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Parameter Estimation in Stochastic Volatility Models Via Approximate Bayesian Computing
Parameter Estimation in Stochastic Volatility Models Via Approximate Bayesian Computing A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Achal Awasthi, B.S. Graduate Program in Department of Statistics The Ohio State University 2018 Master's Examination Committee: Radu Herbei,Ph.D., Advisor Laura S. Kubatko, Ph.D. c Copyright by Achal Awasthi 2018 Abstract In this thesis, we propose a generalized Heston model as a tool to estimate volatil- ity. We have used Approximate Bayesian Computing to estimate the parameters of the generalized Heston model. This model was used to examine the daily closing prices of the Shanghai Stock Exchange and the NIKKEI 225 indices. We found that this model was a good fit for shorter time periods around financial crisis. For longer time periods, this model failed to capture the volatility in detail. ii This is dedicated to my grandmothers, Radhika and Prabha, who have had a significant impact in my life. iii Acknowledgments I would like to thank my thesis supervisor, Dr. Radu Herbei, for his help and his availability all along the development of this project. I am also grateful to Dr. Laura Kubatko for accepting to be part of the defense committee. My gratitude goes to my parents, without their support and education I would not have had the chance to study worldwide. I would also like to express my gratitude towards my uncles, Kuldeep and Tapan, and Mr. Richard Rose for helping me transition smoothly to life in a different country. -
Multi-Period Public Transport Design: a Novel Model and Solution Approaches
S. Gelareh, S. Nickel Multi-period public transport design: A novel model and solution approaches Berichte des Fraunhofer ITWM, Nr. 139 (2008) © Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM 2008 ISSN 1434-9973 Bericht 139 (2008) Alle Rechte vorbehalten. Ohne ausdrückliche schriftliche Genehmigung des Herausgebers ist es nicht gestattet, das Buch oder Teile daraus in irgendeiner Form durch Fotokopie, Mikrofilm oder andere Verfahren zu reproduzieren oder in eine für Maschinen, insbesondere Datenverarbei tungsanlagen, ver- wendbare Sprache zu übertragen. Dasselbe gilt für das Recht der öffentlichen Wiedergabe. Warennamen werden ohne Gewährleistung der freien Verwendbarkeit benutzt. Die Veröffentlichungen in der Berichtsreihe des Fraunhofer ITWM können bezogen werden über: Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM Fraunhofer-Platz 1 67663 Kaiserslautern Germany Telefon: +49 (0) 6 31/3 16 00-0 Telefax: +49 (0) 6 31/3 16 00-10 99 E-Mail: [email protected] Internet: www.itwm.fraunhofer.de Vorwort Das Tätigkeitsfeld des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik ITWM umfasst anwendungsnahe Grundlagenforschung, angewandte Forschung sowie Beratung und kundenspezifische Lösungen auf allen Gebieten, die für Tech- no- und Wirtschaftsmathematik bedeutsam sind. In der Reihe »Berichte des Fraunhofer ITWM« soll die Arbeit des Instituts konti- nuierlich einer interessierten Öffentlichkeit in Industrie, Wirtschaft und Wissen- schaft vorgestellt werden. Durch die enge Verzahnung mit dem Fachbereich Ma- thematik der Universität Kaiserslautern sowie durch zahlreiche Kooperationen mit internationalen Institutionen und Hochschulen in den Bereichen Ausbildung und Forschung ist ein großes Potenzial für Forschungsberichte vorhanden. In die Be- richtreihe sollen sowohl hervorragende Diplom- und Projektarbeiten und Disser- tationen als auch Forschungsberichte der Institutsmitarbeiter und Institutsgäste zu aktuellen Fragen der Techno- und Wirtschaftsmathematik aufgenommen werden. -
Forecasting Security's Volatility Using Low-Frequency Historical Data
