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.

La tesi mette a confronto l'universo delle riorganizzazioni nel Chapter 11 con i nuovi modelli di ristrutturazione concessi dalla riforma del diritto fallimentare. In modo particolare la tesi si sofferma sul mercato del controllo nella crisi di impresa. Negli Stati Uniti c'e' da tempo un mercato dei crediti sofferenti, mentre in Italia scontiamo ancora i ritardi del sistema economico. Il primo capitolo racconta i temi collegati al mercato del controllo nel Chapter 11: gli acquisti dei crediti nelle diverse classi creditorie, la nuova finanza concessa al debtor in possession, il controllo da covenant, la remunerazione degli amministratori con il debito, i derivati sul credito e il voto connesso. Il secondo capitolo si sofferma sull'interpretazione degli artt. 124 e 127 della legge fallimentare letti nell'ottica di un potenziale mercato del controllo nella crisi di impresa come nel caso del concordato con assunzione e si interroga infine sull'esenzione o meno da opa obbligatoria di tali operazioni alla luce dell'art. 106 TUF. / The thesis compares the world of Chapter 11 reorganizations with the new types of reorganizations introduced in Italy by the recent reform of bankruptcy law. In particular the thesis deals with the market for corporate control in the insolvency arena in both countries. In the States bankruptcy claims are traded on a regular basis whereas Italy still hasn't fully experienced transfers of control within the frame of a corporate reorganization. The first chapter focuses on all issues connected to US M&A in bankruptcy: acquisition of claims in the different classes, control rights in covenants, debtor-in-possession financing, pay for performance in bankruptcy, credit default swaps and empty voting. The second chapter focuses on the interpretation of articles 124 and 127 of the new Italian bankruptcy law which may lead to the creation of a market for corporate control within the frame of a composition with a third party buyer and discusses the potential applicability of mandatory bids pursuant to art. 106 TUF to such deals.

Since the global financial crisis of 2008, regulatory bodies worldwide have implementedincreasingly stringent requirements for measuring and pricing default risk in financialderivatives. Counterparty Credit Risk (CCR) serves as the measure for default risk infinancial derivatives, and Credit Valuation Adjustment (CVA) is the pricing method used toincorporate this default risk into derivatives prices. To calculate the CVA, one needs the risk-neutral Probability of Default (PD) for the counterparty, which is the centre in this type ofderivative.The traditional method for calculating risk-neutral probabilities of default involves constructingcredit curves, calibrated using the credit derivative Credit Default Swap (CDS). However,liquidity issues in CDS trading present a major challenge, as the majority of counterpartieslack liquid CDS spreads. This poses the difficult question of how to model risk-neutral PDwithout liquid CDS spreads.The current method for generating proxy credit curves, introduced by the Japanese BankNomura in 2013, involves a cross-sectional linear regression model. Although this model issufficient in most cases, it often generates credit curves unsuitable for larger counterpartiesin more volatile times. In this thesis, we introduce two Long Short-Term Memory (LSTM)models trained on similar entities, which use CDS spreads as input. Our introduced modelsshow some improvement in generating proxy credit curves compared to the Nomura model,especially during times of higher volatility. While the result were more in line with the tradedCDS-market, there remains room for improvement in the model structure by using a moreextensive dataset. / Ända sedan 2008 års finanskris har styrande finansiella organ ökat kraven för mätning ochprissättning av konkursrisk inom derivat. Ett område av särskilt högt intresse för detta arbete ärmotpartskreditrisker (CCR). I detta är Kreditvärdesjustering (CVA) den huvudsakliga metodenför prissättning av konkursrisk inom finansiella derivat och för att kunna få fram ett värde avCVA behövs en risk-neutral konkurssannolikhet (PD).En av de traditionella metoderna för att räkna ut denna sannolikhet är genom att skapakreditkurvor som sedan är kalibrerade utifrån CDS:ar. Detta handlade derivat (CDS) finns baraför ett mindre antal företag över hela världen vilket gör att en majoritet av marknaden saknaren tillräckligt handlad CDS. Lösning på detta är att ta fram proxy CDS för ett motsvarande bolag.Idag görs detta framförallt med en tvärsnitts-regressionsmodell som introducerades 2013 avden japanska banken Nomura. Den skapar i många fall rimliga kurvor men ett problem den harär att den oftare gör proxyn lägre än vad den borde vara.I detta arbete introducerar vi istället en LSTM modell som tränas på liknande företag. Resultatetav detta är att vi får en bättre modell i många fall för att skapa en proxy kurva men som delvishar liknande brister som Nomura modellen. Men med fortsatta undersökningar inom områdetsamt med mer data kan detta skapa en mer exakt och säkrare proxy modell.

