Abstract With the ever-increasing complexity of financial markets and financial products, many investors now choose to benefit from a manager’s expertise by investing in a fund. This fueled a rapid growth of the fund industry over the past decades, and the recent emergence of complex derivatives products written on underlying funds. The diversity (hedge funds, mutual funds, funds of funds, managed accounts…) and the particularities (liquidity, specific risks) of funds call for adapted models and suited risk management. This thesis aims at understanding the issues and difficulties met when dealing with such products. In particular, we will deal in a great extent with CPPI (Constant Proportion Portfolio Insurance) structures written on funds, which combine the specificities of funds with particularities of such structures. Correctly assessing the corresponding market risks is a challenging issue, and is the subject of many investigations.

Abstract In recent years we have witnessed how distress can spread quickly through the financial system and threaten financial stability. Hence there has been increased focus on developing systemic risk indicators that can be used by central banks and others as a monitoring tool. For Sveriges Riksbank it is of great value to be able to quantify the risks that can threaten the Swedish financial system CoVaR is a systemic risk measure implemented here with that with that purpose. CoVaR, which stands for conditional Value at Risk, measures a financial institutions contribution to systemic risk and its contribution to the risk of other financial institutions. The conclusion is that CoVaR can together with other systemic risk indicators help get a better understanding of the risks threatening the stability of the Swedish financial system.

examples - we need models for selecting a small subset of useful features from high-dimensional data, where the useful features are both rare and weak, this being crucial for e.g. supervised classfication of sparse high- dimensional data. A preceding step is to detect the presence of useful features, signal detection. This problem is related to testing a very large number of hypotheses, where the proportion of false null hypotheses is assumed to be very small. However, reliable signal detection will only be possible in certain areas of the two-dimensional sparsity-strength parameter space, the phase space. In this report, we focus on two families of distributions, N and χ2. In the former case, features are supposed to be independent and normally distributed. In the latter, in search for a more sophisticated model, we suppose that features depend in blocks, whose empirical separation strength asymptotically follows the non-central χ2ν-distribution. Our search for informative features explores Tukey's higher criticism (HC), which is a second-level significance testing procedure, for comparing the fraction of observed signi cances to the expected fraction under the global null. Throughout the phase space we investgate the estimated error rate, Err = (#Falsely rejected H0+ #Falsely rejected H1)/#Simulations, where H0: absence of informative signals, and H1: presence of informative signals, in both the N-case and the χ2ν-case, for ν= 2; 10; 30. In particular, we find, using a feature vector of the approximately same size as in genomic applications, that the analytically derived detection boundary is too optimistic in the sense that close to it, signal detection is still failing, and we need to move far from the boundary into the success region to ensure reliable detection. We demonstrate that Err grows fast and irregularly as we approach the detection boundary from the success region. In the χ2ν-case, ν > 2, no analytical detection boundary has been derived, but we show that the empirical success region there is smaller than in the N-case, especially as ν increases.

Basel II consists of international recommendations on banking regulations, mainly concerning how much capital banks and other financial institutions should be made to set aside in order to protect themselves from various types of risks. Implementing Basel II involves estimating risks; one of the main measurements is Probability of Default. Firm specific and macroeconomic risks cause obligors to default. Separating the two risk factors in order to define which of them affect the Probability of Default through the years. The aim of this thesis is to enable a separation of the risk variables in the structure of Probability of Default in order to classify the rating philosophy.

In his five books during 1990-2009, starting with Portfolio Management Formulas, Ralph Vince made accessible to mechanical traders with limited background in mathematics various important concepts in the field of money management. During this process, he coined and popularized the terms “optimal f" and “leverage space trading model." This thesis provides a sound mathematical understanding of these concepts, and adds various extensions and insights of its own. It also provides practical examples of how mechanical traders can use these concepts to their advantage. Although beneficial to all mechanical traders, the examples involve trading futures contracts, and practical details such as the back-adjustment of futures prices are provided along the way.

