Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Volt-e likviditási válság? Volatilitás és likviditás kapcsolatának vizsgálata (Was there a liquidity crisis? Analysis the relationship between volatility and liquidity)

Széleskörűen alátámasztott, empirikus tény, hogy önmagában a nagyobb volatilitás csökkenti a piac likviditását, vagyis változékonyabb piacokon várhatóan nagyobb lesz egy-egy tranzakció áreltérítő hatása. Kutatásomban azt a kérdést vizsgáltam, hogy a Budapesti Értéktőzsdén az OTP-részvény piacán a 2007/2008-as válságban tapasztalható, átmeneti likviditáscsökkenés betudható volt-e egyszerűen a megnövekedett volatilitásnak, vagy ezen túl abban más tényezők (pl. a szereplők körének és viselkedésének drasztikus megváltozása, általános forráscsökkenés stb.) is szerepet játszhattak-e. A volatilitást a loghozamok szórásával, illetve a tényleges ársávval, míg az illikviditást a Budapesti Likviditási Mértékkel (BLM) reprezentáltam. Egyrészt azt állapítottam meg, hogy az OTP esetében a tényleges ársáv szorosabban korrelál a BLM-mel, mint a szórás. Másrészt az is egyértelmű, hogy a válság előtti kapcsolat a volatilitás és a likviditás között a válságban és azután már jelentősen megváltozott. Válságban az illikviditás jóval nagyobb volt, mint amit a volatilitás növekedése alapján vártunk, a válság lecsengése után azonban megfordult ez a reláció. _________ It is a widely supported empirical fact, that the greater volatility in itself decreases the liquidity of the market, namely more volatile a market is, the higher a transaction’s price impact will be. I have examined in my paper the question, whether the decrease of liquidity during the crisis of 2007/2008 in case of the OTP stock – traded on the Budapest Stock Exchange – was the consequence of the increased volatility, or other factors had an effect on the illiquidity as well (e.g.: the drastic change of market participants’ behaviour; reduction of fi nancing sources; etc.). I have represented volatility with the standard deviation of the logreturns, and with the true range, while the illiquidity with the Budapest Liquidity Measure (BLM). On one hand I have identifi ed, that in case of the OTP, the true range has a stronger relationship with the BLM than the standard deviation has. On the other hand it was clear, that the relationship between volatility and liquidity has changed notably during and after the crisis. During crisis the illiquidity was greater than what I have estimated based on the volatility increase, but after the crisis this relation has changed.

An autoregressive conditional filtering process to remove intraday seasonal volatility and its application to testing the noisy rational expectations model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.

The Food Service Industry Environment: Market Volatility Analysis

In their dialogue entitled - The Food Service Industry Environment: Market Volatility Analysis - by Alex F. De Noble, Assistant Professor of Management, San Diego State University and Michael D. Olsen, Associate Professor and Director, Division of Hotel, Restaurant & Institutional Management at Virginia Polytechnic Institute and State University, De Noble and Olson preface the discussion by saying: “Hospitality executives, as a whole, do not believe they exist in a volatile environment and spend little time or effort in assessing how current and future activity in the environment will affect their success or failure. The authors highlight potential differences that may exist between executives' perceptions and objective indicators of environmental volatility within the hospitality industry and suggest that executives change these perceptions by incorporating the assumption of a much more dynamic environment into their future strategic planning efforts. Objective, empirical evidence of the dynamic nature of the hospitality environment is presented and compared to several studies pertaining to environmental perceptions of the industry.” That weighty thesis statement presumes that hospitality executives/managers do not fully comprehend the environment in which they operate. The authors provide a contrast, which conventional wisdom would seem to support and satisfy. “Broadly speaking, the operating environment of an organization is represented by its task domain,” say the authors. “This task domain consists of such elements as a firm's customers, suppliers, competitors, and regulatory groups.” These are dynamic actors and the underpinnings of change, say the authors by way of citation. “The most difficult aspect for management in this regard tends to be the development of a proper definition of the environment of their particular firm. Being able to precisely define who the customers, competitors, suppliers, and regulatory groups are within the environment of the firm is no easy task, yet is imperative if proper planning is to occur,” De Noble and Olson further contribute to support their thesis statement. The article is bloated, and that’s not necessarily a bad thing, with tables both survey and empirically driven, to illustrate market volatility. One such table is the Bates and Eldredge outline; Table-6 in the article. “This comprehensive outline…should prove to be useful to most executives in expanding their perception of the environment of their firm,” say De Noble and Olson. “It is, however, only a suggested outline,” they advise. “…risk should be incorporated into every investment decision, especially in a volatile environment,” say the authors. De Noble and Olson close with an intriguing formula to gauge volatility in an environment.

