memory and fat-tail distributions. First, we forecast price volatilities of spot and futures prices. Our evidence shows that none of the models can consistently outperform others across different criteria of loss functions. We can obtain greater forecasting accuracy by taking the stylized fact of fat-tail distributions into account. Second, we forecast volatility of basis defined as the price differential between spot and futures. Our evidence shows that nonlinear GARCH-class models with asymmetric effects have the greatest forecasting accuracy. Finally, we investigate the source of forecasting loss of models. Our findings based on a detrending moving average indicate that GARCH models cannot capture multifractality in natural gas markets. This may be the plausible explanation for the source of model forecasting losses.     

Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory

Recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets, but also in emerging markets. Taking high-frequency intraday quotes of the Shanghai Stock Exchange Component (SSEC) Index as example, this paper proposes a new method to measure daily Value-at-Risk (VaR) by combining the newly introduced multifractal volatility (MFV) model and the extreme value theory (EVT) method. Two VaR backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) models. The empirical results show the multifractal nature of price volatility in Chinese stock market. VaR measures based on the multifractal volatility model and EVT method outperform many GARCH-type models at high-risk levels.