Three Essays on the Volatility of Finnish Stock Returns (summary section only)

First, in Essay 1, we test whether it is possible to forecast Finnish Options Index return volatility by examining the out-of-sample predictive ability of several common volatility models with alternative well-known methods; and find additional evidence for the predictability of volatility and for the superiority of the more complicated models over the simpler ones. Secondly, in Essay 2, the aggregated volatility of stocks listed on the Helsinki Stock Exchange is decomposed into a market, industry-and firm-level component, and it is found that firm-level (i.e., idiosyncratic) volatility has increased in time, is more substantial than the two former, predicts GDP growth, moves countercyclically and as well as the other components is persistent. Thirdly, in Essay 3, we are among the first in the literature to seek for firm-specific determinants of idiosyncratic volatility in a multivariate setting, and find for the cross-section of stocks listed on the Helsinki Stock Exchange that industrial focus, trading volume, and block ownership, are positively associated with idiosyncratic volatility estimates––obtained from both the CAPM and the Fama and French three-factor model with local and international benchmark portfolios––whereas a negative relation holds between firm age as well as size and idiosyncratic volatility.

Modeling Nonlinearities and Asymmetries in Asset Pricing

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

Price Inflation, Unemployment and Devaluations: The Finnish Experience of the 1990s

In this paper I provide some empirical answers to important questions such as the determinants of price inflation and the role of inflation polices. The results indicate that monetary policy is surprisingly impotent as a device for controlling inflation and there is little support that it influences the real variables. The low inflation after the Finnish devaluations in the beginning of 90s is foremost due to a previous imbalance in the labor markets and depressed aggregate demand.

Maximum Loss Calculation using Scenario Analysis, Heavy Tails and Implied Volatility Patterns

The objective of this paper is to improve option risk monitoring by examining the information content of implied volatility and by introducing the calculation of a single-sum expected risk exposure similar to the Value-at-Risk. The figure is calculated in two steps. First, there is a need to estimate the value of a portfolio of options for a number of different market scenarios, while the second step is to summarize the information content of the estimated scenarios into a single-sum risk measure. This involves the use of probability theory and return distributions, which confronts the user with the problems of non-normality in the return distribution of the underlying asset. Here the hyperbolic distribution is used to describe one alternative for dealing with heavy tails. Results indicate that the information content of implied volatility is useful when predicting future large returns in the underlying asset. Further, the hyperbolic distribution provides a good fit to historical returns enabling a more accurate definition of statistical intervals and extreme events.

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.

Unrealized expectations of jumps in volatility: An explanation to the low and time-varying predictive power of implied volatility

The low predictive power of implied volatility in forecasting the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are indeed priced in implied volatility. This has two important consequences. First, implied volatility is actually expected to exceed realized volatility over long periods of time only to be greatly less than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the classic regression test tends to reject the hypothesis of informational efficiency even if markets are informationally effective.

Short-Horizon Asymmetric Mean-Reversion and Overreactions: Evidence from the Nordic Stock Markets

This paper examines the asymmetric behavior of conditional mean and variance. Short-horizon mean-reversion behavior in mean is modeled with an asymmetric nonlinear autoregressive model, and the variance is modeled with an Exponential GARCH in Mean model. The results of the empirical investigation of the Nordic stock markets indicates that negative returns revert faster to positive returns when positive returns generally persist longer. Asymmetry in both mean and variance can be seen on all included markets and are fairly similar. Volatility rises following negative returns more than following positive returns which is an indication of overreactions. Negative returns lead to increased variance and positive returns leads even to decreased variance.

Intraday Seasonalities and Macroeconomic News Announcements

Using a data set consisting of three years of 5-minute intraday stock index returns for major European stock indices and U.S. macroeconomic surprises, the conditional mean and volatility behaviors in European market were investigated. The findings suggested that the opening of the U.S market significantly raised the level of volatility in Europe, and that all markets respond in an identical fashion. Furthermore, the U.S. macroeconomic surprises exerted an immediate and major impact on both European stock markets’ returns and volatilities. Thus, high frequency data appear to be critical for the identification of news that impacted the markets.

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.

An Empirical Study of the Mixture of Time and Movements in Prices

This paper investigates the persistent pattern in the Helsinki Exchanges. The persistent pattern is analyzed using a time and a price approach. It is hypothesized that arrival times are related to movements in prices. Thus, the arrival times are defined as durations and formulated as an Autoregressive Conditional Duration (ACD) model as in Engle and Russell (1998). The prices are defined as price changes and formulated as a GARCH process including duration measures. The research question follows from market microstructure predictions about price intensities defined as time between price changes. The microstructure theory states that long transaction durations might be associated with both no news and bad news. Accordingly, short durations would be related to high volatility and long durations to low volatility. As a result, the spread will tend to be larger under intensive moments. The main findings of this study are 1) arrival times are positively autocorrelated and 2) long durations are associated with low volatility in the market.

Intraday and Weekend Volatility Patterns- Implications for Option Pricing

This study examines the intraday and weekend volatility on the German DAX. The intraday volatility is partitioned into smaller intervals and compared to a whole day’s volatility. The estimated intraday variance is U-shaped and the weekend variance is estimated to 19 % of a normal trading day. The patterns in the intraday and weekend volatility are used to develop an extension to the Black and Scholes formula to form a new time basis. Calendar or trading days are commonly used for measuring time in option pricing. The Continuous Time using Discrete Approximations model (CTDA) developed in this study uses a measure of time with smaller intervals, approaching continuous time. The model presented accounts for the lapse of time during trading only. Arbitrage pricing suggests that the option price equals the expected cost of hedging volatility during the option’s remaining life. In this model, time is allowed to lapse as volatility occurs on an intraday basis. The measure of time is modified in CTDA to correct for the non-constant volatility and to account for the patterns in volatility.

Volatility Smile Dynamics in Scenario Analysis

The objective of this paper is to suggest a method that accounts for the impact of the volatility smile dynamics when performing scenario analysis for a portfolio consisting of vanilla options. As the volatility smile is documented to change at least with the level of implied at-the-money volatility, a suitable model is here included in the calculation process of the simulated market scenarios. By constructing simple portfolios of index options and comparing the ex ante risk exposure measured using different pricing methods to realized market values, ex post, the improvements of the incorporation of the model are monitored. The analyzed examples in the study generate results that statistically support that the most accurate scenarios are those calculated using the model accounting for the dynamics of the smile. Thus, we show that the differences emanating from the volatility smile are apparent and should be accounted for and that the methodology presented herein is one suitable alternative for doing so.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.