This thesis is focused on elimination of exchange rate risks as well as on possible ways how to ensure the risk, considering actuall situation in the Czech republic and expansive economical crisis in the year 2009. Mentioned is an overview of possible financial derivates and methods how to adapt them to export-oriented company. The work also includes an outline of a question how far the situation would be changed after launching euro.

The subject of the Master thesis „Financial Derivatives in Praxis“ is the analysis of the all kinds of financial derivates.The first part of the thesis deals with the general description of the derivates. In the next part of the thesis analysis of individual spices of derivates and their dividing into interest rate derivates and currency derivates is made. The final, practical part of the thesis, is devoted to the practical using of derivates in the hedging interest rate and currency risk on specific examples of companies and the offer of hedging on the Czech financial market.

Since the deregulation of the Nordic electricity market in 1996, electricity has become one of the most traded commodities in the Nordic region. The electricity price is characterized by large fluctuations as the supply and demand of electricity are seasonally dependent. The main interest of the hydro power producers is to assure that they can sell their hydro power at an attractive rate over time. This means that there is a demand for hedging against these fluctuations which in turn creates trading opportunities for third party actors that offer solutions between consumers and producers. Telge Krafthandel is one of these actors interested in predicting the future supply of hydro power, and consequently the resulting price of electricity. Several existing models employ the assumption of perfect foresight regarding the weather in the future. In this thesis, the authors develop new models for hydro power optimization that take hydrological uncertainty into account by implementing a variation of multi-stage optimization in order to maximize the income of the hydro power producers. The optimization is performed with respect to prices of financial derivatives on electricity. This gives insights into the expected supply of hydro power in the future which in turn can be used as an indicator of the price of electricity. The thesis also discusses, among other things, different methods for modeling stochastic inflow to the reservoirs and scenario construction. This practice will result in different methods that are suitable for various key players in the industry. / Sedan avregleringen av den Nordiska elmarknaden år 1996 har el blivit en av de mest handlade råvarorna i Norden. Elpriset karaktäriseras av stora svängningar eftersom utbudet och efterfrågan på el är säsongsberoende. Huvudintresset för vattenkraftsproducenter är att säkerställa att de kan sälja sin vattenkraft till ett attraktivt pris över tid. Detta innebär att det finns en efterfrågan för skydd mot dessa variationer, vilket i sin tur skapar affärsmöjligheter för tredjepartsaktörer som erbjuder lösningar mellan konsumenter och producenter. Telge Krafthandel är en av dessa aktörer och är därmed intresserad av att förutsäga det framtida utbudet på vattenkraft, och det resulterande elpriset. Flera befintliga modeller använder antagandet om perfekt förutseende när det gäller vädret i framtiden. I denna rapport utvecklar författarna nya modeller för vattenkraftsoptimering, som tar hänsyn till hydrologisk osäkerhet genom att implementera en variant av flerstegsoptimering för att maximera intäkterna för vattenkraftsproducenter. Optimeringen utförs med hänsyn till priserna på elderivat. Detta ger insikter i den förväntade tillgången på vattenkraft i framtiden, vilket i sin tur kan användas som en indikator på elpriset. I rapporten diskuteras också, bland annat, olika metoder för att modellera stokastiskt inflöde till vattenmagasinen och scenariokonstruktion. Detta kommer att leda till flera metoder som är lämpliga för olika aktörer i branschen.

