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.

Evaluating the Predictability of the Volatility Smile Using Return Distributions

In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.

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.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Essays on Stock Options, Incentives, and Managerial Action

Executive compensation and managerial behavior have received an increasing amount of attention in the financial economics literature since the mid 1970s. The purpose of this thesis is to extend our understanding of managerial compensation, especially how stock option compensation is linked to the actions undertaken by the management. Furthermore, managerial compensation is continuously and heatedly debated in the media and an emerging consensus from this discussion seems to be that there still exists gaps in our knowledge of optimal contracting. In Finland, the first executive stock options were introduced in the 1980s and throughout the last 15 years it has become increasingly popular for Finnish listed firms to use this type of managerial compensation. The empirical work in the thesis is conducted using data from Finland, in contrast to most previous studies that predominantly use U.S. data. Using Finnish data provides insight of how market conditions affect compensation and managerial action and provides an opportunity to explore what parts of the U.S. evidence can be generalized to other markets. The thesis consists of four essays. The first essay investigates the exercise policy of the executive stock option holders in Finland. In summary, Essay 1 contributes to our understanding of the exercise policies by examining both the determinants of the exercise decision and the markets reaction to the actual exercises. The second essay analyzes the factors driving stock option grants using data for Finnish publicly listed firms. Several agency theory based variables are found to have have explanatory power on the likelihood of a stock option grant. Essay 2 also contributes to our understanding of behavioral factors, such as prior stock return, as determinants of stock option compensation. The third essay investigates the tax and stock option motives for share repurchases and dividend distributions. We document strong support for the tax motive for share repurchases. Furthermore, we also analyze the dividend distribution decision in companies with stock options and find a significant difference between companies with and without dividend protected options. We thus document that the cutting of dividends found in previous U.S. studies can be avoided by dividend protection. In the fourth essay we approach the puzzle of negative skewness in stock returns from an altogether different angle than in previous studies. We suggest that negative skewness in stock returns is generated by management disclosure practices and find proof for this. More specifically, we find that negative skewness in daily returns is induced by returns for days when non-scheduled firm specific news is disclosed.