Abstract Today’s environmental reports contain flaws in the acquired data. This master thesis has the mission to alleviate the estimations of those flaws. The data in question, originates from Swedish industrial facilities. The thesis involves data-treatment by statistical analysis, which is done through fitting a model by the means of analysis of variance and multilevel modeling. The thesis also involves gathering and work with data from databases, as well as systematic treatment, sorting, categorization and evaluation of the data material. Calculations are made through the SAS statistical analysis program, which rendered estimates of fixed, linear and random effects. The results are presented through graphs and numerical estimates in the later part of the report. Calculations for estimations of the grand pollutant totals are conducted. These are compared to the observed data for relevance. Alternative ways on working on the problem at hand is discussed, as well as problems that have appeared during the work on the master thesis. The relevant code and calculations are attached towards the end. / Sammanfattning   Dagens miljörapportering har brister i den rapporterade datan. Examensarbetet har som avsikt att underlätta skattningen av den saknade datan i rapporteringen, vars data härstammar från svenska företagsutsläpp.   Arbetet innebär en databehandling via statistisk analys, vilken utförs genom modellanpassning via variansanalys och flernivåmodellering. Arbetet omfattar även hämtning och bearbetning av datamaterial ifrån databaser, så väl som systematisk behandling, sortering, indelning och tolkning av dataobservationer.   Beräkningar är utförda i SAS statistiska analysprogram, vilket renderat skattningar och representationer av termer till fasta, linjära och slumpartade effekter. Dessa presenteras med siffror och grafer i senare delen av rapporten. Skattning av totaler beräknas och jämförs med observerad data. Problem och alternativa angreppssätt diskuteras, samt kod och beräkningar bifogas.

Abstract  Spatially proximate amino acid positions in a protein tend to co-evolve, so a protein's 3D-structure leaves an echo of correlations in the evolutionary record. Reverse engineering 3D-structures from such correlations is an open problem in structural biology, pursued with increasing vigor as new protein sequences continue to fill the data banks. Within this task lies a statistical stumbling block, rooted in the following: correlation between two amino acid positions can arise from firsthand interaction, but also be network-propagated via intermediate positions; observed correlation is not enough to guarantee proximity. The remedy, and the focus of this thesis, is to mathematically untangle the crisscross of correlations and extract direct interactions, which enables a clean depiction of co-evolution among the positions. Recently, analysts have used maximum-entropy modeling to recast this cause-and-effect puzzle as parameter learning in a Potts model (a kind of Markov random field). Unfortunately, a computationally expensive partition function puts this out of reach of straightforward maximum-likelihood estimation. Mean-field approximations have been used, but an arsenal of other approximate schemes exists. In this work, we re-implement an existing contact-detection procedure and replace its mean-field calculations with pseudo-likelihood maximization. We then feed both routines real protein data and highlight differences between their respective outputs. Our new program seems to offer a systematic boost in detection accuracy.

Abstract Since different patients may have different causes of getting a disease, treating every patient having a certain disease in the same manner is not always be the best way to go. A treatment having effect in one type of patients may not have the same effect in a different type of patients. This makes it possible to partition a patient population into subpopulations in which a drug has distinct expected response. In this thesis the patient population is partitioned into two subpopulations where we have prior knowledge that one of them has a higher expected response to a drug than the other. Based on responses to a drug in Phase II, it has been analyzed in which of the populations Phase III should continue. The results show that the decision is highly dependent on the utility function on which the analysis is based. One interesting case is when the vast majority of the patient population belongs to the subpopulation with the higher expected response and a utility function that takes into account the prevalence of the populations. In that case the simulations show that when the difference in expected response between the subpopulations is large, it is a safer choice in continuing in Phase III in the subpopulation having the higher expected response than in the full population even though the expected utility will be less. This is an expected result which indicates that the approach used to model the situation studied in this report is reasonable

