A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Sähkönmyyntisopimusten markkinalähtöinen hinnoittelu

Vuonna 1995 alkanut sähkömarkkinoiden vapautuminen on muuttanut sähköyhtiöiden myyntisopimusten hinnoittelua merkittävästi. Ennen markkinauudistusta voitiin sähkön myyntisopimukset hinnoitella perustuen oman sähkön tuotannon kustannuksiin ja haluttuun katteeseen. Nykyään sähköpörssissä noteerattava sähkön hinta muodostaa perustan kaikkien myyntisopimusten hinnoittelulle. Sähkön markkinahinnan lisäksi on myyntisopimusten hinnoittelussa otettava huomioon sähkömarkkinoiden ominaispiirteistä aiheutuvat riskit sähkön myyjälle. Tässä työssä mallinnetaan Lappeenrannan Energia Oy:n markkinalähtöiset hinnoittelumenetelmät kahdelle sähkönmyyntisopimustyypille. Lisäksi tutkitaan markkinalähtöisen hinnoittelun tärkeimpien riskikomponenttien, aluehintaeron sekä profiililisän, merkitystä markkinalähtöisten myyntisopimusten hinnoittelussa. Aluehintaeron hyväksikäyttöä myyntisopimusten hinnoittelussa on tutkittu selvittämällä Suomen hinta-alueen CfD-johdannaisten riskipreemiot. Profiililisän merkitystä myyntisopimusten hinnoittelussa on tutkittu havainnoimalla profiililisän muutoksia hinta- ja kulutusaikasarjoissa sekä suojaushinta ja tehotasossa tapahtuneiden muutosten suhteen. Ennustetun ja toteutuneen profiililisän eroja on tutkittu laskemalla ne seitsemälle Lappeenrannan Energia Oy:n merkittävälle asiakkaalle. Lisäksi on tarkasteltu profiililisän laskentaan tarvittavan hinta-aikasarjan mallintamiseen käytettyjen termiinituotteiden hintojen merkitystä lasketun profiililisän suuruuteen. Työn lopuksi esitetään kaksi vaihtoehtoista sähkösopimusten hinnoittelumenetelmää ja vertaillaan esitettyjä hinnoittelumenetelmiä keskenään. Työssä havaitaan, että aluehintaerolta suojautumiseen käytettävien CfD-johdannaisten avulla olisi ollut mahdollista lisätä markkinalähtöisten myyntisopimusten tuottoa viimeisen kolmen vuoden aikana. Suoritettujen herkkyysanalyysien perusteella voidaan todeta, että toteutuneen ja ennustetun profiililisän erot johtuvat laskentaan käytettävien hinta- sekä kulutusaikasarjojen epätarkkuudesta. Lappeenrannan Energia Oy:n käyttämät profiililisät osoittautuivat ex-post -tarkastelussa liian suuriksi yhtä asiakasta lukuun ottamatta. Lisäksi tarjousaikana laskettujen profiililisien voidaan katsoa muuttuvan täysin samassa suhteessa hinta-aikasarjan mallintamiseen käytettyjen termiinituotteiden volatiliteettien kanssa. Esiteltyjen vaihtoehtoisten myyntisopimusten hinnoittelumenetelmien voidaan katsoa antavan varsin samanlaisia tuloksia kuin Lappeenrannan Energia Oy:n nykyinen hinnoittelumenetelmä. Saatuihin tuloksiin vaikuttavat kuitenkin painokertoimien estimointiin käytetyn vuoden volatiliteetti sekä profiililisän laskentamenetelmä

Market linkages and volatility spillover: evidence from BRIC countries

The aim of this study is to investigate volatility spillover-effect and market integration between BRIC countries. Motivated by existing literature of market integration between developed and emerging markets, we will investigate market linkages using multivariate asymmetric GARCH BEKK model. The increasing globalization of the financial markets and consequent higher volatility transfer between markets makes it more important to understand market integration between BRIC countries. We investigate the stock market integration and volatility transfer between the BRIC countries form 1998 to 2007, using daily data. The empirical results show that there are international diversification benefits among Brazil, Russia, China and India. U.S. influence to these countries has been week, even though U.S. economy has been leading the global financial markets. From Finnish point of view, diversification benefits are robust but we find some correlation with Russia and China.

