The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.

Modern aircraft are getting more and better sensors. As a result of this, the pilots are getting moreinformation than they can handle. To solve this problem one can automate the information processingand instead provide the pilots with conclusions drawn from the sensor information. An aircraft’smovement can be used to determine which class (e.g. commercial aircraft, large military aircraftor fighter) it belongs to. This thesis focuses on comparing three classification schemes; a Bayesianclassification scheme with uniform priors, Transferable Belief Model and a Bayesian classificationscheme with entropic priors.The target is modeled by a jump Markov linear system that switches between different modes (flystraight, turn left, etc.) over time. A marginalized particle filter that spreads its particles over thepossible mode sequences is used for state estimation. Simulations show that the results from Bayesianclassification scheme with uniform priors and the Bayesian classification scheme with entropic priorsare almost identical. The results also show that the Transferable Belief Model is less decisive thanthe Bayesian classification schemes. This effect is argued to come from the least committed principlewithin the Transferable Belief Model. A fixed-lag smoothing algorithm is introduced to the filter andit is shown that the classification results are improved. The advantage of having a filter that remembersthe full mode sequence (such as the marginalized particle filter) and not just determines the currentmode (such as an interacting multiple model filter) is also discussed.

Introduction: The National Hockey League Entry Draft Combine (NHLED Combine) is considered one of the toughest physical fitness tests an ice hockey player has to go through. The NHLED Combine consists of several fitness tests evaluating the athlete’s aerobic- and anaerobic capacity; lower body power, upper body strength and power, flexibility and anthropometrics; no lower body strength test are employed. Squats are the only exercise used by all National Hockey League (NHL) strength and conditioning coaches yet it is not included in the NHLED Combine. Purpose: The purpose of this study was to determine which off-ice test correlates best with on-ice performance measured as forward skating speed. We hypothesised that squat one repetition maximum (squat 1RM) would be a better or equal predictor of on-ice performance compared to the current NHLED Combine tests standing long jump (SLJ) and Wingate anaerobic test (WAnT). Method: Eleven male subjects, aged 17.8 ± 0.8 years, performed an on-ice sprint followed by the off-ice tests SLJ, WAnT and squat 1RM. Results: A correlation was found between sprint time on-ice and SLJ (r= -0,727, p= 0.006), Wingate anaerobic test mean power/ body weight (WAnT MP/BW) (r= -0,607, p= 0,024), squat 1RM (r= -0,600, p= 0.026) and squat 1 repetition maximum/body weight (squat 1RM/BW) (r= -0,609, p= 0.023). Conclusion: The results indicate that squat 1RM and squat 1RM/BW are equally good predictors of hockey performance as SLJ and WAnT MP/BW. / knäböj, hockey, is, nhl, skridskoåkning, skridskoskär, sprint, horisontalhopp, wingate, styrka, kraftutveckling, fystest

Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply. In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

In this thesis, we expand the option pricing and virtual asset model system by Cheng (2005) and include new simulations and maximum likelihood estimation of the parameter of the stochastic differential equations. For easy manipulation of general users, the interface of original option pricing system is modified. In addition, in order to let the system more completely, some stochastic models and methods of pricing and estimation are added. This system can be divided into three major parts. One is an option pricing system; The second is an asset model simulation system; The last is estimation system of the parameter of the model. Finally, the analysis for the data of network are carried out. The differences of the prices between estimator of this system and real market are compared.

Inference of regulatory relations in dynamical systems is a promising active research area. Recently, most of the investigations in this field have been stimulated by the researches in functional genomics. In this thesis, the inferential modeling problem for switching hybrid systems is studied. The hybrid systems refers to dynamical systems in which discrete and continuous variables regulate each other, in other words the jumps and flows are interrelated. In this study, piecewise linear approximations are used for modeling purposes and it is shown that piecewise linear models are capable of displaying the evolutionary characteristics of switching hybrid systems approxi- mately. For the mentioned systems, detection of switching instances and inference of locally linear parameters from empirical data provides a solid understanding about the system dynamics. Thus, the inference methodology is based on these issues. The primary difference of the inference algorithm is the idea of transforming the switch- ing detection problem into a jump detection problem by derivative estimation from discrete data. The jump detection problem has been studied extensively in signal processing literature. So, related techniques in the literature has been analyzed care- fully and suitable ones adopted in this thesis. The primary advantage of proposed method would be its robustness in switching detection and derivative estimation. The theoretical background of this robustness claim and the importance of robustness for real world applications are explained in detail.

In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

A Constant Proportion Debt Obligation is a credit derivative which has been introduced to generate a surplus return over a riskless market return. The surplus payments should be obtained by synthetically investing in a risky asset (such as a credit index) and using a linear leverage strategy which is capped for bounding the risk. In this thesis, we investigate two approaches for investigation of constant proportion debt obligations. First, we search for an optimal leverage strategy which minimises the mean-square distance between the final payment and the final wealth of constant proportion debt obligation by the use of optimal control methods. We show that the optimal leverage function for constant proportion debt obligations in a mean-square sense coincides with the one used in practice for geometric type diffusion processes. However, the optimal strategy will lead to a shortfall for some cases. The second approach of this thesis is to develop a pricing formula for constant proportion debt obligations. To do so, we consider both the early defaults and the default on the final payoff features of constant proportion debt obligations. We observe that a constant proportion debt obligation can be modelled as a barrier option with rebate. In this respect, given the knowledge on barrier options, the pricing equation is derived for a particular leverage strategy.

Day-ahead spot electricity markets are the most transparent spot markets where one can find integrated supply and demand curves of the market players for each settlement period. Since it is an indicator for the market players and regulators, in this thesis we model the spot electricity prices. Logarithmic daily average spot electricity prices are modeled as a summation of a deterministic function and multi-factor stochastic process. Randomness in the spot prices is assumed to be governed by three jump processes and a Brownian motion where two of the jump processes are mean reverting. While the Brownian motion captures daily regular price movements, the pure jump process models price shocks which have long term effects and two Ornstein Uhlenbeck type jump processes with different mean reversion speeds capturing the price shocks that affect the price level for relatively shorter time periods. After removing the seasonality which is modeled as a deterministic function from price observations, an iterative threshold function is used to filter the jumps. The threshold function is constructed on volatility estimation generated by a GARCH(1,1) model. Not only the jumps but also the mean reverting returns following the jumps are filtered. Both of the filtered jump processes and residual Brownian components are estimated separately. The model is applied to Austrian, Italian, Spanish and Turkish electricity markets data and it is found that the weekly forecasts, which are generated by the estimated parameters, turn out to be able to capture the characteristics of the observations. After examining the future contracts written on electricity, we also suggest a decision technique which is built on risk premium theory. With the help of this methodology derivative market players can decide on taking whether a long or a short position for a given contract. After testing our technique, we conclude that the decision rule is promising but needs more empirical research.