The investment and financing instrument AT1, or Contingent Convertible bond, has become popular in the post-crisis capital markets, prompting interest and research in the academic world. The instrument's debt definition but equity boosting properties makes it rather extraordinary, and its stochastic features makes multiple mathematical valuation methodologies relevant, especially with regard to the risk of extending the call date of the instrument. With investors still relying on screening tools for valuation, there is an absence of applications using existing mathematical approaches. This report therefore aims to narrow the gap between academia and industry by evaluating the use of such mathematical approaches in a practical investment setting, in particular the Improved Credit Derivative approach and the Extension Premium Relative Value approach shall be examined. Both models strive to account for the extension risk, a commonly disregarded yet critical risk, adding computational challenges to the implementation. Besides from discovering necessary practical adjustments, and their effects, the two pricing approaches are compared in an attempt to confirm their joint purpose of accounting for extension risk. Ending up with varying results consisting of evident offsets for the improved credit derivative model but significant correlations in the case of the extension premium model, their individual performance was diverse while the hypothesis of joint behaviour could be dismissed. / Investerings- och finansieringsinstrumentet AT1, eller Contingent Convertible bond, har blivit populärt i kapitalmarknaderna efter finanskrisen, vilket lett till intresse och forskning i den akademiska världen. Instrumentets grund som skuld men egenskaper för att tillskjuta eget kapital gör det extraordinärt, och dess stokastiska funktioner öppar upp för flertalet värderingsmetoder, speciellt gällande förlängningsrisken hos datumet för kallning. Eftersom att investerare fortfarande använder sig utav screening-verktyg för värdering finns det endast begränsad forskning rörande användande av matematiska metoder. Denna rapport har därför som mål att minska avståndet mellan den akademiska världen och industrin genom att utvärdera användandet av sådana matematiska metoder för praktiska investeringar, särskillt skall Improved Credit Derivative och Extension Premium Relative Value metoderna användas. Båda modellerna strävar efter att ta hänsyn till förlängningsrisken, en risk vanligtvis bortsedd ifrån men trots det kritisk, vilket tillägger ytterligare beräkningsutmaningar vid implementationen. Bortsätt ifrån att upptäcka praktiska justeringar och dess effekter jämförs de två värderingsmetoderna i ett försök att bekräfta deras gemensamma syfte, att ta hänsyn till förlängningsrisken. Att i slutändan nå blandade resultat besående av uppenbara avvikelser för improved credit derivative modellen men starka korrelationer i fallet av extension premium modellen gjorde att man kunde dra slutsatsen att deras individuella prestanda skilde sig medan hypotesen om gemensamt beteende kunde avfärdas.

Contingent convertible bonds (often referred to as CoCo bonds, or simply CoCos) are a relatively new financial instrument designed to absorb unexpected losses. This instrument became increasingly more common after the financial crisis of 2008, as a way to decrease the risk of insolvency among banks and other financial institutions. In this thesis, we will investigate two mathematical models for valuation of CoCo bonds, known as the credit derivative approach and the equity derivative approach, previously developed by De Spiegeleer and Schoutens [1]. We will investigate how these models can be modified in order to be applied to a large set of bonds available on the market. The effect of parameter alterations will also be studied, in order to determine which parameters that influence the pricing accuracy the most. We reach the conclusion that by estimating market triggers, conversion prices and by computing a continuous interest rate from a discrete rates table, the models are indeed executable on a large set of bonds available on the market. However, these parameter estimations come at the cost of reduced accuracy. In general, both investigated models produces prices which follows the overall movements of the market prices quite well, but at the same time with a relatively large absolute distance from the market prices. In other words, the correlation with the market is often high, but the absolute error (measure by root mean square error) is often large. The sensitivity analysis of the parameters shows that the market trigger is the most influential parameter in both investigated models. The fact that we had to estimate the market trigger in order to be able to price a large number of bonds is believed to be the main cause of reduced accuracy. By utilizing a more bond-specific parameter estimation, the accuracy of the investigated models could most likely be improved. We can conclude that there is a trade-off between being able to price a large set of bonds with a mediocre accuracy, or being able to price a few bonds with high accuracy. / Det finansiella instrumentet contingent convertible bond (ofta benämnt CoCo bond, eller endast CoCo) är en relativt ny obligationstyp som används av banker och andra finansiella institutioner för att absorbera oväntade förluster. Instrumentet blev mer vanligt förekommande efter finanskrisen 2008, som ett sätt att minska risken för insolvens. I detta examensarbete undersöker vi två matematiska modeller för värdering av CoCo bonds, nämligen den så kallade credit derivative approach och equity derivative approach, som tidigare har utvecklats av De Spiegeleer och Schoutens [1]. Vi kommer att undersöka hur dessa modeller kan modifieras för att bli applicerbara på ett stort antal obligationer tillgängliga på marknaden. En omfattande parameterstudie kommer att genomföras, för att dra slutsatser kring de mest betydelsefulla parametrarna för prissättningen. Genom att skatta så kallade market triggers, conversion prices och en kontinuerlig ränta är det möjligt att exekvera de undersökta modellerna på ett stort antal obligationer. Dessa skattningar medför dock en viss försämrad noggrannhet. Generellt sett följer priserna från modellerna marknadens rörelser ganska väl, men är samtidigt ganska långt ifrån marknadspriset. Med andra ord är korrelationen hög, men absolutfelet är relativt stort. Parameterstudien visar att parametern som kallas market trigger är mest betydelsefull för prissättningen. Faktumet att vi måste skatta market triggers för att kunna prissätta ett stort antal obligationer tros vara den största anledningen till försämrad noggrannhet. Genom att använda en mer ”obligationsspecifik” skattning av parametrar bör noggrannheten kunna förbättras. I dessa modeller är det en tydlig avvägning mellan att kunna prissätta många obligationer med relativt låg noggrannhet, och att kunna prissätta få obligationer med hög noggrannhet.