本研究透過聯合系統與獨特風險綜合評估違約的強度，假設市場上經濟變數或資訊影響系統之違約強度，然若直接考慮所有經濟變數到模型中將可能會有共線性或維度過高之疑慮，因此透過狀態空間模型來設定狀態變數以及經濟變數之關係並將萃取三大狀態變數分別用以描述市場實質活動面、通貨膨脹以及信用環境。另外，將透過結構式模型來計算獨特性風險大小，當個別潛在的變數低於一定數值將導致個別的違約事件發生。而因布朗運動可能無法描述或校準市場上違約之鋒態以及偏態，將進一步考慮Variance Gamma過程用以更準確描述真實違約狀況。最後透過結合以上兩個風險綜合評估下，考慮一個聯合違約模型來評價信用違約交換之信用價差。 / Systematic and idiosyncratic risks are supposed to jointly trigger the default events. This paper identifies three fundamental risks to capture the systematic movement: real activity, inflation, and credit environment. Since most macroeconomic variables fluctuate together, the state-space model is imposed to extract the three variables from macroeconomic data series. In the idiosyncratic part, the structural model is applied. That is, idiosyncratic default is triggered by the crossing of a barrier. For improvement of the underlying lognormal distribution, we assume the process for the potential variable of the firm follows a Variance Gamma process, sufficient dimensions of which can fit the skewed and leptokurtic distributions. Under the specific setting of combinations of the two risks (the so-called joint default model), we price credit default swaps.

違約事件受到系統性風險與獨特性風險的綜合影響。本研究建構一狀態相依公司信用模型，該模型能反映出系統環境對市場造成的影響與個別公司獨特因子帶來的個別衝擊。 本模型透過從總體環境中萃取出的狀態變數來捕捉系統性變化，另外透過Variance Gamma過程來描繪個別公司的獨特因子帶來的影響。Variance Gamma過程可藉由調整分配的鋒態及偏態來調整布朗運動無法反映出的分配，以更貼近真實的市場訊息。 與縮減試模型相較之下，本模型無需參考信評機構的信用評等資訊，僅依賴市場上公開且透明的資訊，並且與結構式模型相同的是其富有經濟意涵。我們可以透過本模型來同時生成公司流動性危機發生機率與預期流動性危機造成的損失，進而利用本模型評價出個別公司信用違約交換的價格。 關鍵字：信用違約交換；系統風險；獨特性風險；狀態空間模型；Variance Gamma 過程 / Systematic and idiosyncratic risks are thought to affect the default events. This study develops a state-dependent corporate credit model that reflects both systematic movement and idiosyncratic shocks. To capture the systematic movement, the model extracts state factors from macroeconomics data. For the idiosyncratic part, the model applied Variance Gamma Process in depicting the potential variable of the firm by altering the distribution’s skewness and kurtosis. The model contains abundant economic significance as structural-form model does. Comparing to the reduced-form model, it does not rely on the information provided by rating agency but use information that is transparent and public. One can generate a firm’s probabilities of liquidity crisis and expected liquidity shortfalls endogenously and concurrently by employing the model. Credit derivative such as Single-name CDS can be priced under the model.

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as mth to default Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation (CDO). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events¿ probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the 'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading Copula Model'. Then the Lévy process has been applied through a number of proposed Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized Hyperbolic distribution. Numerically, the characteristic functions of the mth to default CDS's and (n/m) th to default CDS's number of defaults, the CDO's cumulative loss, and loss given default are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the proposed Very Fast form (VFFT). This technique through its fast and very fast forms reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and O(N ).