Options for selecting dairy cattle for milk coagulation ability

Lypsylehmien maidon juoksettumiskyvyn jalostuskeinot Väitöskirjassa tutkittiin lypsylehmien maidon juustonvalmistuslaadun parantamista jalostusvalinnan avulla. Tutkimusaihe on tärkeä, sillä yhä suurempi osa maidosta käytetään juustonvalmistukseen. Tutkimuksen kohteena oli maidon juoksettumiskyky, sillä se on yksi keskeisistä juustomäärään vaikuttavista tekijöistä. Maidon juoksettumiskyky vaihteli huomattavasti lehmien, sonnien, karjojen, rotujen ja lypsykauden vaiheiden välillä. Vaikka tankkimaidon juoksettumiskyvyssä olikin suuria eroja karjoittain, karja selitti vain pienen osan juoksettumiskyvyn kokonaisvaihtelusta. Todennäköisesti perinnölliset erot lehmien välillä selittävät suurimman osan karjojen tankkimaitojen juoksettumiskyvyssä havaituista eroista. Hyvä hoito ja ruokinta vähensivät kuitenkin jossain määrin huonosti juoksettuvien tankkimaitojen osuutta karjoissa. Holstein-friisiläiset lehmät olivat juoksettumiskyvyltään ayrshire-rotuisia lehmiä parempia. Huono juoksettuminen ja juoksettumattomuus oli vain vähäinen ongelma holstein-friisiläisillä (10 %), kun taas kolmannes ayrshire-lehmistä tuotti huonosti juoksettuvaa tai juoksettumatonta maitoa. Maitoa sanotaan huonosti juoksettuvaksi silloin, kun juustomassa ei ole riittävän kiinteää leikattavaksi puolen tunnin kuluttua juoksetteen lisäyksestä. Juoksettumattomaksi määriteltävä maito ei saostu lainkaan puolen tunnin aikana ja on siksi erittäin huonoa raaka-ainetta juustomeijereille. Noin 40 % lehmien välisistä eroista maidon juoksettumiskyvyssä selittyi perinnöllisillä tekijöillä. Juoksettumiskykyä voikin sanoa hyvin periytyväksi ominaisuudeksi. Kolme mittauskertaa lehmää kohti riittää varsin hyvin lehmän maidon keskimääräisen juoksettumiskyvyn arvioimiseen. Tällä hetkellä juoksettumiskyvyn suoran jalostamisen ongelmana on kuitenkin automatisoidun, laajamittaiseen käyttöön soveltuvan mittalaitteen puute. Tämän takia väitöskirjassa tutkittiin mahdollisuuksia jalostaa maidon juoksettumiskykyä epäsuorasti, jonkin toisen ominaisuuden kautta. Tällaisen ominaisuuden pitää olla kyllin voimakkaasti perinnöllisesti kytkeytynyt juoksettumiskykyyn, jotta jalostus olisi mahdollista sen avulla. Tutkittavat ominaisuudet olivat sonnien kokonaisjalostusarvossa jo mukana olevat maitotuotos ja utareterveyteen liittyvät ominaisuudet sekä kokonaisjalostusarvoon kuulumattomat maidon valkuais- ja kaseiinipitoisuus sekä maidon pH. Väitöskirjassa tutkittiin myös mahdollisuuksia ns. merkkiavusteiseen valintaan tutkimalla maidon juoksettumattomuuden perinnöllisyyttä ja kartoittamalla siihen liittyvät kromosomialueet. Tutkimuksen tulosten perusteella lehmien utareterveyden jalostaminen parantaa jonkin verran myös maidon juoksettumiskykyä sekä vähentää juoksettumattomuutta ayrshire-rotuisilla lehmillä. Lehmien maitotuotos ja maidon juoksettumiskyky sekä juoksettumattomuus ovat sen sijaan perinnöllisesti toisistaan riippumattomia ominaisuuksia. Myöskin maidon valkuais- ja kaseiinipitoisuuden perinnöllinen yhteys juoksettumiskykyyn oli likimain nolla. Maidon pH:n ja juoksettumiskyvyn välillä oli melko voimakas perinnöllinen yhteys, joten maidon pH:n jalostaminen parantaisi myös maidon juoksettumiskykyä. Todennäköisesti sen jalostaminen ei kuitenkaan vähentäisi juoksettumatonta maitoa tuottavien lehmien määrää. Koska maidon juoksettumattomuus on niin yleinen ongelma suomalaisilla ayrshire-lehmillä, väitöksessä selvitettiin tarkemmin ilmiön taustoja. Kaikissa kolmessa tutkimusaineistoissa noin 10 % ayrshire-lehmistä tuotti juoksettumatonta maitoa. Kahden vuoden kuukausittaisen seurannan aikana osa lehmistä tuotti juoksettumatonta maitoa lähes joka mittauskerralla. Maidon juoksettumattomuus oli yhteydessä lypsykauden vaiheeseen, mutta mikään ympäristötekijöistä ei pystynyt täysin selittämään sitä. Sen sijaan viitteet sen periytyvyydestä vahvistuivat tutkimusten edetessä. Lopuksi tutkimusryhmä onnistui kartoittamaan juoksettumattomuutta aiheuttavat kromosomialueet kromosomeihin 2 ja 18, lähelle DNA-merkkejä BMS1126 ja BMS1355. Tulosten perusteella maidon juoksettumattomuus ei ole yhteydessä maidon juoksettumistapahtumassa keskeisiin kaseiinigeeneihin. Sen sijaan on mahdollista, että juoksettumattomuusongelman aiheuttavat kaseiinigeenien syntetisoinnin jälkeisessä muokkauksessa tapahtuvat virheet. Asia vaatii kuitenkin perusteellista tutkimista. Väitöksen tulosten perusteella maidon juoksettumattomuusgeeniä kantavien eläinten karsiminen jalostuseläinten joukosta olisi tehokkain tapa jalostaa maidon juoksettumiskykyä suomalaisessa lypsykarjapopulaatiossa.

