Abstract In today¡¦s worldwide economy, to stay competitive a company needs to take advantage of every opportunity to lower their costs, to increase margins and realize the saving that can come from doing business overseas. Today trillions of dollars in the currencies trade everyday in markets around the world. The currency markets are considered to be one of the most efficient markets. As companies dealing with import and export, they have exposure to currencies risk. The increasing difficulty in understanding exchange rate determination has led to for corporations how to approach the currency hedging decision. The importance of financial and operational hedges as tools for managing foreign-currency exposure is examined. In this thesis, the three basic methods for evaluating the currency risks are with the use of the spot rate method, the future rate method and the currency options. The results are summarized as follow: 1. In terms of currency exposure, the sport rate method leaves the currency exposure un-hedged. Futures and the options hedge technique are most widely used and the information to evaluate the use of these instruments as a hedging tool is readily available. Still, the less efficiency method is the future rate method. The most effective approach is the currency options, have the advantage of more flexibility than the future rate. 2. By comparison with the future rate and currency options, the future rate is determinate by swap point, the negative connotations attached to its disadvantage is the ¡§fixed currency rate¡¨. No matter the currency moves toward company¡¦s favor or unflavored, the funds to fulfill the forward contract will be exercised in maturity date. Other than the future rate hedge, the currency options are based upon the ¡§Buy Call¡¨. Within a certain period in the future, when currency rate is moving toward currency¡¦s profit or loss, the company could decide to exercise or give up the ¡§Buy Call¡¨. The difference is that the currency option hedge is determined by the ¡§Right to Exercise Buy Call¡¨ or ¡§Right No to Exercise Buy Call¡¨ which give company more flexibility in FX hedging. In conclusion, the re-thinking of currency hedging is conservative because it is single-mindedly focused on risk-reducing approaches to exchange rate risk management.

The use of currency options has been grown widely during the latest years. This paper tries to answer whether hedge strategies using currency options are superior to forward exchange contracts or not.

Little research has been done into implied correlations, and the small literature grows even smaller when referring to currency options. The existing literature has established that implied correlation is a good if not the best forecaster of future realized correlation, and that this ability to forecast is not necessarily universal. This paper will establish that the forecasting ability of implied correlations in currency options varies across currency pairs, thus proving that not all implied correlations are created equal. Using two different proxies for the quality of the forecaster, the paper attempts to explain which characteristics of an option on a currency pair affect the variation in forecasting ability.

Diploma thesis is focused on analysis and comparison using financial derivatives to hedge currency risk. The first part of the thesis describes instruments used for hedging: forex forwards, futures contracts and currency options. Those instruments are used for back-testing in analytical part, currency crosses used for back-testing are EUR/USD, EUR/GBP and GBP/USD. The main goal of this thesis is to evaluate the posibility of using them to hedge currency risk, comparison of their efectivity and application.

