Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Essays on Risk Modeling. Applications to Portfolio and Risk Management (summary section only)

In this thesis we deal with the concept of risk. The objective is to bring together and conclude on some normative information regarding quantitative portfolio management and risk assessment. The first essay concentrates on return dependency. We propose an algorithm for classifying markets into rising and falling. Given the algorithm, we derive a statistic: the Trend Switch Probability, for detection of long-term return dependency in the first moment. The empirical results suggest that the Trend Switch Probability is robust over various volatility specifications. The serial dependency in bear and bull markets behaves however differently. It is strongly positive in rising market whereas in bear markets it is closer to a random walk. Realized volatility, a technique for estimating volatility from high frequency data, is investigated in essays two and three. In the second essay we find, when measuring realized variance on a set of German stocks, that the second moment dependency structure is highly unstable and changes randomly. Results also suggest that volatility is non-stationary from time to time. In the third essay we examine the impact from market microstructure on the error between estimated realized volatility and the volatility of the underlying process. With simulation-based techniques we show that autocorrelation in returns leads to biased variance estimates and that lower sampling frequency and non-constant volatility increases the error variation between the estimated variance and the variance of the underlying process. From these essays we can conclude that volatility is not easily estimated, even from high frequency data. It is neither very well behaved in terms of stability nor dependency over time. Based on these observations, we would recommend the use of simple, transparent methods that are likely to be more robust over differing volatility regimes than models with a complex parameter universe. In analyzing long-term return dependency in the first moment we find that the Trend Switch Probability is a robust estimator. This is an interesting area for further research, with important implications for active asset allocation.

Modeling Nonlinearities and Asymmetries in Asset Pricing

Financial time series tend to behave in a manner that is not directly drawn from a normal distribution. Asymmetries and nonlinearities are usually seen and these characteristics need to be taken into account. To make forecasts and predictions of future return and risk is rather complicated. The existing models for predicting risk are of help to a certain degree, but the complexity in financial time series data makes it difficult. The introduction of nonlinearities and asymmetries for the purpose of better models and forecasts regarding both mean and variance is supported by the essays in this dissertation. Linear and nonlinear models are consequently introduced in this dissertation. The advantages of nonlinear models are that they can take into account asymmetries. Asymmetric patterns usually mean that large negative returns appear more often than positive returns of the same magnitude. This goes hand in hand with the fact that negative returns are associated with higher risk than in the case where positive returns of the same magnitude are observed. The reason why these models are of high importance lies in the ability to make the best possible estimations and predictions of future returns and for predicting risk.

Examining and Modeling the Dynamics of the Volatility Surface

The objective of this paper is to investigate and model the characteristics of the prevailing volatility smiles and surfaces on the DAX- and ESX-index options markets. Continuing on the trend of Implied Volatility Functions, the Standardized Log-Moneyness model is introduced and fitted to historical data. The model replaces the constant volatility parameter of the Black & Scholes pricing model with a matrix of volatilities with respect to moneyness and maturity and is tested out-of-sample. Considering the dynamics, the results show support for the hypotheses put forward in this study, implying that the smile increases in magnitude when maturity and ATM volatility decreases and that there is a negative/positive correlation between a change in the underlying asset/time to maturity and implied ATM volatility. Further, the Standardized Log-Moneyness model indicates an improvement to pricing accuracy compared to previous Implied Volatility Function models, however indicating that the parameters of the models are to be re-estimated continuously for the models to fully capture the changing dynamics of the volatility smiles.

Chemicals risk modeling : toxic effect risks imposed on aquatic organisms by industrial activity

Yhteenveto: Kemikaalien teollisesta käsittelystä vesieliöille aiheutuvien riskien arviointi mallin avulla.

Physical Properties of Deep Drill Cores : Implications for Meteorite Impact Effects and Crustal Structures

Physical properties provide valuable information about the nature and behavior of rocks and minerals. The changes in rock physical properties generate petrophysical contrasts between various lithologies, for example, between shocked and unshocked rocks in meteorite impact structures or between various lithologies in the crust. These contrasts may cause distinct geophysical anomalies, which are often diagnostic to their primary cause (impact, tectonism, etc). This information is vital to understand the fundamental Earth processes, such as impact cratering and associated crustal deformations. However, most of the present day knowledge of changes in rock physical properties is limited due to a lack of petrophysical data of subsurface samples, especially for meteorite impact structures, since they are often buried under post-impact lithologies or eroded. In order to explore the uppermost crust, deep drillings are required. This dissertation is based on the deep drill core data from three impact structures: (i) the Bosumtwi impact structure (diameter 10.5 km, 1.07 Ma age; Ghana), (ii) the Chesapeake Bay impact structure (85 km, 35 Ma; Virginia, U.S.A.), and (iii) the Chicxulub impact structure (180 km, 65 Ma; Mexico). These drill cores have yielded all basic lithologies associated with impact craters such as post-impact lithologies, impact rocks including suevites and breccias, as well as fractured and unfractured target rocks. The fourth study case of this dissertation deals with the data of the Paleoproterozoic Outokumpu area (Finland), as a non-impact crustal case, where a deep drilling through an economically important ophiolite complex was carried out. The focus in all four cases was to combine results of basic petrophysical studies of relevant rocks of these crustal structures in order to identify and characterize various lithologies by their physical properties and, in this way, to provide new input data for geophysical modellings. Furthermore, the rock magnetic and paleomagnetic properties of three impact structures, combined with basic petrophysics, were used to acquire insight into the impact generated changes in rocks and their magnetic minerals, in order to better understand the influence of impact. The obtained petrophysical data outline the various lithologies and divide rocks into four domains. Based on target lithology the physical properties of the unshocked target rocks are controlled by mineral composition or fabric, particularly porosity in sedimentary rocks, while sediments result from diverse sedimentation and diagenesis processes. The impact rocks, such as breccias and suevites, strongly reflect the impact formation mechanism and are distinguishable from the other lithologies by their density, porosity and magnetic properties. The numerous shock features resulting from melting, brecciation and fracturing of the target rocks, can be seen in the changes of physical properties. These features include an increase in porosity and subsequent decrease in density in impact derived units, either an increase or a decrease in magnetic properties (depending on a specific case), as well as large heterogeneity in physical properties. In few cases a slight gradual downward decrease in porosity, as a shock-induced fracturing, was observed. Coupled with rock magnetic studies, the impact generated changes in magnetic fraction the shock-induced magnetic grain size reduction, hydrothermal- or melting-related magnetic mineral alteration, shock demagnetization and shock- or temperature-related remagnetization can be seen. The Outokumpu drill core shows varying velocities throughout the drill core depending on the microcracking and sample conditions. This is similar to observations by Kern et al., (2009), who also reported the velocity dependence on anisotropy. The physical properties are also used to explain the distinct crustal reflectors as observed in seismic reflection studies in the Outokumpu area. According to the seismic velocity data, the interfaces between the diopside-tremolite skarn layer and either serpentinite, mica schist or black schist are causing the strong seismic reflectivities.