Credit default swaptions (CDS options) are credit derivatives that are widely used by finan-cial institutions such as banks and hedging companies to manage their credit risk. These options are usually priced using Black-Scholes model, but the assumptions underlying this model do not always hold especially when solving complex financial problems. The proposed solution is to use numerical methods such as finite difference method (FDM) to approximate the solution of the Black-Scholes PDE in cases where closed form solutions cannot be obtained. The pricing of swaptions are important in financial markets, hence we specifically discuss the pricing of interest rate swaptions, CDS options, commodity swaptions and energy swap-tions using Black-Scholes model. Simple parabolic PDE known as heat equation given at (Higham, 2004) forms a foundations to understand the application of FDM when solving a PDE. Since, Black-Scholes PDE is also a parabolic equation it is transformed to a form of a heat equation (diffusion equation) by applying change of variables technique. FDM, specifically Crank-Nicolson method can be applied to the heat equation but in this dissertation it is applied directly to the Black-Scholes PDE to approximate its solution. Therefore, it is preferable to use Crank-Nicolson method because it is known to be second- order accurate, unconditionally stable, very flexible, suitable and can accommodate varia- tions in financial problems, (Duffy, 2008). The stability of this method is investigated using a matrix approach because it accommodates the effect of boundary conditions. To test the convergence of Crank-Nicolson method, it is compared with the Black-Scholes method used in (Tucker and Wei, 2005) to price CDS options. Conclusively the results obtained by Crank-Nicolson method to price CDS options are similar to those obtained using Black-Scholes method. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.

Credit default swaptions (CDS options) are credit derivatives that are widely used by finan-cial institutions such as banks and hedging companies to manage their credit risk. These options are usually priced using Black-Scholes model, but the assumptions underlying this model do not always hold especially when solving complex financial problems. The proposed solution is to use numerical methods such as finite difference method (FDM) to approximate the solution of the Black-Scholes PDE in cases where closed form solutions cannot be obtained. The pricing of swaptions are important in financial markets, hence we specifically discuss the pricing of interest rate swaptions, CDS options, commodity swaptions and energy swap-tions using Black-Scholes model. Simple parabolic PDE known as heat equation given at (Higham, 2004) forms a foundations to understand the application of FDM when solving a PDE. Since, Black-Scholes PDE is also a parabolic equation it is transformed to a form of a heat equation (diffusion equation) by applying change of variables technique. FDM, specifically Crank-Nicolson method can be applied to the heat equation but in this dissertation it is applied directly to the Black-Scholes PDE to approximate its solution. Therefore, it is preferable to use Crank-Nicolson method because it is known to be second- order accurate, unconditionally stable, very flexible, suitable and can accommodate varia- tions in financial problems, (Duffy, 2008). The stability of this method is investigated using a matrix approach because it accommodates the effect of boundary conditions. To test the convergence of Crank-Nicolson method, it is compared with the Black-Scholes method used in (Tucker and Wei, 2005) to price CDS options. Conclusively the results obtained by Crank-Nicolson method to price CDS options are similar to those obtained using Black-Scholes method. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.

In this thesis, the pricing of counterparty credit risk on an OTC plain vanilla interest rate swap is investigated. Counterparty credit risk can be defined as the risk that a counterparty in a financial contract might not be able or willing to fulfil their obligations. This risk has to be taken into account in the valuation of an OTC derivative. The market price of the counterparty credit risk is known as the Credit Value Adjustment (CVA). In a bilateral contract, such as a swap, the party’s own creditworthiness also has to be taken into account, leading to another adjustment known as the Debit Value Adjustment (DVA). Since 2013, the international accounting standards (IFRS) states that these adjustments have to be done in order to reflect the fair value of an OTC derivative. A short background and the derivation of CVA and DVA is presented, including related topics like various risk mitigation techniques, hedging of CVA, regulations etc.. Four different pricing frameworks are compared, two more sophisticated frameworks and two approximative approaches. The most complex framework includes an interest rate model in form of the LIBOR Market Model and a credit model in form of the Cox-Ingersoll- Ross model. In this framework, the impact of dependencies between credit and market risk factors (leading to wrong-way/right-way risk) and the dependence between the default time of different parties are investigated. / I den här uppsatsen har prissättning av motpartsrisk för en OTC ränteswap undersökts. Motpartsrisk kan definieras som risken att en motpart i ett finansiellt kontrakt inte har möjlighet eller viljan att fullfölja sin del av kontraktet. Motpartsrisken måste tas med I värderingen av ett OTC-derivat. Marknadspriset på motpartrisken är känt som Credit Value Adjustment (CVA). I ett bilateralt kontrakt, t.ex. som en swap, måste även den egna kreditvärdighet tas med i värderingen, vilket leder till en justering som är känd som Debit Value Adjustment (DVA). Sedan 2013 skall, enligt den internationella redovisningsstandarden (IFRS), dessa prisjusteringar göras vid redovisningen av värdet för ett OTC derivat. En kort bakgrund samt härledningen av CVA och DVA ar presenterade tillsammans med relaterade ämnen. Fyra olika metoder för att beräkna CVA har jämförts, två mer sofistikerade metoder och två approximativa metoder. I den mest avancerade metoden används en räntemodell i form av LIBOR Market Model samt en kreditmodell i form av en Cox-Ingersoll-Ross modell. I den här metoden undersöks även påverkan av CVA då det existerar beroenden mellan marknads