Forecasting security’s volatility using low-frequency historical data, high-frequency historical data and option-implied volatility Huiling Yuana, Yong Zhoub,c, Zhiyuan Zhangd, Xiangyu Cuid,∗ aSchool of Statistics and Information, Shanghai University of International Business and Economics. bInstitute of Statistics and Interdisciplinary Sciences and School of Statistics, Faculty of Economics and Management, East China Normal University. cAcademy of Mathematics and Systems Sciences, Chinese Academy of Sciences. dSchool of Statistics and Management, Shanghai University of Finance and Economics. Abstract Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security’s volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-Itˆo-OI model, we assume that the option-implied volatility can influence the security’s future volatility, and the option-implied volatility is treated as an observable exogenous variable. In GARCH- Itˆo-IV model, we assume that the option-implied volatility can not influence the security’s volatility directly, and the relationship between the option-implied volatility and the security’s volatility is constructed to extract useful information of the underlying security. After providing the quasi-maximum likelihood estimators for the parameters and establishing their asymptotic properties, we also conduct a series of simulation analysis and empirical analysis to compare the arXiv:1907.02666v1 [q-fin.ST] 5 Jul 2019 proposed models with other popular models in the literature. We find that when the sampling interval of the high-frequency data is 5 minutes, the GARCH-Itˆo-OI model and GARCH-Itˆo-IV model has better forecasting performance than other models. -
The Heston Model - Stochastic Volatility and Approximation -
B.Sc. Thesis The Heston Model - Stochastic Volatility and Approximation - Author Patrik Karlsson, [email protected] Supervisor Birger Nilsson (Department of Economics, Lund University) Abstract The crude assumption on log normal stock returns and constant volatility in the Black-Scholes model is a big constraint which constructs smile and skew inconsistent prices. The Heston model and its suggested approximation built on stochastic volatility are introduced and faced against the Black-Scholes model in hope of producing option prices where the smile and skew are taken into account.. As one will observe later on is that numerical calculation and approximation of the Heston model will provide us with more accurate calculations. Keywords Black-Scholes, Derivative Pricing, Heston, Monte Carlo, Volatility Smile. List of notation cdf - Normal cumulative density function. E [X] - Expected value of s.v. X. f (·) - Normal pdf. F (·) - Normal cdf. X Ft - Filtration, all information about X until time t. GBM - Geometric Brownian motion. K - Strike price. L - Likelihood function. MC - Monte Carlo. N (0; 1) - Normal distribution with mean 0 and variance 1. P - Historical measure. PDE - Partial differential equation. pdf - Probability density function. φ (·) - Normal pdf. Φ - Payoff. Π(S; t) - Derivative value, with underlying asset S at time t. Q - Risk neutral martingale measure. Rd - (d × 1) −dimensional real value. rt - Interest rate at time t. σ - Volatility. SDE - Stochastic differential equation. s.v. - Stochastic variable 3 St - Stock Value at time t. T - Time to maturity. θ- Parameter set. Θ - Parameter space. W - Wiener process, standard N (0; 1). ⊆ - Subset. - End of proof or derivation. -
126 FM12 Abstracts
126 FM12 Abstracts IC1 which happens in applications to barrier option pricing or Optimal Execution in a General One-Sided Limit structural credit risk models. In this talk, I will present Order Book novel adaptive discretization schemes for the simulation of stopped Lvy processes, which are several orders of magni- We construct an optimal execution strategy for the pur- tude faster than the traditional approaches based on uni- chase of a large number of shares of a financial asset over form discretization, and provide an explicit control of the a fixed interval of time. Purchases of the asset have a non- bias. The schemes are based on sharp asymptotic estimates linear impact on price, and this is moderated over time by for the exit probability and work by recursively adding dis- resilience in the limit-order book that determines the price. cretization dates in the parts of the trajectory which are The limit-order book is permitted to have arbitrary shape. close to the boundary, until a specified error tolerance is The form of the optimal execution strategy is to make an met. initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is Peter Tankov set to match the order book resiliency. At the end of this Universit´e Paris-Diderot (Paris 7) period, another lump purchase is made, and following that [email protected] there is again a period of purchasing continuously at a rate set to match the order book resiliency. At the end of this second period, there is a final lump purchase. -
