This thesis considers the price and characteristics of an exotic option called the Volatility-Cap-Target-Level(VCTL) option. The payoff function is a simple European option style but the underlying value is a dynamic portfolio which is comprised of two components: A risky asset and a non-risky asset. The non-risky asset is a bond and the risky asset can be a fund or an index related to any asset category such as equities, commodities, real estate, etc. The main purpose of using a dynamic portfolio is to keep the realized volatility of the portfolio under control and preferably below a certain maximum level, denoted as the Volatility-Cap-Target-Level (VCTL). This is attained by a variable allocation between the risky asset and the non-risky asset during the maturity of the VCTL-option. The allocation is reviewed and if necessary adjusted every 15th day. Adjustment depends entirely upon the realized historical volatility of the risky asset. Moreover, it is assumed that the risky asset is governed by a certain group of stochastic differential equations called affine jump-diffusion models. All models will be calibrated using out-of-the money European call options based on the Deutsche-Aktien-Index(DAX). The numerical implementation of the portfolio diffusions and the use of Monte Carlo methods will result in different VCTL-option prices. Thus, to price a nonstandard product and to comply with good risk management, it is advocated that the financial institution use several research models such as the SVSJ- and the Seppmodel in addition to the Black-Scholes model. Keywords: Exotic option, basket option, risk management, greeks, affine jumpdiffusions, the Black-Scholes model, the Heston model, Bates model with lognormal jumps, the Bates model with log-asymmetric double exponential jumps, the Stochastic-Volatility-Simultaneous-Jumps(SVSJ)-model, the Sepp-model.

The very specific features of the spot prices, especially occurrence of severe jumps, create a spot price risk for retailers who purchase electricity at unregulated highly volatile prices but resell it to consumers at fixed price. Therefore, it is of high im- portance to forecast whether jump is likely to occur during the next hour. However, to the best of our knowledge, such research has not been devoted to the Czech power market yet. Therefore, the aim of this thesis is to forecast the jump occurrence in the Czech day-ahead market. For this purpose we suggest four logit model spec- ifications, each containing various independent variables (for example, electricity demand, outside temperature, lagged price and various dummy variables) where the variable selection is supported by the previous literature and by the characteristic features of the spot prices. Within the in-sample period we compare the suggested models based on the values of pseudo-R squared and Bayesian information criterion. When evaluating the out-of sample performance of suggested models we apply jump prediction accuracy and confidence, but opposed to the previous literature we sug- gest a kind of sensitivity analysis which, to the best of our knowledge, has not be proposed by any other power research. JEL Classification C25, C32, C51,...

We give an overview of recent progress in the research of hypergraph jumps -- a problem from extremal combinatorics. The number $\alpha \in [0, 1)$ is a jump for $r$ if for any $\epsilon > 0$ and any integer $m \ge r$ any $r$-graph with $N > N(\epsilon, m)$ vertices and at least $(\alpha + \epsilon) {N \choose r}$ edges contains a subgraph with $m$ vertices and at least $(\alpha + c) {m \choose r}$ edges, where $c := c(\alpha)$ does depend only on $\alpha$. Baber and Talbot \cite{Baber} recently gave first examples of jumps for $r = 3$ in the interval $[2/9, 1)$. Their result uses the framework of flag algebras \cite{Raz07} and involves solving a semidefinite optimization problem. A software implementation of their method is a part of this work.