This paper familiarizes the reader with contingent convertibles and their role in the current financial landscape. A contingent convertible is a security behaving like a bond in normal times, but that converts into equity or is written down in times of turbulence. The paper presents a few existing pricing approaches and introduces an extension to one of these, the equity derivatives approach, by letting the underlying asset follow a jump-diffusion process instead of a standard Geometrical Brownian Motion. The extension requires sophisticated computational techniques in order for the pricing to stay within reasonable time frames. Since market data is sparse and incomplete in this area, the validation of the model is not performed quantitatively, but instead supported by qualitative arguments.

Contingent convertible bonds are hybrid capital instruments, contingent on some form of indicator of financial distress of the issuing bank. Following the financial crisis, these instruments are proposed as a solution to the moral hazard issue of banks too big to fail. With the increased capital requirements of the Basel III directive, contingent capital enables banks to increase their capitalization without issuing expensive equity. Also, in times of historically low interest rates, these instruments might be interesting for investors in search of higher yields, as well as long term investors wanting to implement countercyclical investment strategies. However, due to the high complexity of these instruments, valuation has proven diffcult. The purpose of this thesis is to value instruments contingent on the bank's common equity tier 1 to risk-weighted assets ratio. We build our model upon the work of Glasserman & Nouri (2012), and extend it to include contingency on risk-weighted assets, instant non-continuous conversion to equity, and a combination of fixed imposed loss and fixed conversion price as terms of conversion. We use a capital structure model in continuous time to define asset dynamics, asset claims and the event of conversion and liquidation of the bank. Thereafter we use two important results from Glasserman & Nouri (2012) to value the discounted cash flows to holders of debt and contingent debt. From this, we arrive at closed form solutions for the coupon rates of these securities. / Contingent convertible bonds (villkoradeobligationer) är hybrida kapitalinstrument som beror på någon form av indikator på finansiell instabilitet i den emitterande banken. Efter finanskrisen har dessa finansiella produkter föreslagits som en lösning på dilemmat som uppstår när banker är för stora för att låtas gå omkull. Villkorade obligationer är en väg för banker att ta in kapital och uppfylla de ökade kapitalkrav som ställs av direktiven i Basel III utan att emittera kostsamt aktiekapital. I dessa tider av historiskt låga räntesatser är den relativt höga avkastning, tillsammans med de kontracykliska effekter produkterna ger dessutom intressanta för många investerare. Att värdera dessa produkter har dock visat sig svårt då de är mycket komplexa. Syftet med denna uppsats är att värdera villkorade obligationer som beror på relationen mellan bankens kärnprimärkapital och riskviktade tillgångar. Vi använder omvandling till aktiekapital som förlustabsorberingsmekanism och använder en kombination av fixerade konverteringspris och fixerade ålagda förluster som villkor för konversion. Vi använder en kapitalstrukturell modell i kontinuerlig tid för att definiera tillgångarnas rörelser, fordringar på tillgångarna och händelsen av konversion av kontraktet eller likvideringen av banken. Därefter använder vi två viktiga resultat från Glasserman & Nouri (2012) för att värdera de diskonterade kassaflöden till ägaren av obligationer och villkorade obligationer. Från detta hittar vi analytiska lösningar för storleken av kupongräntorna på obligationerna, villkorade som normala.