Idiosyncratic Volatility Puzzle: Influence of Macro-Finance Factors

In this paper, we scrutinize the cross-sectional relation between idiosyncratic volatility and stock returns. As a novelty, the idiosyncratic volatility is obtained by conditioning upon macro-finance factors as well as upon traditional asset pricing factors. The macro-finance factors are constructed from a large pool of macroeconomic and financial variables. Cleaning for macro-finance e§ects reverses the puzzling negative relation between returns and idiosyncratic volatility documented previously. Portfolio analysis shows that the effects from macro-finance factors are economically strong. The relation between idiosyncratic volatility and returns does not vary with the NBER business cycles. The empirical results are highly robust. Keywords: Idiosyncratic volatility puzzle; Macro-finance predictors; Factor analysis; Business cycle. JEL Classifications: G12; G14

Financial stress transmission in EMU sovereign bond market volatility: a connectedness analysis

This paper measures the connectedness in EMU sovereign market volatility between April 1999 and January 2014, in order to monitor stress transmission and to identify episodes of intensive spillovers from one country to the others. 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 Yılmaz (2014). Second, we make use of a dynamic analysis to evaluate the net directional connectedness for each country and apply panel model techniques to investigate its determinants. Finally, to gain further insights, we examine the timevarying behaviour of net pair-wise directional connectedness at different stages of the recent sovereign debt crisis.

Volatility spillovers in EMU sovereign bond markets

We analyse volatility spillovers in EMU sovereign bond markets. First, we examine the unconditional patterns during the full sample (April 1999-January 2014) using a measure recently proposed by Diebold and Yılmaz (2012). Second, we make use of a dynamic analysis to evaluate net directional volatility spillovers for each of the eleven countries under study, and to determine whether core and peripheral markets present differences. Finally, we apply a panel analysis to empirically investigate the determinants of net directional spillovers of this kind.

Rocking the Euro boat: scheduled market announcements' effects on Euro implied volatility

The purpose of this thesis is to investigate scheduled market announcements’ effects on Euro implied volatility. Timeline selected for this study ranges from 2005 to 2009. The method chosen is so-called event study approach, in which five days prior to a news announcement stand for a pre-event period, and five days after the announcement form a post-event period. Statistical research method employed is Mann-Whitney-Wilcoxon test, which examines two evenly-sized distributions’ equality, in this case the distributions being the pre- and post-event periods. Observations are based on daily data of US dollar nominated Euro at-the-money call options. Research results partially back up previous literature’s view of uncertainty increasing prior to the news announcement. After the exact contents of the news is public, uncertainty levels measured by implied volatility tend to lower.

Observations of Industry Momentum Effect in European Equity Indices

This thesis examines the existence and nature of momentum effect in European equity indices. A set of predefined indicators is used to compose momentum portfolios and different holding periods are used to test the strategies over variable time periods as well as under different economical conditions. The data consists of daily closing prices of STOXX Europe 600 index and its 18 super sector indices. Over the study period we follow the performances of a long position in the Winner portfolio, a position in the market neutral zero-cost portfolio and also a position in the risk-controlled zero-cost portfolio. The investment ratio of the risk-controlled zero-cost portfolio is negatively correlated with the realized market volatility. The results show that momentum effect is present in European industries and is most prominent in the short-term. Indicators that are based on short-term performance tend predict the over- and underperformers for the 1-month holding period more reliably than any other indicator/holding period combination. The examination of the strategies under different economical conditions shows that the market neutral approach can create significant returns in times of recession but in times of economic boom the long position in Winner portfolio outperforms the market neutral portfolio by an extensive margin.

Effects of a Financial Transaction Tax - Do Transaction Costs Lower Volatility?: A Literature Review

In this literature review the theorethical framework of Financial transaction taxes and their assumed effect on market volatility is assessed. The empirical evidence from various studies is compared against the theory and a simple empirical review of the Finnish stock market is conducted. The findings implicate that financial transaction taxes can not reduce volatility and their actual effect on markets is dependend by many other factors as well. Some evidence even suggests that transactions taxes may actually raise volatility.