Foreign Capital and Finland : Central government's first period of reliance on international financial markets, 1862-1938

The main objective of the study is to evaluate the Finnish central government s foreign borrowing between the years 1862 and 1938. Most of this period was characterised by deep capital market integration that bears resemblance to the liberal world financial order at the turn of the millennium. The main aim is to analyse the credit risk associated with the state and its determination by evaluating the world financial market centres perception of Finland. By doing this, the study is also expected to provide an additional dimension to Finland s political and economic history by incorporating into the research the assessments of international capital markets regarding Finland during a period that witnessed profound political and economic changes in Finnish society. The evaluation of the credit risk mainly relies on exchange-rate risk free time series of the state s foreign bonds. They have been collected from quotations in the stock exchanges in Helsinki, Hamburg, Paris and London. In addition, it investigates Finland s exposure to short-term debt and Moody s credit ratings assigned to Finland. The study emphasises the importance of the political risk. It suggests that the hey-day of the state s reliance on foreign capital markets took place during last few decades of the 19th century when Finland enjoyed a wide autonomy in the Russian Empire and prudently managed its economy, highlighted in Finland s adherence to the international gold standard. Political confrontations in Finland and, in particular, in Russia and the turbulence of the world financial system prevented the return of this beneficial position again. Through its issuance of foreign bonds the state was able to import substantial amounts of foreign capital, which was sorely needed to foster economic development in Finland. Moreover, the study argues that the state s presence in the western capital markets not only had economic benefits, but it also increased the international awareness of Finland s distinct and separate status in the Russian Empire and later underlined its position as an independent republic.

Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.

Epidemiology and Treatment Options of Primary Biliary Cirrhosis

Primary biliary cirrhosis (PBC) is caused by an autoimmune inflammation of the small bile ducts. It results to destruction of bile ducts, accumulation of the bile in the liver, and cirrhosis. The prevalence and incidence of PBC is increasing in the Western world. The prevalence is highest in the USA (402 per million) and incidence in Scotland (49/million/year). Our aim was to assess the epidemiology of PBC in Finland. Patients for the epidemiological study were searched from the hospital discharge records from year 1988 to 1999.The prevalence rose from 103 to 180/million from 1988 to 1999, an annual increase of 5.1%. The incidence rose from 12 to 17 /million/year, an annual increase of 3.5%. The age at death increased markedly from 65 to 76 years. The risk of liver related deaths diminished over time. The treatment of PBC is based on Ursodeoxycholic acid (UDCA). During 20 years 50% of patients end up with cirrhosis. Our treatment option was to combine budesonide, a potent corticosteroid with a high first pass metabolism in the liver, to UDCA and evaluate the liver effects and systemic effects such as bone mass density (BMD) changes. Our aim was to find out if combination of laboratory tests would serve as a surrogate marker for PBC and help reducing the need for liver biopsy. Non-cirrhotic PBC patients were randomized to receive budesonide 6 mg/day combined to UDCA 15 mg /kg/day or UDCA alone for three years. The combination therapy with UDCA and budesonide was effective: stage improved 22%, fibrosis 25%, and inflammation 32%. In the UDCA group the changes were: 20% deterioriation in stage and 70% in fibrosis, but a 10% improvement in inflammation. BMD in femoral neck decreased by 3.6% in the combination group and by 1.9% in the UDCA group. The reductions in lumbar spine were 2.8% and 0.7%. Pharmacokinetics did not differ between the stages of PBC. HA, PIIINP, bile acids, and AST were significantly different within stages I-III and could differentiate the mild fibrosis (F0F1) from the moderate (F2F3). The combination of these individual markers (PBC-score) further improved the accuracy. The area under the ROC of the PBC score, using a cut of value 66, had a sensitivity of 81.4% and a specificity of 65.2% to classify the stage of PBC. The prevalence of PBC in Finland increases, which results from increasing incidence and improved survival. The combination of budesonide and UDCA improves liver histology compared to UDCA alone in non-cirrhotic stages of PBC. The treatment may reduce BMD. Hyaluronic acid, PIIINP, AST, and bile acids may serve as tools to monitor the treatment response in the early stages of PBC. The budesonide and UDCA combination therapy is an option for those patients who do not receive full response from UDCA and are still at the non-cirrhotic stage of PBC.