Ever since the great financial crisis of 2008 regulators have pushed toward more resilient banks, resulting in more demanding regulation and an increase of regulator’s insight and power. Through the revision of the BASEL framework, Contingent Convertible Bonds were introduced in 2010 as a part of regulatory capital and has since then grown increasingly popular. However, these instruments have never been tested in a stressed European financial system. Hence, there is no genuine information of how these instruments would behave. Neither have there been any published efforts in testing this through simulation, to the best of my knowledge. Using a temporally disaggregated augmentation of the EBA 2016 stress test, I simulate how the financial system would be affected by triggering the CoCos. Studying the implications of both low and high trigger instruments. Results indicate that there are low risks for a systemic fallout and showcases some notable differences as a result of CoCo design and type of trigger.

Submitted by Karina Cyganczuk Goes (karinagoes@uol.com.br) on 2014-06-06T20:34:21Z No. of bitstreams: 1 Estrutura de Capital e CoCos sob a otica de Basileia III - Um estudo empirico sobre o Brasil.pdf: 699008 bytes, checksum: 8646f039c659f7f9e7a793f98d9b1bf5 (MD5) / Approved for entry into archive by JOANA MARTORINI (joana.martorini@fgv.br) on 2014-08-19T14:19:50Z (GMT) No. of bitstreams: 1 Estrutura de Capital e CoCos sob a otica de Basileia III - Um estudo empirico sobre o Brasil.pdf: 699008 bytes, checksum: 8646f039c659f7f9e7a793f98d9b1bf5 (MD5) / Made available in DSpace on 2014-08-19T16:15:05Z (GMT). No. of bitstreams: 1 Estrutura de Capital e CoCos sob a otica de Basileia III - Um estudo empirico sobre o Brasil.pdf: 699008 bytes, checksum: 8646f039c659f7f9e7a793f98d9b1bf5 (MD5) Previous issue date: 2014-05-07 / It is a fact that banks worldwide maintain excess regulatory capital, either to minimize cost of recapitalization or to mitigate risks of financial difficulties. But only after the 2007/2008 crisis, the quality of that excess capital has been important to regulators, who proposed a new capital structure in the Basel III agreement, creating new hybrid bonds, the contingent convertible, whose main objective is to recapitalize the bank automatically in times of financial difficulties. In this context, we analyzed the 10 largest banks in Brazil in total assets, comparing the structure of each bank with straight bond, against the same structure with contingent convertible under the Basel III rules and without regulations or when they are fragile. The evidence suggests that, by the model, Brazilian banks were better capitalized with contingent convertible, than straight bond under Basel III rules, but in unregulated environments or where they are fragile, contingent convertibles induce increased risk and may lead to new financial crisis. / É fato, que os bancos do mundo inteiro mantêm excesso de capital regulatório, seja para minimizar custos de recapitalização, seja para mitigar riscos de dificuldades financeiras. Mas somente depois da crise de 2007/2008, a qualidade desse capital em excesso, passou a ganhar importância entre os órgãos reguladores, que propuseram uma nova estrutura de capital no Acordo de Basiléia III, criando novos instrumentos híbridos de capital e dívidas, os contingentes conversíveis, cujo principal objetivo é, recapitalizar o banco automaticamente em momentos de dificuldades financeiras. Neste contexto, analisamos os 10 maiores bancos do Brasil, em total de ativos, comparando a estrutura de cada banco com dívidas subordinadas, contra a mesma estrutura com contingentes conversíveis, sob as regra de Basiléia III e, em ambientes sem regulamentações ou quando estas são frágeis. As evidências sugerem que, segundo o modelo utilizado, os bancos brasileiros estariam mais bem capitalizados com contingentes conversíveis, do que com dívidas subordinadas sob as regras de Basiléia III, mas em ambientes sem regulamentação ou quando estas são frágeis, os contingentes conversíveis induzem o aumento de riscos, podendo levar a novas crises financeiras.