Abstract   An Asian option is a path-depending exotic option, which means that either the settlement price or the strike of the option is formed by some aggregation of underlying asset prices during the option lifetime. This thesis will focus on European style Arithmetic Asian options where the settlement price at maturity is formed by the arithmetic average price of the last seven days of the underlying asset. For this type of option it does not exist any closed form analytical formula for calculating the theoretical option value. There exist closed form approximation formulas for valuing this kind of option. One such, used in this thesis, approximate the value of an Arithmetic Asian option by conditioning the valuation on the geometric mean price. To evaluate the accuracy in this approximation and to see if it is possible to use the well known Black-Scholes formula for valuing Asian options, this thesis examines the bias between Monte-Carlo simulation pricing and these closed form approximate pricings. The bias examination is done for several different volatility schemes. In general the Asian approximation formula works very well for valuing Asian options. For volatility scenarios where there is a drastic volatility shift and the period with higher volatility is before the average period of the option, the Asian approximation formula will underestimate the option value. These underestimates are very significant for OTM options, decreases for ATM options and are small, although significant, for ITM options. The Black-Scholes formula will in general overestimate the Asian option value. This is expected since the Black-Scholes formula applies to standard European options which only, implicitly, considers the underlying asset price at maturity of the option as settlement price. This price is in average higher than the Asian option settlement price when the underlying asset price has a positive drift. However, for some volatility scenarios where there is a drastic volatility shift and the period with higher volatility is before the average period of the option, even the Black-Scholes formula will underestimate the option value. As for the Asian approximation formula, these over-and underestimates are very large for OTM options and decreases for ATM and ITM options. / Sammanfattning En Asiatisk option är en vägberoende exotisk option, vilket betyder att antingen settlement-priset eller strike-priset beräknas utifrån någon form av aggregering av underliggande tillgångens priser under optionens livstid. Denna uppsats fokuserar på Aritmetiska Asiatiska optioner av Europeisk karaktär där settlement-priset vid lösen bestäms av det aritmetiska medelvärdet av underliggande tillgångens priser de sista sju dagarna. För denna typ av option finns det inga slutna analytiska formler för att beräkna optionens teoretiska värde. Det finns dock slutna approximativa formler för värdering av denna typ av optioner. En sådan, som används i denna uppsats, approximerar värdet av en Aritmetisk Asiatisk option genom att betinga värderingen på det geometriska medelpriset. För att utvärdera noggrannheten i denna approximation och för att se om det är möjligt att använda den väl kända Black-Scholes-formeln för att värdera Asiatiska optioner, så analyseras differenserna mellan Monte-Carlo-simulering och dessa slutna formlers värderingar i denna uppsats. Differenserna analyseras utifrån ett flertal olika scenarion för volatiliteten. I allmänhet så fungerar Asiatapproximationsformeln bra för värdering av Asiatiska optioner. För volatilitetsscenarion som innebär en drastisk volatilitetsförändring och där den perioden med högre volatilitet ligger innan optionens medelvärdesperiod, så undervärderar Asiatapproximationen optionens värde. Dessa undervärderingar är mycket påtagliga för OTM-optioner, avtar för ATM-optioner och är små, om än signifikanta, för ITM-optioner. Black-Scholes formel övervärderar i allmänhet Asiatiska optioners värde. Detta är väntat då Black-Scholes formel är ämnad för standard Europeiska optioner, vilka endast beaktar underliggande tillgångens pris vid optionens slutdatum som settlement-pris. Detta pris är i snitt högre än Asiatisk optioners settlement-pris när underliggande tillgångens pris har en positiv drift. Men, för vissa volatilitetsscenarion som innebär en drastisk volatilitetsförändring och där den perioden med högra volatilitet ligger innan optionens medelvärdesperiod, så undervärderar även Black-Scholes formel optionens värde. Som för Asiatapproximationen så är dessa över- och undervärderingar mycket påtagliga för OTM-optioner och avtar för ATM och ITM-optioner.

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