We introduce a new insurance instrument allowing retirees to hedge against risk of mortality and risk of default. At retirement, the retiree is allowed to purchase an annuity that provides a defaultable income stream over his lifetime. The time of mortality and time of default are both uncertain, but are accompanied by determined hazard rates. The retiree will make consumption and investment choices throughout his lifetime, which have certain restrictions: the retiree can never enter a bankruptcy state (negative total wealth), and the investment choices are made in a risk-free financial instrument (such as a treasury bill or bond) and a risky instrument (such as commodities or stock). The retiree also makes insurance premium payments which hedge against mortality and default risks simultaneously. This new form of insurance is one which can be implemented by financial institutions as a means for retirees to protect their illiquid assets. In doing so, we calculate the optimal annuity rate a retiree should purchase to maximize his utility of consumption and bequest.Throughout the paper, we develop stochastic control models for a retiree's optimal investment and consumption policies over an uncertain planning horizon in several models which may or may not allow for insurance purchases. We find exact solutions to several models, and apply dynamic programming and the logarithmic transformation to other models to find numerical solutions when constraints are needed. We also analyze the effects of loading on insurance, analyzing the effects of more expensive insurance on the retiree's control policies and value functions. In particular, we will consider the model in which the retiree can purchase life insurance and credit default insurance (in the form of a credit default swap, or CDS) separately to hedge against life events. CDS's do not exist for annuities, but we extend this model by incorporating life insurance and the CDS into a single entity, which can be a viable, and realistic, option to hedge against risk. This model is beneficial in providing a solution to the annuity problem by showing that minimal annuity purchase is optimal.

In this paper dependence between credit default swap (CDS) values and stock price movements of the largest European banking groups is examined and effectiveness of the usage of CDS contracts as a tool to hedge exposure to the price movements of the underlying stock during the pre-crisis and crisis periods is assessed. The effectiveness is evaluated by comparing estimated Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures of portfolios consisting of stocks and CDS vis-à-vis portfolios consisting of only stocks. CDS are valued using mark-to-market approach. Marginal distributions of CDS value changes and stock returns are estimated using Kernel density estimate from historical time-series data of daily stock returns and CDS value changes. Dependence between marginal distributions is estimated using Gaussian, Gumbel and Student‟s t copulas. Random portfolio values are simulated using Monte Carlo Simulation from estimated copulas parameters and marginal distributions for daily, quarterly and yearly time horizons. VaR and ES with 90%, 95% and 99% confidence level are estimated from the simulated portfolio return distribution. The results show that there is a significant negative dependence between CDS values and stock prices during financial crisis while dependence is weak in the pre-crisis period. The main finding of the paper is that CDS added into the portfolio of stocks significantly reduces VaR and ES of a portfolio during the period of financial crisis while they... [to full text] / Šiame darbe tikrinama didţiausių Europos bankų grupių kredito rizikos apsikeitimo sandorių (CDS) ir akcijų kainų priklausomybė bei vertinamas CDS efektyvumas, jei jais draudţiamasi nuo akcijų kainų svyravimų prieš kriziniu ir kriziniu laikotarpiu. Efektyvumas yra įvertinamas lyginant apskaičiuotas rizikos vertes (VaR) ir tikėtinus vertės trūkumus (ES) dviejų portfelių: akcijų portfelio bei akcijų ir CDS portfelio. CDS vertinti yra naudojamas pagal rinką vertinimo būdas (mark-to-market approach). CDS verčių pasikeitimo ir akcijų grąţos ribiniai pasiskirstymai yra įvertinami, naudojant Kernel įvertinimą (Kernel Estimator) iš istorinių akcijų grąţų ir CDS verčių pokyčių duomenų. Priklausomybė tarp ribinių pasiskirstymų yra įvertinama naudojant Gauso, Gumbelio ir Studento t kopulas (copulas). Atsitiktinės portfelių vertės yra susimuliuojamos naudojant Monte Carlo simuliaciją, pritaikant kopulų parametrus bei kintamųjų ribinius pasiskirstymus vienos dienos, ketvirčio bei metų periodams. VaR ir ES su 90%, 95% ir 99% pasitikėjimo intervalais yra skaičiuojami iš susimuliuotų portfelio grąţų pasiskirstymo. Gauti rezultatai rodo, kad tarp akcijų kainų ir CDS verčių yra stipri priklausomybė krizės laikotarpiu, tuo tarpu prieš kriziniu laikotarpiu priklausomybė yra silpna. Pagrindinė darbo išvada yra ta, jog CDS įtraukti į akcijų portfelį reikšmingai sumaţina portfelio VaR ir ES kriziniu laikotarpiu, tačiau nesumaţina prieš kriziniu laikotarpiu. Portfelio rizika gali būti sumaţinta, jei... [toliau žr. visą tekstą]

