Convertible bond underpricing in the french market : an empirical study

The pricing of convertible bonds is a fairly unstudied field of asset pricing due to the instruments’ complex nature and its niche character. The aim of this dissertation is to compute model implied prices for convertible bonds and compare it to their market value in order to determine whether the market truly underprices convertible bonds, a financial theory that has been discussed broadly in the academic community. As a pricing model I applied a Monte Carlo simulation for stock prices and determined the optimal exercise strategy through the Least-Squares method. With this methodology I priced 34 convertible bonds in the French market and obtained an average underpricing of 4.17%, which reduces to 2.72% when excluding outliers. The results align with previous conducted studies of the French market but are in contrast with some other empirical results in the United States, but due to the substantial difference in convertible bond markets worldwide a direct comparison is not appropriate. Although the finding supports the general claim of convertible bond underpricing and encourages investors to engage in hedging strategies, the lack of substantial research in the European market calls for further empirical studies and improvements of the work presented.A valorização de obrigações convertíveis é um campo muito pouco estudado da valorização de ativos devido à complexidade dos instrumentos e ao seu carácter de nicho. O objetivo desta dissertação é calcular os preços implícitos de obrigações convertíveis e compará-los com o seu valor de mercado a fim de determinar se o seu mercado está realmente subvalorizado, um fenómeno frequentemente descrito por outros autores. Como modelo de preços, apliquei uma simulação Monte-Carlo para os preços das ações e determinei a estratégia ótima de exercício através do método de Least-Squares. Com esta metodologia, fixei o preço de 34 obrigações convertíveis no mercado francês e obtive uma subvalorização média de 4,17%, que reduz para 2,72% ao excluir os outliers. Os resultados estão em linha com estudos anteriores realizados no mercado francês, mas contrastam com outros resultados empíricos nos Estados Unidos; no entanto, devido à diferença substancial nos mercados de obrigações convertíveis em todo o mundo, uma comparação direta não é apropriada. Embora a conclusão apoie a alegação geral de subvalorização de obrigações convertíveis e encoraje os investidores a adotar estratégias de cobertura, a falta de investigação substancial no mercado europeu requer mais estudos empíricos e melhorias do trabalho apresentado

Primal-dual methods for dynamic programming equations arising in non-linear option pricing

When discretizing non-linear pricing problems, one ends up with stochastic dynamic programs which often possess a concave-convex structure. The key challenge in solving these dynamic programs numerically is the high-order nesting of conditional expectations. In practice, these conditional expectations have to be replaced by some approximation operator, which can be nested several times without leading to exploding computational costs. In the first part of this thesis, we provide a posteriori criteria for validating approximate solutions to such dynamic programs. To this end, we rely on a primal-dual approach, which takes an approximate solution of the dynamic program as an input and allows the computation of upper and lower bounds to the true solution. The approach proposed here unifies and extends existing results and applies regardless of whether a comparison principle holds or not. The second part of this thesis establishes an iterative improvement approach for upper and lower bounds in the special case of convex dynamic programs. This approach allows the computation of tight confidence intervals for the true solution, even if the input upper and lower bounds stem from a possibly crude approximate solution to the dynamic program. The applicability of the presented approaches is demonstrated in various numerical examples.Die Diskretisierung nicht linearer Preisprobleme führt typischerweise zu stochastischen dynamischen Programmen, die eine konkav-konvexe Struktur aufweisen. Möchte man solche dynamischen Programme numerisch lösen, stellen die hochgradig verschachtelten bedingten Erwartungen die größte Herausforderung dar. In Anwendungen müssen diese bedingten Erwartungen mit Hilfe eines geeigneten Operators approximiert werden, der mehrfach angewendet werden kann, ohne zu explodierenden Rechenkosten zu führen. Im ersten Teil dieser Arbeit stellen wir Kriterien zur nachträglichen Validierung approximativer Lösungen solcher dynamischer Programme bereit. Dazu stützen wir uns auf einen primal-dualen Ansatz, der ausgehend von einer approximativen Lösung des dynamischen Programms die Konstruktion oberer und unterer Schranken an die wahre Lösung ermöglicht. Der hier vorgeschlagene Ansatz vereinheitlicht und verallgemeinert bisher bekannte Resultate und kann ungeachtet der Existenz eines Vergleichsprinzips genutzt werden. Der zweite Teil der Arbeit befasst sich mit einem iterativen Ansatz zur Verbesserung oberer und unterer Schranken im Spezialfall konvexer dynamischer Programme. Dieser Ansatz erlaubt die Konstruktion enger Konfidenzintervalle an die wahre Lösung, selbst wenn die gegebenen Schranken auf einer möglicherweise groben approximativen Lösung des dynamischen Programms beruhen. In verschiedenen numerischen Beispielen demonstrieren wir die Anwendbarkeit der vorgeschlagenen Ansätze

The valuation of collateralised debt obligations: multi-period modelling in a risk-neutral framework

