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3-Month Euribor Expectations and Uncertainty Using Option-Impliedprobability Densities

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3-Month Euribor Expectations and Uncertainty Using Option-Impliedprobability Densities 3 - month Euribor expectations and uncertainty using option - implied probability densities Josep Maria Puigvert ADVERTIMENT . La consulta d’aquesta tesi queda condicionada a l’acceptació de les següents condicions d'ús: La difusió d’aquesta tesi per mitjà del servei TDX ( www.tdx.cat ) i a través del Dipòsit Digital de la UB ( diposit.ub.edu ) ha estat autoritzada pels titulars dels drets de propietat intel·lectual únicament per a usos privats emmarcats en activitats d’investigació i docència. No s’autoritza la seva repr oducció amb finalitats de lucre ni la seva difusió i posada a disposició des d’un lloc aliè al servei TDX ni al Dipòsit Digital de la UB . No s’autoritza la presentació del seu contingut en una finestra o marc aliè a TDX o al Dipòsit Digital de la UB (frami ng). Aquesta reserva de drets afecta tant al resum de presentació de la tesi com als seus continguts. En la utilització o cita de parts de la tesi és obligat indicar el nom de la persona autora. ADVERTENCIA . La consulta de esta tesis queda condicionada a la aceptación de las siguientes condiciones de uso: La difusión de esta tesis por medio del servicio TDR ( www.tdx.cat ) y a través del Repositorio Digital de la UB ( diposit.ub.edu ) ha sido autorizada por los titulares de los derechos de propiedad intelectu al únicamente para usos privados enmarcados en actividades de investigación y docencia. No se autoriza su reproducción con finalidades de lucro ni su difusión y puesta a disposición desde un sitio ajeno al servicio TDR o al Repositorio Digital de la UB . No se autoriza la presentación de su contenido en una ventana o marco ajeno a TDR o al Repositorio Digital de la UB (framing). Esta reserva de derechos afecta tanto al resumen de presentación de la tesis como a sus contenidos. En la utilización o cita de par tes de la tesis es obligado indicar el nombre de la persona autora. WARNING . On having consulted this thesis you’re accepting the following use conditions: Spreading this thesis by the TDX ( www.tdx.cat ) service and by the UB Digital Repository ( diposit.ub.edu ) has been authorized by the titular of the intellectual property rights only for private uses placed in investigation and teaching activities. Reproduction with lucrati ve aims is not authorized n or its spreading and availability from a site foreign to the TDX service or to the UB Digital Repository . Introducing its content in a window or frame foreign to the TDX service or to the UB Digital Repository is not authorized (framing). Tho s e rights affect to the presentation summary of the thesis a s well as to its contents. In the using or citation of parts of the thesis it’s obliged to indicate the name of the author. 3-MONTH EURIBOR EXPECTATIONS AND UNCERTAINTY USING OPTION-IMPLIED PROBABILITY DENSITIES Doctoral thesis presented by Josep Maria Puigvert in the Doctoral Program of Mathematics and Informatics Directed by Dr. Josep Fortiana Gregori The doctoral candidate The director Barcelona, October 2015 3-month Euribor expectations and uncertainty using option-implied probability densities Author: Josep Maria Puigvert Gutierrez´ Advisor: Dr Josep Fortiana Gregori The views expressed in this doctoral thesis are the ones of the author and do not necessarily represent those of the European Central Bank. Text printed in Frankfurt am Main. First edition, October 2015 to Ramon and Maria Llu¨ısa to Eulalia,` Pau, Laia and Teo Preface This work aims to contribute to the study and interpretation of the 3-month Euribor risk-neutral option-implied probability density func- tions (PDFs). The focus is mainly on the study of daily options on 3-month Euribor futures, but the estimation is also extended to tick by tick data. This type of models have already been widely used in some other markets, like the equity and index markets, and several authors have already contributed to the existing literature. However, this work fo- cuses on the interest rate derivatives market and, in particular, on the Euribor one, which so far was rather unexplored. In particular, the study analyses Euribor options from the first trading date until the present time. Moreover, the study also focuses on how this type of functions reacted during periods of economic crisis, financial turbu- lences and around ECB Governing Council decisions. In addition, this works shows how this type of functions can also be used to forecast the Euribor futures rates by using real-world PDFs which are derived from risk-neutral PDFs. The ratio between the risk and the real-world PDFs, i.e. the state