The calibration of model parameters is a crucial step in the process of valuation of complex derivatives. It consists of choosing the model parameters that correspond to the implied market data especially the call and put prices. We discuss in this thesis the calibration strategy for the Heston model, one of the most used stochastic volatility models for pricing complex derivatives. The main problem with this model is that the asset price does not have a known probability distribution function. Thus we use either Fourier expansions through its characteristic function or Monte Carlo simulations to have access to it. We hence discuss the approximation induced by these methods and elaborate a calibration strategy with a focus on the choice of the objective function and the choice of inputs for the calibration. We assess that the put option prices are a better input than the call prices for the optimization function. Then through a set of experiments on simulated put prices, we find that the sum of squared error performs better choice of the objective function for the differential evolution optimization. We also establish that the put option prices where the Black Scholes delta is equal to 10\%, 25\%, 50\% 75\% and 90\% gives enough in formations on the implied volatility surface for the calibration of the Heston model. We then implement this calibration strategy on real market data of Eurostoxx50 Index and observe the same distribution of errors as in the set of experiments. / Kalibreringen av modellparametrar är ett viktigt steg i värderingen av komplexa derivat. Den består av att välja modellparametrar som motsvarar de implicita marknadsdata, särskilt köp- och säljpriserna. I denna avhandling diskuterar vi kalibreringsstrategin för Hestonmodellen, en av de mest använda modellerna för stokastisk volatilitet för prissättning av komplexa derivat. Huvudproblemet med denna modell är att tillgångspriset inte har en känd sannolikhetsfördelningsfunktion. Därför använder vi antingen Fourier-expansioner genom dess karakteristiska funktion eller Monte Carlo-simuleringar för att få tillgång till den. Vi diskuterar därför den approximation som dessa genereras av dessa metoder och utarbetar en kalibreringsstrategi med fokus på valet av målfunktion och valet av indata för kalibreringen. Vi bedömer att säljoptionspriserna är en bättre input än samtalspriserna för differentialutvecklingsoptimeringsfunktionen. Genom flera experiment med simulerade säljpriser finner vi sedan att summan av kvadratfel ger bättre val av objektivfunktionen för differentialutvecklingsoptimering. Vi konstaterar också att säljoptionspriserna där Black Scholes deltat är lika med 10\%, 25\%, 50\%, 75\% och 90\% ger tillräcklig information om den implicita volatilitetsytan för kalibrering av Hestonmodellen. Vi tillämpar sedan denna kalibreringsstrategi på verkliga marknadsdata för Eurostoxx50-indexet och observerar samma felfördelning som i experimenten.

The focus of this thesis is alternative methods used to determine transfer pricing in practice, mainly in the environment where there is a lack of available comparable information in the market. The paper is divided into four chapters. The first lists basic terminology, available relevant legislation and briefly outlines particular methods of determining a transfer pricing as recommended by OECD directives and the use of those. The second chapter focuses mostly on identifying of an interval for transfer pricing acceptable for tax authorities under a sale of an enterprise or its part. The third chapter mentions further alternative methods for which the underlying asset for determining of transfer price are financial derivatives. The last chapter discusses the results of carried out analyses and presents recommendations to using alternative methods. The thesis contents are supported by a designed computer program, which is a key element for using the alternative methods in practice.