An Autoregressive Conditional Filtering Process to remove Intraday Seasonal Volatility and its Application to Testing the Noisy Rational Expectations Model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.

Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers

The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988, 39(1-2), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESV-ALM, and the finite sample properties of the quasi-maximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. The volatility and co-volatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and co-volatility.

Electoral Volatility, Political Sophistication, Trust and Efficacy

In this article we investigate voter volatility and analyze the causes and motives of switching vote intentions. We test two main sets of variables linked to volatility in literature; political sophistication and ‘political (dis)satisfaction’. Results show that voters with low levels of political efficacy tend to switch more often, both within a campaign and between elections. In the analysis we differentiate between campaign volatility and inter-election volatility and by doing so show that the dynamics of a campaign have a profound impact on volatility. The campaign period is when the lowly sophisticated switch their vote intention. Those with higher levels of interest in politics have switched their intention before the campaign has started. The data for this analysis are from the three wave PartiRep Belgian Election Study (2009).

Future Earnings Growth Volatility and the Value Premium

The value premium is well established in empirical asset pricing, but to date there is little understanding as to its fundamental drivers. We use a stochastic earnings valuation model to establish a direct link between the volatility of future earnings growth and firm value. We illustrate that risky earnings growth affects growth and value firms differently. We provide empirical evidence that the volatility of future earnings growth is a significant determinant of the value premium. Using data on individual firms and characteristic-sorted test portfolios, we also find that earnings growth volatility is significant in explaining the cross-sectional variation of stock returns. Our findings imply that the value premium is the rational consequence of accounting for risky earnings growth in the firm valuation process.

Measuring, Modeling, and Forecasting Volatility and Correlations from High-Frequency Data

This dissertation contains four essays that all share a common purpose: developing new methodologies to exploit the potential of high-frequency data for the measurement, modeling and forecasting of financial assets volatility and correlations. The first two chapters provide useful tools for univariate applications while the last two chapters develop multivariate methodologies. In chapter 1, we introduce a new class of univariate volatility models named FloGARCH models. FloGARCH models provide a parsimonious joint model for low frequency returns and realized measures, and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the models in a realistic numerical study and on the basis of a data set composed of 65 equities. Using more than 10 years of high-frequency transactions, we document significant statistical gains related to the FloGARCH models in terms of in-sample fit, out-of-sample fit and forecasting accuracy compared to classical and Realized GARCH models. In chapter 2, using 12 years of high-frequency transactions for 55 U.S. stocks, we argue that combining low-frequency exogenous economic indicators with high-frequency financial data improves the ability of conditionally heteroskedastic models to forecast the volatility of returns, their full multi-step ahead conditional distribution and the multi-period Value-at-Risk. Using a refined version of the Realized LGARCH model allowing for time-varying intercept and implemented with realized kernels, we document that nominal corporate profits and term spreads have strong long-run predictive ability and generate accurate risk measures forecasts over long-horizon. The results are based on several loss functions and tests, including the Model Confidence Set. Chapter 3 is a joint work with David Veredas. We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances on the basis of noisy and asynchronous prices. Along these lines, a minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics. Chapter 4 is co-authored with Niels S. Hansen, Asger Lunde and Kasper V. Olesen, all affiliated with CREATES at Aarhus University. We propose to use the Realized Beta GARCH model to exploit the potential of high-frequency data in commodity markets. The model produces high quality forecasts of pairwise correlations between commodities which can be used to construct a composite covariance matrix. We evaluate the quality of this matrix in a portfolio context and compare it to models used in the industry. We demonstrate significant economic gains in a realistic setting including short selling constraints and transaction costs.