The world is getting more and more globalized and more countries choose to make business abroad today compared to only ten years ago. To establish abroad involves a lot of risks for a company and one important risk a company need to pay attention to is thecurrency risk. A corporation can be exposed to different kinds of currency risks and there is a lot of derivates to use when hedging against those risks. Which strategy or method a company uses is regulated in its financial policy, which constitutes an important part in the work against currency exposure. The main purpose of this dissertation is to investigate which currency hedging methods and derivates Swedish export companies are using when trading on the international market. Another part of the purpose is to explore if there is a difference between large and small companies when it comes to currency hedging and if there is, why there is a difference. To get the answers of the purpose a qualitative study were used and three intervjues with three companies of different sizes in the energy industry were made. The study also included one interview with an expert in the area of currency hedging. Together with theory and earlier studies the dissertation came to a conclusion. The conclusion of this study was that companies are using different derivates to protect themselves against currency risks and there is a difference between small and large companies in the hedging, mainly in the number of different derivates. Another conclusion that can be drawn was that warrants and futures is the most common derivates among swedish export companies which also is supported by theory and earlier studies. / Världen blir allt mer globaliserad och fler och fler länder väljer att röra sig utanför de nationella gränserna och göra affärer internationellt. Att etablera sig utomlands innebär många risker för ett företag och en viktig risk ett företag måste beakta vid handel internationellt är valutarisken. Ett företag kan bli exponerade mot olika typer av valutarisker och det finns flera instrument att använda sig av för att skydda sig mot dessa. Vilken metod ett företag använder sig av finns reglerat i företagens finanspolicy, vilken utgör en viktig del i arbetet mot valutaexponering. Syftet med uppsatsen är att undersöka vilka valutasäkringsmetoder och instrument svenska exportföretag använder sig av vidinternationell handel för att säkra sig mot valutarisker, samt undersöka om det skiljer sig i hur företag av olika storlek hanterar dessa risker. För att besvara vår frågeställning genomfördes forskningen genom en kvalitativ studie där tre stycken energiföretaget av olika storlek intervjuades. I studien intervjuades även en expert inom området och genom en jämförelse av empirin samt tidigare forskning kunde det dras en slutsats. Undersökningens slutsats var att företagen använder sig av flera olika metoder och instrument vid hanteringen av valutarisker. Den typ avvalutarisk de främst är utsatta för är transaktionsexponeringar på samtliga företag. Studien visade också att det skiljde sig i hur företagen av olika storlek hanterar dessa risker, främst i form av antalet instrument företagen använde sig av. En annan slutsats som kunde göras med en jämförelse av tidigare teori är att swappar och terminer är vanliga instrument medan optioner är ett mindre använt instrument för företag vid valutasäkring.

Subject of the submitted thesis is the issue of currency options. The aim is the detailed analysis of currency options forcefully on dealing, characteristics, methods of pricing and their use for hedging strategies. The first part of the thesis presents an introduction into the option theory. The second part is about dealing, pricing and arbitrage relationships of currency options. In this part are two option pricing model extracted -- the binomial options pricing model for pricing currency options and the Garman-Kohlhagen model for pricing European currency options. In the third part is an example for a currency put option hedging strategy.

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.

Submitted by Ricardo Consonni (ricardo.consonni@gmail.com) on 2011-09-09T12:42:48Z No. of bitstreams: 1 +Dissetacao RC 2011 - v1g - Revisado.pdf: 2814391 bytes, checksum: f5888f2effddf979aa33bd15b87760d2 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2011-09-09T13:14:56Z (GMT) No. of bitstreams: 1 +Dissetacao RC 2011 - v1g - Revisado.pdf: 2814391 bytes, checksum: f5888f2effddf979aa33bd15b87760d2 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2011-09-09T13:15:04Z (GMT) No. of bitstreams: 1 +Dissetacao RC 2011 - v1g - Revisado.pdf: 2814391 bytes, checksum: f5888f2effddf979aa33bd15b87760d2 (MD5) / Made available in DSpace on 2011-09-09T13:17:32Z (GMT). No. of bitstreams: 1 +Dissetacao RC 2011 - v1g - Revisado.pdf: 2814391 bytes, checksum: f5888f2effddf979aa33bd15b87760d2 (MD5) Previous issue date: 2011-08-12 / Este trabalho apresenta um modelo para determinação da superfície de volatilidades de um par de moedas cujas opções têm baixa liquidez, utilizando superfícies de volatilidade com maior liquidez, de pares de moedas em que as moedas estudadas sejam uma de suas componentes. Esse objetivo é atingido através da utilização de um modelo de volatilidade estocástica. A calibração de seus parâmetros é feita a partir dos valores de mercado de Butterfly Spreads e Risk Reversals dos pares de moedas líquidos. O trabalho contribui em relação à literatura no sentido de ampliar a cobertura de strikes e vencimentos considerados, permitindo que, tanto opções pouco líquidas e fora do dinheiro, como notas estruturadas com opções embutidas possam ser mais adequadamente apreçadas. / This work presents a model for determining the volatility surface of a currency pair whose options have low liquidity, using higher liquidity volatility surfaces of other currency pairs, in which the desired currencies are one of their components. This goal is achieved through the use of a stochastic volatility model. The calibration of its parameters is done from market values of the Butterfly Spreads and Risk Reversals of the liquid-currency pairs. This work contributes to the literature in an effort to broaden the scope of strikes and maturities considered, allowing for both illiquid and out of-the-money options, as well as structured notes with embedded options, to be more appropriately priced.