Esse trabalho contempla o estudo sobre o estimador de mínimos quadrados obtido para sistemas lineares discretos sujeitos a ruídos aditivos e a ruídos multiplicativos em seus parâmetros. Supõe-se, adicionalmente, que os parâmetros do sistema estão sujeitos a saltos Markovianos, e que a cadeia de Markov não é conhecida. A solução do problema, sob essas hipóteses, é uma inovação apresentada nesse trabalho. Sob as mesmas hipóteses, o caso estacionário também foi contemplado, e o trabalho apresenta uma demonstração para a convergência da matriz de covariância dos erros do estimador a um valor estacionário, supondo-se estabilidade do sistema e ergodicidade da cadeia de Markov associada. Mostra-se, também, que existe uma única solução positiva semi-definida para a equação de Riccati estacionária e, ainda mais, que tal solução é o limite da matriz de covariância dos erros. A partir da introdução de uma hipótese adicional - de que os parâmetros do sistema estão sujeitos a incertezas na forma de politopos convexos - constrói-se um filtro linear dinâmico em que as iterações possuem estabilidade na média quadrática e que minimiza o limitante superior para o valor esperado do erro quadrático. Uma formulação do tipo LMI (Linear Matrix Inequalities) é proposta para a solução do problema. / This thesis deals with the linear filtering problem for discrete-time Markov jump linear systems with both additive and multiplicative noises. It is assumed that the values of the Markov chain are not available. This is the first time that a solution to the problem with these parameters is presented. By using some usual geometric arguments it is obtained a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the associated Lyapunov and Riccati like equations is presented. By adding an additional hypotesis - that the parameters of the systems are subject to convex polytopic uncertainties - it was designed a dynamic linear filter such that the closed loop system is mean square stable and minimizes an upper bound for the stationary expected value of the square error. A Linear Matrix Inequalities (LMI) formulation is proposed to solve the problem.

We analyze the relation between volatility spillovers and jumps in financial markets. For this, we compared the volatility spillover index proposed by Diebold and Yilmaz (2009) with a global volatility component, estimated through a multivariate stochastic volatility model with jumps in the mean and in the conditional volatility. This model allows a direct dating of events that alter the global volatility structure, based on a permanent/transitory decomposition in the structure of returns and volatilities, and also the estimation of market risk measures. We conclude that the multivariate stochastic volatility model solves some limitations in the spillover index and can be a useful tool in measuring and managing risk in global financial markets. / Analisamos a relação existente entre spillovers e saltos na volatilidade nos mercados financeiros. Para isso, comparamos o índice de spillover de volatilidade proposto por Diebold and Yilmaz (2009), com um componente de volatilidade global, estimado através de um modelo multivariado de volatilidade estocástica com saltos na média e na volatilidade condicional. Este modelo permite uma datação direta dos eventos que alteram a estrutura de volatilidade global, baseando-se na decomposição das estruturas de retorno e volatilidade entre efeitos permanentes/transitórios, como também a estimação de medidas de risco de mercado. Concluímos que este modelo resolve algumas das limitações do índice de spillover além de fornecer um método prático para mensurar e administrar o risco nos mercados financeiros globais.

The assessment of vertical jump performance is widely undertaken by coaches and sports scientists because of its strong relationship with sports performances including those in weightlifting, sprinting, and cycling. With the development of accelerometer based testing devices the traditional vertical jump field test may offer a more detailed evaluation of an athlete's performance capacity. However, little data are available on the reliability of this technology and the impact of sampling frequency on reliability. PURPOSE: To determine the reliability of accelerometer based performance measurements during countermovement vertical jumps and the influence of sampling frequency on reliability. METHODS: Ten college aged men (age = 23.6 ± 3.1 y; height = 180.1 ± 6.3 cm; mass = 85.0 ± 15.2kg; body fat = 14.2 ± 6.5%) performed two series of five restricted (no arm swing) zero load countermovement vertical jumps. During each jump a triaxial accelerometer that sampled at 500 Hz was used to assess acceleration, from which peak force (PF), rate of force development (RFD), peak power output (PP), peak velocity (PV), flight time (FT), and peak vertical displacement (VD) were derived and analyzed using a custom LabView Program. This program was used to re-sample the data collected at 500 Hz to 250Hz, 125 Hz and 50 Hz, which were then analyzed. The reliability of the accelerometer system was assessed with the use of intraclass correlations, while precision was determined with the use of the coefficient of variation (CV), and criterion validity was assessed via Pearsons correlation. RESULTS: At 500 Hz the accelerometer was reliable for PF (ICC = 0.94), RFD (ICC = 0.92), PP (ICC = 0.87), FT (ICC = 0.93), and VD (ICC = 0.93). Additionally, reliability was maintained at 250Hz for PF(0.95), RFD(0.92), PP(ICC = 0.86), FT(ICC = 0.93) and VD(ICC = 0.92). Good precision was determined for PF (CV = 7.3%), PV (CV = 7.6%), FT (CV = 2.3%), and VD(CV = 4.7%) at 500 Hz. Additionally precision was maintained at 250Hz for PF (CV = 6.8%), PV (CV = 7.7%), FT (CV = 2.4%), and VD(CV = 4.9%). Finally, criterion validity was high for PF(r = 0.96), RFD(r = 0.97), PP(r = 0.99), PV(r = 0.99), FT(r = 0.99) and VD(r = 0.99) when comparing the 250Hz data to the 500 Hz data. When sampling frequency was decreased below 250Hz reliability, precision and criterion validity all decreased. CONCLUSIONS: The accelerometer used in this investigation produced reliable, precise and valid for assessments of PF, PP, FT, and VD data at sampling frequencies ≥250Hz. PRACTICAL APPLICATIONS: For vertical jump applications it appears that accelerometers must have a minimum sampling frequency of 250Hz in order to maintain reliability, precision and validity. Therefore when assessing athlete performance, it is essential that the strength and conditioning professional consider sampling rate when utilizing this technology. ACKNOWLEDGMENTS: This investigation was partially supported by MyoTest Inc., which donated the accelerometer system used in this investigation.