Different capital regulatory requirements in the bank and insurer markets lead to finding and using of new more complex financial tools linked with capital release and subsequent optimization of the investment objectives, but they are also linked with promises and risk transfers that could cause a collapse or a systemic risk of the financial markets, as evidence by the recent financial crisis. The aim of my work is to examine the behavior of credit default swap spreads on the securitization and reinsurance markets, followed by analyzing arbitrage conditions between securitization and reinsurance markets by cointegration analysis. The thesis focuses on Italy because it is one of four main European players in the securitization market and it has highly developed bank and insurer markets. Moreover, it still faces to consequences of the recent financial crisis that is indicator of strong possible bases for above mentioned complex financial instruments. On the dataset of Top 8 Italian banks and insurer companies in the period 2006 - 2012 I showed by cointegration analysis a presence of just one cointegration relationship between securitization and reinsurance market, therefore I rejected possibility of arbitrage between these markets. But on the other hand, they converge to long term equilibrium slowly...

This thesis analyses long and short-term perception of announcements issued by leading credit rating agencies (Fitch, Moody's and S&P) in sovereign bond markets. Using three empirical approaches we assess the nature of impact of CRAs on 10Y sovereign bond yields and 5Y CDS of 24 countries of EU between 2002 and 2012. We find significant response of sovereign bond yield and CDS spreads to downgrades and negative outlooks. Furthermore there is evidence of anticipative power of sovereign bond markets in foreseeing negative events implying CRAs lag the market. The spillover effect from credit rating announcements has been revealed between both EMU and non-EMU parts of EU implying the financial integration is not limited only to countries with common currency. Well performing economies outside EMU are resistant to contagion. JEL Classification C23, F34, G10, G14, G15 Keywords credit rating; credit default swap; rating agency; sovereign bond; EU Author's e-mail tomhav@gmail.com Supervisor's e-mail roman.horvath@gmail.com

The paper is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of Brigo et al. 2012 and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The first-to-default Credit Default Swap (CDS) with multiple assets is priced when the default barrier is changing over time, which is contrast to the assumption in most of the structural-form models. The survival function of each asset follows the lognormal distribution and the interest rate is constant over time in this article. We define the joint survival function of these assets by employing the normal and Student-t copula functions to characterize the dependence among different default probability of each asset. In addition, we investigate the empirical evidences in the pricing of CDS with two or three companies by changing the values of parameters in the model. The more interesting results show that the joint default probability increases as these assets are more positive correlated. Consequently, the price of the first-to-default CDS is much higher.

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.

Universiẗat, Diss.--Linz, 2007.

Submitted by Guilherme Candido (gui0488@hotmail.com) on 2018-03-07T00:37:23Z No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2018-03-07T23:11:03Z (GMT) No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) / Made available in DSpace on 2018-03-08T13:03:44Z (GMT). No. of bitstreams: 1 Dissertação - Guilherme Amaral Candido.pdf: 2626690 bytes, checksum: 1e894027eeaf3360d910fb69a4a1f0b2 (MD5) Previous issue date: 2018-02-07 / Extensa literatura existe acerca de apreçamento de derivativos de crédito, em especial Credit Default Swaps, porém pouco foi discutido sobre o caso peculiar brasileiro, com convenções de taxas de juros e legislação específicas. Este trabalho foca na implementação de um modelo de intensidade, em particular o modelo padrão da ISDA, adaptado à um contrato de CDS no Brasil sobre um emissor corporativo. Spreads de Credit Default Swaps negociados no mercado offshore, yields de bonds e yields de debêntures foram utilizados como insumos para obtenção das taxas implícitas de intensidade de default e backtesting do modelo. Os dados utilizados compreendem o período de 2015 a 2017, englobando momentos de estresse relacionados à crise política brasileira. Algumas aplicações são, então, apresentadas, entre elas hedging, basis trading e estruturação de Credit Linked Notes. / Extensive literature exists on the pricing of credit derivatives, particularly Credit Default Swaps, yet little has been discussed about the distinctive Brazilian case, with specific legislation and interest rate conventions. This work aims to implement an intensity model, in particular the standard ISDA model, adapted to a CDS contract in Brazil on a corporate issuer. Spreads of Credit Default Swaps traded in the offshore market, offshore bond yields and local bond yields were used as inputs for obtaining the implicit hazard rates and for back testing the model. The data used cover the period from 2015 to 2017, including relevant moments of stress related to the Brazilian political crisis. Some applications are then presented, including hedging, basis trading and Credit Linked Notes structuring.