差額互換是一種能提供投資人在不直接引起匯率風險的情況下，參與他國貨幣市場，以增加投資收益及降低資金成本的新金融商品。依照支付與計價貨幣的不同，可分為以本國貨幣、外國貨幣以及第三國貨幣為支付與計價貨幣三種不同的型態。由於Wei(1994)、唐英傑(1997)的定價模型僅評價出上述前兩種型態的差額互換，本研究的主要目的即為延續Wei(1994)的定價方法，評價出最一般化的差額互換，即本國與外國利率交換而以第三國貨幣為支付貨幣的差額互換，並且證明上述的兩種差額互換為此一般化差額互換的特例。三種差額互換詳細的評價過程均附於附錄，提供有興趣的讀者參考。 評價方法主要是分別計算本國與外國的現金流量，再以本國與外國的期望值折現到目前的時點，同時透過匯率效果將外國的期望值轉換為本國的期望值，於是可將每期所支付利息的現值整理為各國零息債券價格與相關參數的組合。 最後分別針對三種差額互換的評價結果與避險比率從事敏感度分析，以及嘗試由模擬數據探討評價與利差、到期日以及相關係數的關聯性，由模擬數據分析顯示以下結果： 1.利率隨機過程的風險市價並未直接出現在公式中，而隱含在各國的零息債券中。 2.國內的利率風險對差額互換的評價影響程度較國外大。 3.利率風險相較於匯率風險對評價影響更劇烈。 4.差額互換的評價中，利率與匯率的相關性風險比利率間的相關性風險所佔的份量更為吃重。 5.匯率主要是透過利率與匯率的相關係數來影響差額互換的評價。 6.差額互換的到期日越長，目前市場上的利差對評價的影響越小，尤其是以第三國貨幣為支付貨幣的差額互換。 7.契約訂定升水的絕對值會小於目前的利差的情況，僅在以本國貨幣為支付貨幣的差額互換發生，而其餘兩種差額互換則因被匯率風險所干擾，而無法直接從模擬數據中看出契約訂定升水能否反映兩國利率期間結構的相對性。 8.利率與匯率的相關性風險對差額互換評價的影響效果最明顯，其次為匯率間的相關性風險，利率間的相關性風險則居最末位。 此篇論文主要探討一般化的差額互換評價與避險，以及變數對差額互換評價與避險的影響。透過模擬數據的整理與分析，能讓我們對該新金融商品的特性與所面臨風險有更進一步的了解，以期在從事該商品的交易與操作更能得心應手。 第一章 緒論…………………………………………………………………1 第一節 研究動機與研究目的………………………………………………1 第二節 研究方法與研究架構………………………………………………2 第二章 差額互換概述………………………………………………………4 第一節 差額互換簡介………………………………………………………4 第二節 差額互換的產生動機………………………………………………6 第三節 差額互換的應用……………………………………………………8 第四節 差額互換的風險…………………………………………………14 第三章 文獻回顧……………………………………………………………16 第四章 理論模型與評價……………………………………………………18 第一節 理論模型假設……………………………………………………18 第二節 差額互換評價……………………………………………………19 第五章 差額互換避……………………………………………………27 第六章 模擬與相關問題探討………………………………………………32 第一節 參數變動對差額互換評價的敏感度分析………………………32 第二節 敏感度分析模擬總結……………………………………………35 第三節 問題探討…………………………………………………………36 第四節 避險比率相關模擬………………………………………………39 第七章 結論…………………………………………………………………40 附錄A…………………………………………………………………………41 附錄B…………………………………………………………………………44 附錄C…………………………………………………………………………50 附錄D…………………………………………………………………………57 附錄E…………………………………………………………………………65 附錄F…………………………………………………………………………67 附錄G…………………………………………………………………………69 附錄H…………………………………………………………………………75 參考書目與文獻……………………………………………………………100

Doctor Scientiae - DSc / Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the invention of the classical Black-Scholes formula to price the financial derivatives, a number of mathematical models have been proposed by numerous researchers in this direction. Many of these models are in general very complex, thus closed form analytical solutions are rarely obtainable. In view of this, we present a class of efficient spectral methods to numerically solve several mathematical models of pricing options. We begin with solving European options. Then we move to solve their American counterparts which involve a free boundary and therefore normally difficult to price by other conventional numerical methods. We obtain very promising results for the above two types of options and therefore we extend this approach to solve some more difficult problems for pricing options, viz., jump-diffusion models and local volatility models. The numerical methods involve solving partial differential equations, partial integro-differential equations and associated complementary problems which are used to model the financial derivatives. In order to retain their exponential accuracy, we discuss the necessary modification of the spectral methods. Finally, we present several comparative numerical results showing the superiority of our spectral methods.

Financial derivatives have been constituting one of the most dynamic fields in the mathematical finance. The main task is represented by the valuation or pricing of these instruments. This theses deals with standard models and their limits, tries to explore advanced methods of continuous martingale measures and on their bases proposes numerical methods applicable to derivatives valuation. Some procedures leading to elimination of certain simplifying assumptions are presented as well.

This thesis describes hedging transactions against foreign exchange rate risk which is a significant problem for a number of domestic companies trading with foreign partners. The objective of this paper is to characterize possible ways to eliminate or minimize a foreign exchange rate risk and to assess effects on economic results and liquidity of the company arising from the use of hedging instruments compared to the situation without hedging transactions. The practical analysis is shown on two Czech companies exposed to a foreign exchange rate risk. The analysis is focused on currency forwards negotiated with the bank and natural hedging in connection with an application of a hedge accounting.

Basic motive for the work comes out of the hypothesis of growing need of non-financial Czech companies to manage foreign exchange risk, which is demonstrated by foreign trade development. In the work, there are also specified basic species of entrepreneurial risks. Main attention of the writing is paid to currency hedging by finance derivatives, like futures, forwards, swaps and options. Single chapters are dedicated to their basic characteristics and to their function logic and, above all, to alternatives of their usage for currency hedging in different situations at Czech nonfinancial companies.