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as mth to default Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation (CDO). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events' probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the 'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading Copula Model'. Then the Lévy process has been applied through a number of proposed Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized Hyperbolic distribution. Numerically, the characteristic functions of the mth to default CDS's and (n/m) th to default CDS's number of defaults, the CDO's cumulative loss, and loss given default are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the proposed Very Fast form (VFFT). This technique through its fast and very fast forms reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and O(N ).

Cette thèse s'intéresse aux questions d'accès aux marchés financiers dans les économies émergentes et en développement. La première partie donne un aperçu général des conséquences macroéconomiques de l'un des régimes de politique monétaire le plus favorable au marché - le ciblage d'inflation - en utilisant le cadre d'analyse de la méta-analyse. La deuxième partie analyse le risque et la stabilité des marchés obligataires des États. La troisième et dernière partie examine les effets disciplinaires résultant de la participation aux marchés obligataires souverains. Plusieurs résultats émergent. Au chapitre 1, les résultats indiquent que la littérature sur les effets macroéconomiques du ciblage d'inflation est sujette à des biais de publication. Après avoir purgé ces biais, le véritable effet du ciblage d'inflation reste statistiquement et économiquement significatif à la fois sur le niveau de l'inflation et la volatilité de la croissance économique, mais ne l’est pas sur la volatilité de l'inflation ou le taux de croissance économique réel. Aussi, les caractéristiques des études déterminent l’hétérogénéité des résultats de l'impact du ciblage d’inflation dans les études primaires. Le chapitre 2 montre que l'adoption d'un régime de ciblage d'inflation réduit le risque souverain dans les pays émergents. Cependant, cet effet varie systématiquement en fonction du cycle économique, de la politique budgétaire suivie, du niveau de développement et de la durée dans le ciblage. Le chapitre 3 montre que les envois de fonds des migrants, contrairement aux flux d'aide au développement, permettent de réduire le risque souverain. Cette réduction est plus marquée dans un pays avec un système financier moins développé, un degré d'ouverture commerciale élevé, un espace budgétaire faible et sans effet dans les pays dépendants des envois de fonds. Le chapitre 4 montre que les pays ayant des contrats d’échange sur risque de crédit sur leurs dettes sont plus sujets à des crises de dette. Il constate également que cet effet reste sensible aux caractéristiques structurelles des pays. Le chapitre 5 montre que la participation aux marchés obligataires de long terme (domestiques et internationaux) encourage les gouvernements des pays en développement à accroître leurs recettes fiscales intérieures. Il révèle également que l'effet favorable dépend du niveau des recettes de seigneuriage, d’endettement, du régime de change, du niveau de développement économique, du degré d’ouverture financière, et du développement financier. Le chapitre 6 montre que la présence de marchés obligataires domestiques, de long terme et liquides réduit considérablement le degré de dollarisation financière dans les pays en développement. Cet effet est plus important dans les pays avec un régime monétaire de ciblage d’inflation ou de change flottant, et à règles budgétaires. Enfin, il constate que la présence de marchés obligataires domestiques réduit la dollarisation financière à travers la baisse du niveau et de la variabilité de l'inflation, de la variabilité du taux de change nominal, et des revenus de seigneuriage. / This thesis focuses on some critical issues of the access to international financial markets in developing and emerging market economies. The first part provides a general overview of the macroeconomic consequences of one of the most market-friendly monetary policy regime—inflation targeting—using a meta-regression analysis framework. The second part analyses government bond market risk and stability. The last part investigates the disciplining effects of government bond market participation—bond vigilantes. In Chapter 1, the results indicate that the literature of the macroeconomic effects of inflation targeting adoption is subject to publication bias. After purging the publication bias, the true effect of inflation targeting appears to be statistically and economically meaningful both on the level of inflation and the volatility of economic growth, but not statistically significant on inflation volatility or real GDP growth. Third, differences in the impact of inflation targeting found in primary studies can be explained by differences in studies characteristics including the sample characteristics, the empirical identification strategies, the choice of the control variables, inflation targeting implementation parameters, as well as the study period and some parameters related to the publication process. Chapter 2 shows that the adoption of inflation targeting regime reduces sovereign debt risk in emerging countries. However, this relative advantage of inflation targeting—compared to money or exchange rate targeting—varies systematically depending on the business cycle, the fiscal policy stance, the level of development, and the duration of countries’ experience with inflation targeting. Chapter 3 shows that remittances inflows significantly reduce bond spreads, whereas development aid does not. It also highlights that the effect of remittances on spreads arises in a regimes of lower developed financial system, higher degree of trade openness, lower fiscal space, and exclusively in non-remittances dependent regimes. Chapter 4 indicates that countries with credit default swaps contracts on their debts have a higher probability of experiencing a debt crisis, compared to countries without credit default swaps contracts. It also finds that the impact of credit default swaps initiation is sensitive to several structural characteristics including the level of economic development, the country creditworthiness at the timing of credit default swaps introduction, the public sector transparency, the central bank independence; and to the duration of countries’ experiences with credit default swaps transactions. Chapter 5 shows that bond markets participation encourages government in developing countries to increase their domestic tax revenue mobilization. Finally, it finds that bond markets participation improves the mobilization of internal taxes, compared to tax on international trade, and reduces their instability. Chapter 6 shows that the presence of domestic bond markets significantly reduces financial dollarization in domestic bond markets countries. This effect is larger for inflation targeting countries compared to non-inflation targeting countries, is apparent exclusively in a non-pegged exchange rate regime, and is larger when there is a fiscal rule that constrains the conduct of fiscal policy. Finally, it finds that the induced drop in inflation rate and its variability, nominal exchange rate variability, and seigniorage revenue are potential transmission mechanisms through which the presence of domestic bond markets reduces financial dollarization in domestic bond markets countries.

