Optimal investment under stochastic volatility and power type utility function

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

Trading-up on unmet expectations? Evaluating consumers’ expectations in online premium grocery shopping logistics

Geography and retail store locations are inherently bound together; this study links food retail changes to systemic logistics changes in an emerging market. The later include raising income and education, access to a wide range of technologies, traffic and transport difficulties, lagging retail provision, changing family structure and roles, as well as changing food culture and taste. The study incorporates demand for premium products defined by Kapferer and Bastien [2009b. The Luxury Strategy. London: Kogan Page] as comprising a broad variety of higher quality and unique or distinctive products and brands including in grocery organic ranges, healthy options, allergy free selections, and international and gourmet/specialty products through an online grocery model (n = 356) that integrates a novel view of home delivery in Istanbul. More importantly from a logistic perspective our model incorporates any products from any online vendors broadening the range beyond listed items found in any traditional online supermarkets. Data collected via phone survey and analysed via structural equation modelling suggest that the offer of online premium products significantly affects consumers’ delivery logistics expectations. We discuss logistics operations and business management implications, identifying the emerging geography of logistic models which respond to consumers’ unmet expectations using multiple sourcing and consolidation points.

A bizonytalanságnak és a vevőkör nagyságának együttes hatása az árakra (Investigating how the number of policies effect the optimum insurance premium)

Ebben a cikkben azzal foglalkozom, hogy a kockázat és a vevőkör nagysága együttesen hogyan hat a termék árára. Kétféle piacot hasonlítok össze: egy biztosítási piacot, és egy termékpiacot. A kétféle piac között az a legfontosabb különbség, hogy termékpiac esetében az eladó számára csak ott jelentkezik kockázat, hogy el tudja-e adni a terméket, míg biztosítási piac esetében az eladó a termék értékesítése után is szembesül kockázattal. A cikk során megmutatom, hogy a vevőkör növekedésének ellentétes hatása lehet a termék árára termék- illetve biztosítási piacok esetében. / === / An economic approach for modeling the insurance markets. The study focuses on the monopolistic market, where one insurance company sells a product with predetermined benefits for the customers. An outline of the company and the insureds' behavior with utility functions is given. The study investigates the problem of policy pricing in relation to the number of clients the company acquires. Analytic tools will be used to further clarify the points.

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.

Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

A study of stock market linkages between the US and frontier countries

My dissertation investigates the financial linkages and transmission of economic shocks between the US and the smallest emerging markets (frontier markets). The first chapter sets up an empirical model that examines the impact of US market returns and conditional volatility on the returns and conditional volatilities of twenty-one frontier markets. The model is estimated via maximum likelihood; utilizes the GARCH model of errors, and is applied to daily country data from the MSCI Barra. We find limited, but statistically significant exposure of Frontier markets to shocks from the US. Our results suggest that it is not the lagged US market returns that have impact; rather it is the expected US market returns that influence frontier market returns The second chapter sets up an empirical time-varying parameter (TVP) model to explore the time-variation in the impact of mean US returns on mean Frontier market returns. The model utilizes the Kalman filter algorithm as well as the GARCH model of errors and is applied to daily country data from the MSCI Barra. The TVP model detects statistically significant time-variation in the impact of US returns and low, but statistically and quantitatively important impact of US market conditional volatility. The third chapter studies the risk-return relationship in twenty Frontier country stock markets by setting up an international version of the intertemporal capital asset pricing model. The systematic risk in this model comes from covariance of Frontier market stock index returns with world returns. Both the systematic risk and risk premium are time-varying in our model. We also incorporate own country variances as additional determinants of Frontier country returns. Our results suggest statistically significant impact of both world and own country risk in explaining Frontier country returns. Time-variation in the world risk premium is also found to be statistically significant for most Frontier market returns. However, own country risk is found to be quantitatively more important.

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.

Essays on Exchange Rate Economics

Exchange rate economics has achieved substantial development in the past few decades. Despite extensive research, a large number of unresolved problems remain in the exchange rate debate. This dissertation studied three puzzling issues aiming to improve our understanding of exchange rate behavior. Chapter Two used advanced econometric techniques to model and forecast exchange rate dynamics. Chapter Three and Chapter Four studied issues related to exchange rates using the theory of New Open Economy Macroeconomics. Chapter Two empirically examined the short-run forecastability of nominal exchange rates. It analyzed important empirical regularities in daily exchange rates. Through a series of hypothesis tests, a best-fitting fractionally integrated GARCH model with skewed student-t error distribution was identified. The forecasting performance of the model was compared with that of a random walk model. Results supported the contention that nominal exchange rates seem to be unpredictable over the short run in the sense that the best-fitting model cannot beat the random walk model in forecasting exchange rate movements. Chapter Three assessed the ability of dynamic general-equilibrium sticky-price monetary models to generate volatile foreign exchange risk premia. It developed a tractable two-country model where agents face a cash-in-advance constraint and set prices to the local market; the exogenous money supply process exhibits time-varying volatility. The model yielded approximate closed form solutions for risk premia and real exchange rates. Numerical results provided quantitative evidence that volatile risk premia can endogenously arise in a new open economy macroeconomic model. Thus, the model had potential to rationalize the Uncovered Interest Parity Puzzle. Chapter Four sought to resolve the consumption-real exchange rate anomaly, which refers to the inability of most international macro models to generate negative cross-correlations between real exchange rates and relative consumption across two countries as observed in the data. While maintaining the assumption of complete asset markets, this chapter introduced endogenously segmented asset markets into a dynamic sticky-price monetary model. Simulation results showed that such a model could replicate the stylized fact that real exchange rates tend to move in an opposite direction with respect to relative consumption.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

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.

Forecasting the term structure of volatility of crude oil price changes

Peer reviewed

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).