Finnish and Austrian Wood Markets in a Changing Environment

At present the operating environment of sawmills in Europe is changing and there are uncertainties related in raw material supply in many countries. The changes in the operating environment of roundwood markets and the effects followed by these changes have brought up several interesting issues from the viewpoint of research. Lately new factors have been influencing the roundwood markets, such as increasing interest towards wood-based energy and implementation of new energy policies as well as changes in wood trade flows that affect the domestic markets in many countries. This Master’s thesis studies the adaptation ability of Finnish roundwood markets in a changing operating environment, aiming to produce an up-to-date analysis considering new development trends. The study concentrates on the roundwood markets from the viewpoint of sawmill industry since the industry is dependent on the functioning of the markets and sawmills are highly affected by the changes on the roundwood markets. To facilitate international comparison, the study is implemented by comparing Finnish and Austrian roundwood markets and analysing changes happening in the two countries. Finland and Austria share rather similar characteristics in the roundwood market structures, forest resources and forest ownership as well as production of roundwood and sawnwood. In addition they both are big exporters of forest industry products. In this study changes in the operating environment of sawmill industry both in Finland as well as in Austria are compared to each other aiming to recognise the main similarities and differences between the countries. In addition both development possibilities as well as challenges followed by the changes are discussed. The aim of the study is to define the main challenges and possibilities confronted by the actors on the markets and also to find new perspectives to approach these. The study is implemented as a qualitative study. The theoretical framework of the study describes the operating environment of wood markets from the viewpoint of the sawmill industry and represents the effects of supply and demand on the wood markets. The primary research material of the study was gathered by interviewing high level experts of forestry and sawmill industry in both Finland and Austria. The aim was to receive as extensive country specific viewpoint from the markets as possible, hence interviewees represented different parties of the markets. After creating country-specific profiles based on the theoretical framework a cross-country comparison was implemented. As a consequence the main similarities and differences in the operating environment and on the roundwood markets of Finland and Austria were recognized. In addition the main challenges and possibilites were identified. The results of the study offer a wide analysis regarding the main similarities and differences of the wood markets of Finland and Austria and their operating environments as well as concerning challenges and possibilities faced on the markets.

Finnish Short-Term Stock Returns

Functioning capital markets are a crucial part of a competitive economy since they provide the mechanisms to allocate resources. In order to be well functioning a capital market has to be efficient. Market efficiency is defined as a market where prices at any time fully reflect all available information. Basically, this means that abnormal returns cannot be predicted since they are dependent on future, presently unknown, information. The debate of market efficiency has been going on for several decades. Most academics today would probably agree that financial markets are reasonably efficient since virtually nobody has been able to achieve continuous abnormal positive returns. However, it is clear that a set of return anomalies exists, although they are apparently to small to enable substantial economic profit. Moreover, these anomalies can often be attributed to market design. The motivation for this work is to expand the knowledge of short-term trading patterns and to offer some explanations for these patterns. In the first essay the return pattern during the day is examined. On average stock prices move during two time periods of the day, namely, immediately after the opening and around the formal close of the market. Since stock prices, on average, move upwards these abnormal returns are generally positive and cause the distinct U-shape of intraday returns. In the second essay the results in the first essay are examined further. The return pattern around the former close is shown to partly be the result of manipulative action by market participants. In the third essay the focus is shifted towards trading patterns of the underlying stocks on days when index options and index futures on the stocks expire. Generally no expiration day effect was found. However, some indication of an expiration day effect was found when a large amount of open in- or at-the-money contracts existed. Also, the effects were likelier to be found for shares with high index-weight but fairly low trading volume. Last, in the forth essay the attention is turned to the behaviour of different tax clienteles around the dividend ex-day. Two groups of investors showed abnormal trading behaviour. Domestic non-financial investors, especially domestic companies, showed a dividend capturing behaviour, i.e. buying cum-dividend and selling ex-dividend shares. The opposite behaviour was found for foreign investors and domestic financial institutions. The effect was more notable for high yield, high volume stocks.