A Monthly Volatility Index for the US Economy

We estimate the monthly volatility of the US economy from 1968 to 2006 by extending the coincidentindex model of Stock and Watson (1991). Our volatility index, which we call VOLINX, hasfour applications. First, it sheds light on the Great Moderation. VOLINX captures the decrease in thevolatility in the mid-80s as well as the different episodes of stress over the sample period. In the 70sand early 80s the stagflation and the two oil crises marked the pace of the volatility whereas 09/11 is themost relevant shock after the moderation. Second, it helps to understand the economic indicators thatcause volatility. While the main determinant of the coincident index is industrial production, VOLINXis mainly affected by employment and income. Third, it adapts the confidence bands of the forecasts.In and out-of-sample evaluations show that the confidence bands may differ up to 50% with respect to amodel with constant variance. Last, the methodology we use permits us to estimate monthly GDP, whichhas conditional volatility that is partly explained by VOLINX. These applications can be used by policymakers for monitoring and surveillance of the stress of the economy.

Low-Volatility Anomaly in Helsinki Stock Exchange

International research shows that low-volatility stocks have beaten high-volatility stocks in terms of returns for decades on multiple markets. This abbreviation from traditional risk-return framework is known as low-volatility anomaly. This study focuses on explaining the anomaly and finding how strongly it appears in NASDAQ OMX Helsinki stock exchange. Data consists of all listed companies starting from 2001 and ending close to 2015. Methodology follows closely Baker and Haugen (2012) by sorting companies into deciles according to 3-month volatility and then calculating monthly returns for these different volatility groups. Annualized return for the lowest volatility decile is 8.85 %, while highest volatility decile destroys wealth at rate of -19.96 % per annum. Results are parallel also in quintiles that represent larger amount of companies and thus dilute outliers. Observation period captures financial crisis of 2007-2008 and European debt crisis, which embodies as low main index annual return of 1 %, but at the same time proves the success of low-volatility strategy. Low-volatility anomaly is driven by multiple reasons such as leverage constrained trading and managerial incentives which both prompt to invest in risky assets, but behavioral matters also have major weight in maintaining the anomaly.

Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Volatility transmission between stock and exchange-rate markets: A connectedness analysis

This paper empirically investigates volatility transmission among stock and foreign exchange markets in seven major world economies during the period July 1988 to January 2015. To this end, we first perform a static and dynamic analysis to measure the total volatility connectedness in the entire period (the system-wide approach) using a framework recently proposed by Diebold and Yilmaz (2014). Second, we make use of a dynamic analysis to evaluate the net directional connectedness for each market. To gain further insights, we examine the time-varying behaviour of net pair-wise directional connectedness during the financial turmoil periods experienced in the sample period Our results suggest that slightly more than half of the total variance of the forecast errors is explained by shocks across markets rather than by idiosyncratic shocks. Furthermore, we find that volatility connectedness varies over time, with a surge during periods of increasing economic and financial instability.

The EU ban on uncovered sovereign credit default swaps: assessing impacts on liquidity, volatility and price discovery

This article addresses the effects of the prohibition against naked CDS buying implemented by the European Union in November 2012. Three aspects of market quality are analyzed: liquidity, volatility, and price informativeness. Overall, our results suggest that the ban produced negative effects on liquidity and price informativeness. First, we find that in territories within the scope of the EU regulation, the bid–ask spreads on sovereign CDS contracts rose after the ban, but fell for countries outside its bounds. Open interest declined for both groups of CDS reference entities in our sample, but significantly more in the constraint group. Price delay increased more prominently for countries affected by the ban, whereas price precision decreased for these countries while increasing for CDSs written on other sovereign reference entities. Most notably, our findings indicate that hese negative effects were more pronounced amid reference entities exhibiting lower credit risk. With respect to volatility, the evidence suggests that the ban was successful in stabilizing the CDS market in that volatility decreased, particularly for contracts written on riskier CDS entities.

Environmental monitoring of airborne nanoparticles

The aim of this work was to review the existing instrumental methods to monitor airborne nanoparticle in different types of indoor and outdoor environments in order to detect their presence and to characterise their properties. Firstly the terminology and definitions used in this field are discussed, which is followed by a review of the methods to measure particle physical characteristics including number concentration, size distribution and surface area. An extensive discussion is provided on the direct methods for particle elemental composition measurements, as well as on indirect methods providing information on particle volatility and solubility, and thus in turn on volatile and semivolatile compounds of which the particle is composed. A brief summary of broader considerations related to nanoparticle monitoring in different environments concludes the paper.