For over fifty years, mortgages have been securitised by selling the rights to the mortgage cash flows to third party investors. Over the past ten years or so, a similar securitisation process has been undertaken with corporate debt. The claims on the cash flowing from the corporate debt portfolio are called collateralised debt obligations (CDO). CDO cash flows are dependent on the interaction of a portfolio of debt securities over many time periods. They are particularly sensitive to the correlation among the underlying secunties and to the terms of the indenture. While much progress has been made in modelling debt portfolios over a single period, there has been a lot less published about the interaction of debt secunties m a portfolio over many penods. This thesis develops a model for valuing CDOs using a nsk-neutral approach in a multiperiod setting. A model is also developed which reproduces Moody’s CDO rating. The Moody’s rating is compared to that which is implied from applying the nsk-neutral model, the differences analysed and the implications for regulatory capital for CDOs explored

Designing capital-ratio triggers for Contingent Convertibles

Contingent Convertible (CoCo) bonds represent a novel category of debt financial instruments, recently introduced into the financial landscape. Their primary role is to bolster financial stability by maintaining healthy capital levels for the issuing entity. This is achieved by converting the bond principal into equity or writing it down once the minimum capital ratios are violated. CoCos aim to recapitalize the bank before it is on the brink of collapse, to avoid a state bailout at a huge cost to the taxpayer. Under normal circumstances, CoCo bonds operate as ordinary coupon-paying bonds, which only in case of insufficient capital ratios are converted into equity of the issuer. However, the CoCo market has struggled to expand over the years, and the recent tumult involving Credit Suisse and its enforced CoCo write-off has underscored these challenges. The focus of this research work is on the first hand to understand the reasons for this failure, and, on the other hand, to modify its underlying design in order to restore its intended purpose: to act as a liquidity buffer, strengthening the capital structure of the issuing firm. The cornerstone of the proposed work is the design of a self-adaptive model for leverage. This model features an automatic conversion that does not hinge on the judgment of regulatory authorities. Notably, it allows the issuer's debt-to-assets ratio to remain within predetermined boundaries, where the likelihood of default on outstanding liabilities remains minimal. The pricing of the proposed instruments is difficult as the conversion is dynamic. We view CoCos essentially as a portfolio of different financial instruments. This treatment makes it easier to analyze their response to different market events that may or may not trigger their conversion to equity. We provide evidence of the model's effectiveness and discuss it implications of its implementation, in light of the regulatory environment and best market practices.Skilyrt breytanleg (e. Contingent Convertible, skammstafað CoCo) skuldabréf eru nýstárleg gerð af fjármálagerningum sem nýlega komu fram á sjónarsvið fjármálamarkaða. Helsta hlutverk þeirra er að e a fjármálastöðugleika með því að viðhalda hæfilegum eiginfjárgrunni fyrir útgefendur þeirra. Þetta er gert með því að umbreyta höfuðstól skuldabréfs í hlutafé eða með því færa þau niður þegar krafa um eiginfjárhlutföll eru rofin. CoCo hefur það markmið að endurfjármagna bankann áður en hann fellur og þar með koma í veg fyrir björgunaraðgerðir af hálfu ríkisins, sem hefur í för með sér mikinn kostnað fyrir skattgreiðendur. Undir venjulegum kringumstæðum virka CoCo skuldabréf eins og hefðbundin arðgreiðslu- skuldabréf, sem einungis er breytt í hlutafé þegar eiginfjárhlutföll útgefanda þeirra eru ekki nægjanleg. Eigi að síður hefur markaður fyrir CoCo átt erfitt uppdráttar í gegnum tíðina og hefur nýlegur titringur í kringum Credit Suisse og þvingaðar afskriftir þeirra á CoCo skuldabréfum ýtt enn frekar undir erfiðleikana. Helsti tilgangur þessarar rannsóknar er tvíþættur. Annars vegar er ætlunin að skilja hvers vegna CoCo hefur ekki átt meiri velgengni að fagna en raun ber vitni. Hins vegar er henni ætlað að breyta grundvallarhönnun CoCo í þeim tilgangi að endurheimta upprunalegan tilgang þeirra: sem er að vera stuðpúði lausafés sem styrkir fjármagnsskipan útgáfu fyrirtækisins. Hornsteinn verkefnisins er hönnun á líkani með sjálfaðlögunarhæfni með tilliti til skuldsetningarhlutfalls. Líkanið býr yfir sjálfvirkri umbreytingu sem ræðst því ekki af reglum eftirlitsyfirvalda. Það gerir útgefanda því kleift að viðhalda hlutfalli skulda á móti eignum innan fyrirfram skilgreindra marka, þar sem líkur á vanskilum vegna útistandandi skuldbindinga haldast í lágmarki. Verðlagning gerninganna sem lagðir eru til í rannsókninni er þó vandasöm þar sem umbreytingin er dýnamísk. Í meginatriðum verður litið á CoCos sem safn ólíkra fjármálagerninga. Með þessari aðferð er hægt að greina viðbrögð þeirra við mismunandi markaðsatburðum sem geta mögulega hrint af stað umbreytingu yfir í hlutafé. Sýnt verður fram á skilvirkni líkansins ásamt því að álykta um innleiðingu þess með tilliti til regluverks og bestu markaðsvenja.RU Research Fund Icelandic Research Fun