price densities, allows us also to analyse investor behaviours during different financial time periods. Hence, this works contributes not only to the analysis of the implied PDFs and their forecasts but also shows how this type of models can be used for monetary policy and financial stability purposes. i Acknowledgements The drafting of this thesis has been a rather long process and I am thankful to many people who have contributed to this final outcome. I initially started this thesis as a PhD. Student at the Institut Municipal d’Investigacio´ Medica´ (IMIM) in Barcelona. From this initial period, I am deeply in debt to Jordi Alonso, who gave me a PhD. grant and encouraged me to start this thesis in his Research department. I also would like to express my gratitude to all the wonderful colleagues I had during my stay at IMIM: Gemma, Berta, Eli, Miquel, Carmen, Josue,´ Montse, Antonia,` Olatz, Angels,` Sali, Sandra, Puri, Vladimir. I remember with true nostalgia the good times we spent together. I am also really thankful to Holger Neuhaus who, in fact, introduced me to the risk-neutral option-implied probability density functions, most probably without him all this work would not have been pos- sible. I also would like to express my gratitude to my three co-authors: Rupert, Olivier and Vesela. We have had many interesting discussions and we have enjoyed the time we spent while drafting our articles and preparing for international conferences. I have learnt a lot from the three of you and working with you has just been a true pleasure. I am very thankful to Juan Angel,´ who introduced me to two of my three co-authors and with whom I had many discussions on options data quality and how to further extend the implied-density functions to inflation options data. iii To all my European Central Bank colleagues with whom I discussed this topic over the years: Jean-Marc, Patrick, Bjorn,¨ Nicolas,` Enric, Pucho, Cristian, Enrique, Gemma and Andrej. Moreover, I cannot for- get Ron, who in addition of being an extraordinary colleague during the last year also helped me solving some doubts on LaTeX. I cannot forget to mention my thesis director, Josep Fortiana. Thank you for your patience, your guidance and the understanding of my fa- mily situation which has delayed the publication of this thesis. You have been truly a model director and an outstanding person. I very much appreciated the time we spent together in our first conference and the time you devoted to this thesis. To all my friends from Frankfurt and Barcelona who encouraged me to finish this thesis and for all the unforgettable moments we spent together. To my family in Barcelona, Par´ıs, Olot, Burgos, Madrid, Singapur and London for being such an important part of my life. Finally, I am truly thankful to my parents, this work is the result of their support and education over the years. In particular, to my father who passed away last year who I am sure would have been very proud of this. To Eulalia,` who after more than twenty years being together has given me all the support I needed to finalise this thesis. Finally to my three kids: Pau, Laia and Teo. I just hope that I manage to educate them as well as my parents did with me and that the four of you keep on being the sunshine of my life. Thank you! Gracies!` Gracias! Danke! Merci! Xie` xie!` Pep Puigvert April 2015 iv Contents Preface i Acknowledgements iii Contents v List of Figures ix List of Tables xi Abstract xiii I Introduction 1 1 Preliminary theory 3 1.1 Basic definitions . .3 1.2 Arrow-Debreu Securities . .6 1.3 Cox-Ross Theorem . .6 1.4 Breeden and Litzenberger Theorem . .7 1.5 Black and Scholes . 10 1.6 The Greeks . 12 2 Context 15 2.1 Literature review and methodology classification of option-implied probability density functions . 16 v CONTENTS 2.2 Methodology comparison of option-implied probability density func- tions . 20 2.3 Bliss and Panigirtzoglou method to estimate the option-implied probability density functions . 23 3 The Data 27 3.1 3-Months Euribor futures and options . 27 3.2 Volume analysis and out-of-the-money options . 31 3.3 Convexity and monotonicity . 34 4 Underlying methodology 37 4.1 Bliss-Panigirzoglou method . 37 4.1.1 Methodology description . 37 4.1.1.1 Delta, Sigma and Vega calculation . 38 4.1.1.2 Delta-Sigma space . 38 4.1.1.3 Back to premium strike space . 41 4.1.1.4 Option-implied probability density functions . 41 4.2 Fitting option-implied probability density functions for constant maturity contracts . 42 4.2.1 Constant maturity option-implied probability density func- tions . 43 4.3 Risk-neutral and real world option-implied probability density func- tions . 46 4.3.1 Risk neutrality assumption . 46 4.3.2 Real world option-implied probability density functions .
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