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.

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.

Bioremediation of diesel oil contaminated soil and water

Diesel spills contaminate aquatic and terrestrial environments. To prevent the environmental and health risks, the remediation needs to be advanced. Bioremediation, i.e., degradation by microbes, is one of the suitable methods for cleaning diesel contamination. In monitored natural attenuation technique are natural processes in situ combined, including bioremediation, volatilization, sorption, dilution and dispersion. Soil bacteria are capable of adapting to degrade environmental pollutants, but in addition, some soil types may have indigenous bacteria that are naturally suitable for degradation. The objectives for this work were (1) to find a feasible and economical technique to remediate oil spilled into Baltic Sea water and (2) to bioremediate soil contaminated by diesel oil. Moreover, the aim was (3) to study the potential for natural attenuation and the indigenous bacteria in soil, and possible adaptation to degrade diesel hydrocarbons. In the aquatic environment, the study concentrated on diesel oil sorption to cotton grass fiber, a natural by-product of peat harvesting. The impact of diesel pollution was followed in bacteria, phytoplankton and mussels. In a terrestrial environment, the focus was to compare the methods of enhanced biodegradation (biostimulation and bioaugmentation), and to study natural attenuation of oil hydrocarbons in different soil types and the effect that a history of previous contamination may have on the bioremediation potential. (1) In the aquatic environment, rapid removal of diesel oil was significant for survival of tested species and thereby diversity maintained. Cotton grass not only absorbed the diesel but also benefited the bacterial growth by providing a large colonizable surface area and hence oil-microbe contact area. Therefore use of this method would enhance bioremediation of diesel spills. (2) Biostimulation enhances bioremediation, and (3) indigenous diesel-degrading bacteria are present in boreal environments, so microbial inocula are not always needed. In the terrestrial environment experiments, the combination of aeration and addition of slowly released nitrogen advanced the oil hydrocarbon degradation. Previous contamination of soil gives the bacterial community the potential for rapid adaptation and efficient degradation of the same type of contaminant. When the freshly contaminated site needs addition of diesel degraders, previously contaminated and remediated soil could be used as a bacterial inoculum. Another choice of inoculum could be conifer forest soil, which provides a plentiful population of degraders, and based on the present results, could be considered as a safe non-polluted inoculum. According to the findings in this thesis, bioremediation (microbial degradation) and monitored natural attenuation (microbial, physical and chemical degradation) are both suitable techniques for remediation of diesel-contaminated sites in Finland.