Abstract available in the Annual coaches and Sport Science College.

Abstract available in the Annual Coaches and Sport Science College.

This thesis has applied the theory of real options to study forestry investment decision-making under stochastic timber prices. Suitable models have been developed for the stochastic timber prices, after addressing major issues in characterisation of the price process. First, the assumption of stochastic timber price process was based on detailed unit root tests, incorporating structural breaks in time-series analysis. The series was found to be stationary around shifting mean, justifying the assumption of mean reversion model. Due to shift in the mean, long-run mean to which the prices tended to revert could not be assumed constant. Accordingly, it was varied in discreet steps as per the breaks identified in the tests. The timber price series failed the normality test implying fat tails in the data. To account for these fat tails, ‘jumps’ were incorporated in the mean reversion model. The results showed that the option values for the jump model were higher than the mean reversion model and threshold levels for investment implied different optimal paths. Ignoring jumps could provide sub-optimal results leading to erroneous decisions. Second, the long-run mean to which prices reverted was assumed to shift continuously in a random manner. This was modeled through the incorporation of stochastic level and slope in the trend of the prices. Since the stochastic level and slope were not observable in reality, a Kalman-filter approach was used for the estimation of model parameters. The price forecasts from the model were used to estimate option values for the harvest investment decisions. Third, investment in a carbon sequestration project from managed forests was evaluated using real options, under timber price stochasticity. The option values and threshold levels for investment were estimated, under baseline and mitigation scenarios. Results indicated that carbon sequestration from managed forests might not be a viable investment alternative due to existing bottlenecks. Overall, the research stressed upon the need for market information and adaptive management, with a pro-active approach, for efficient investment decisions in forestry.

This thesis has applied the theory of real options to study forestry investment decision-making under stochastic timber prices. Suitable models have been developed for the stochastic timber prices, after addressing major issues in characterisation of the price process. First, the assumption of stochastic timber price process was based on detailed unit root tests, incorporating structural breaks in time-series analysis. The series was found to be stationary around shifting mean, justifying the assumption of mean reversion model. Due to shift in the mean, long-run mean to which the prices tended to revert could not be assumed constant. Accordingly, it was varied in discreet steps as per the breaks identified in the tests. The timber price series failed the normality test implying fat tails in the data. To account for these fat tails, ‘jumps’ were incorporated in the mean reversion model. The results showed that the option values for the jump model were higher than the mean reversion model and threshold levels for investment implied different optimal paths. Ignoring jumps could provide sub-optimal results leading to erroneous decisions. Second, the long-run mean to which prices reverted was assumed to shift continuously in a random manner. This was modeled through the incorporation of stochastic level and slope in the trend of the prices. Since the stochastic level and slope were not observable in reality, a Kalman-filter approach was used for the estimation of model parameters. The price forecasts from the model were used to estimate option values for the harvest investment decisions. Third, investment in a carbon sequestration project from managed forests was evaluated using real options, under timber price stochasticity. The option values and threshold levels for investment were estimated, under baseline and mitigation scenarios. Results indicated that carbon sequestration from managed forests might not be a viable investment alternative due to existing bottlenecks. Overall, the research stressed upon the need for market information and adaptive management, with a pro-active approach, for efficient investment decisions in forestry.