Market makers such as large banks are exposed to market risk in fixed income by acting as a counterparty for customers that enter swap contracts. This master thesis addresses the problem of creating a cost-effective hedge for a realistic swap book of a market maker in a multiple yield curve setting. The proposed hedge model is the two-stage stochastic optimisation problem created by Blomvall and Hagenbjörk (2020). Systematic term structure innovations (components) are estimated using six different component models including principal component analysis (PCA), independent component analysis (ICA) and rotations of principal components. The component models are evaluated with a statistical test that uses daily swap rate observations from the European swap market. The statistical test shows that for both FRA and IRS contracts, a rotation of regular principal components is capable of a more accurate description of swap rate innovations than regular PCA. The hedging model is applied to an FRA and an IRS swap book separately, with daily rebalancing, over the period 2013-06-21 to 2021-05-11. The model produces a highly effective hedge for the tested component methods. However, replacing the PCA components with improved components does not improve the hedge. The study is conducted in collaboration with two other master theses, each done at separate banks. This thesis is done in collaboration with Swedbank and the simulated swap book is based on the exposure of a typical swap book at Swedbank, which is why the European swap market is studied.

Denna uppsats behandlar vilka faktorer som påverkar svenska fastighetsbolags syn på ränteswappar och huruvida coronapandemin, IFRS regelverket, den nya referensräntan Swestr eller bolagens rating har någon betydelse i detta. Studien undersöker vidare hur stor efterfrågan på räntederivat tidigare har varit, samt hur framtidsutsikterna ser ut gällande användandet av ränteswappar. För att besvara studiens problemformulering har en kvalitativ metod använts, där fem semistrukturerade intervjuer med både fastighetsbolag och en bank varit utgångspunkten till arbetets slutsats. Studiens resultat visar att samtliga tillfrågade fastighetsbolag har en egen räntesäkringsstrategi och egna preferenser vad gäller räntederivat. Idag använder en klar majoritet av svenska fastighetsbolag ränteswappar i sina räntesäkringsstrategier, men studien tyder på att mindre aktörer på marknaden eventuellt i framtiden kommer söka sig till simplare lösningar. Vidare visar studien att varken coronapandemin, IFRS regelverket eller Swestr påverkar fastighetsbolagens förhållningssätt till ränteswappar. Däremot kan det externa ratingbetyget indirekt ha en koppling till hur ett fastighetsbolag väljer att hedga sig mot räntefluktuationer.  Studiens område är fortsatt vagt undersökt och ämnet kommer förbli intressant att forska vidare på i framtiden. / This study deals with the factors that affect Swedish real estate companies´ views on interest rate swaps and whether the corona pandemic, the IFRS regulations, the new reference interest rate Swestr or the companies external rating have any significance in this. The study further examines how the demand for interest rate swaps has changed and how the future looks like. To fulfill the purpose of the study, a qualitative method has been used, with five semi-structured interviews with both real estate companies and a bank. The collected answers have formed the basis of this paper's conclusion.  The results of the study show that all real estate companies surveyed have their own interest rate hedging strategy, and their own preferences on interest rate derivatives. A majority of Swedish real estate companies use interest rate swaps today in their interest rate hedging strategies, but this study indicates that smaller real estate corporations in the market may seek more simple solutions in the future. Furthermore, the study indicates that neither the coronavirus pandemic, the IFRS regulations nor Swestr has an impact in the real estate companies´ approach towards interest rate swaps. On the other hand, the external rating can indirectly be a reason why real estate companies choose to hedge with interest rate derivatives against interest rate fluctuations. The field of study is still vaguely researched and the subject will remain interesting to research in the future.

The output of this Master´s Thesis on the theme "Valuation of the company Tank ONO, s.r.o." is the estimation of market value of company as at the date of December 31, 2014, with the goal of selling off the company to a hypothetical general investor in the future. The theoretical part includes metodology and instruments used for company valuation, eg definition of main terms, explanation of valuation proces and methods, that are recognised as valid by specialised public. Afterwards, the second part (eg practical part) is aimed at applying the metodology in practice. First, the valuated company is shortly introduced and it is followed by financial and strategic analysis in order to evaluate the financial soundness and assess the perspective for company future. The conclusions of the above analysis are used for elaborating the value drivers and complex financial plan, that is followed by valuation of Tank ONO, s.r.o. In light of the company capital structure, there is chosen DCF equity method for final valuation, in this Thesis.