蒙地卡羅模擬是在組合信用風險的管理上相當實用的計算工具。衡量組合信用風險時，必須以適當的模型描述資產間的相依性。常態關聯結構是目前最廣為使用的模型，但實證研究認為 t 關聯結構更適合用於配適金融市場的資料。在本文中，我們採用 Bassamboo et al. (2008) 提出的極值相依模型建立 t 關聯結構用以捕捉資產之間的相關性。同時，為增進蒙地卡羅法之收斂速度，我們以 Chiang et al. (2007) 的重要性取樣法為基礎，將其拓展到極值相依模型下，並提出兩階段的重要性取樣技巧確保使用此方法估計一籃子信用違約時，所有模擬路徑均會發生信用事件。數值結果顯示，所提出的演算法皆達變異數縮減。而在模型自由度較低或是資產池較大的情況下，兩階段的重要性取樣法將會有更佳的估計效率。我們也以同樣的思路，提出用以估計投資組合損失機率的演算法。雖然所提出的演算法經過重要性取樣的技巧後仍無法使得欲估計的事件在所有模擬路徑下都會發生，但數值結果仍顯示所提出的方法估計效率遠遠優於傳統蒙地卡羅法。 / Monte Carlo simulation is a useful tool on portfolio credit risk management. When measuring portfolio credit risk, one should choose an appropriate model to characterize the dependence among all assets. Normal copula is the most widely used mechanism to capture this dependence structure, however, some emperical studies suggest that $t$-copula provides a better fit to market data than normal copula does. In this article, we use extremal depence model proposed by Bassamboo et al. (2008) to construct $t$-copula. We also extend the importance sampling (IS) procedure proposed by Chiang et al. (2007) to evaluate basket credit default swaps (BDS) with extremal dependence and introduce a two-step IS algorithm which ensures credit events always take place for every simulation path. Numerical results show that the proposed methods achieve variance reduction. If the model has lower degree of freedom, or the portfolio size is larger, the two-step IS method is more efficient. Following the same idea, we also propose algorithms to estimate the probability of portfolio losses. Althought the desired events may not occur for some simulations, even if the IS technique is applied, numerical results still show that the proposed method is much better than crude Monte Carlo.