Valuing a European Option with the Heston Model Yuan Yang
Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 5-10-2013 Valuing a European option with the Heston model Yuan Yang Follow this and additional works at: http://scholarworks.rit.edu/theses Recommended Citation Yang, Yuan, "Valuing a European option with the Heston model" (2013). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Valuing a European Option with the Heston Model Rochester Institute of Technology School of Mathematical Sciences College of Science Applied & Computational Mathematics Program Master’s Thesis Applicant‟s Name: Yuan Yang Proposed Defense Date: 05/10/2013 Advisor‟s Name: Dr. Bernard Brooks Committee Member 1: Dr. Raluca Felea Committee Member 2: Dr. James Marengo Graduate Program Director: Dr. Tamas Wiandt - 1 - Valuing a European Option with the Heston Model Valuing a European Option with the Heston Model A thesis present by Yuan Yang to The School of the Mathematical Sciences in partial fulfillment of the requirements for the degree of Master of Science in the subject of Applied and Computational Mathematics Rochester Institute of Technology Rochester, New York May 2013 - 2 - Valuing a European Option with the Heston Model Abstract In spite of the Black-Scholes (BS) equation being widely used to price options, this method is based on a hypothesis that the volatility of the underlying is a constant. -
GARCH Option Pricing Models and the Variance Risk Premium
Journal of Risk and Financial Management Article GARCH Option Pricing Models and the Variance Risk Premium Wenjun Zhang 1,* and Jin E. Zhang 2 1 Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland 1142, New Zealand 2 Department of Accountancy and Finance, Otago Business School, University of Otago, Dunedin 9054, New Zealand; [email protected] * Correspondence: [email protected] Received: 3 February 2020; Accepted: 4 March 2020; Published: 9 March 2020 Abstract: In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models. Keywords: GARCH option-pricing models; stochastic volatility; the CBOE VIX; variance risk premium JEL Classification: G13; C52 1. Introduction In this paper, we modify the local risk-neutral valuation relationship (mLRNVR) in the GARCH option-pricing models. The GARCH option-pricing model was first introduced by Duan(1995) with a locally risk-neutral valuation relationship (LRNVR), in which the conditional variances and model parameters remained the same under the physical measure and the risk-neutral measure. -
Surname First Name Chip Number Wave Number Day Wave Time A
Surname First name Chip Number Wave Number Day Wave Time A Kyte Joscelyne 6554 48 Sunday 08:40 Abbott Andrew 2293 11 Saturday 10:40 Abbott Damien 5895 43 Sunday 07:50 Abbott Steve 5142 38 Sunday 07:10 Abbotts Laura 7060 51 Sunday 09:10 Abbotts Richard 7155 52 Sunday 09:20 Abbouda Iklam 1756 7 Saturday 10:00 Abellan Manuel 7156 52 Sunday 09:20 Abello Lozano Albert 7014 51 Sunday 09:10 Abington Jeremy 3387 21 Saturday 12:40 Abington Stuart 3388 21 Saturday 12:40 Abolaban Fouad 5289 39 Sunday 07:15 Abraham Ian 7157 52 Sunday 09:20 Absolon Jonathan 1871 8 Saturday 10:10 Accardo Paolo 5450 40 Sunday 07:20 Achampong Benjamin 4702 32 Saturday 14:40 Acheson Graeme 4640 31 Saturday 14:20 Achilleos Stavria 5183 38 Sunday 07:10 Acker Anton 1067 2 Saturday 09:10 Ackerley Thomas 1354 4 Saturday 09:30 Ackrell Leanne 6555 48 Sunday 08:40 Acreman Charlie 5868 42 Sunday 07:40 Adair Conor 1743 7 Saturday 10:00 Adamindes Eros 2733 16 Saturday 11:30 Adams Edward 1069 2 Saturday 09:10 Adams Katherine 4865 34 Saturday 15:00 Adams Lewis 1070 2 Saturday 09:10 Adams Tom 4263 28 Saturday 13:50 Adams Will 5896 43 Sunday 07:50 Adams William 1068 2 Saturday 09:10 Adams William 7158 52 Sunday 09:20 Addicott Paul 1872 8 Saturday 10:10 Address Choose 3705 24 Saturday 13:10 Ademolu Kenny 5358 39 Sunday 07:15 Adepegba Victor 5515 40 Sunday 07:20 Adesanya Femi 7886 58 Sunday 10:40 Adeyeye Ifedayo 3297 20 Saturday 12:30 Adeyoola Seun 3706 24 Saturday 13:10 Adhikari Bhups 6911 50 Sunday 09:00 Adjaye Araba 4132 27 Saturday 13:40 Adler William 7159 52 Sunday 09:20 Adorisio-Hughes -
Cell Biology Annual Meeting Program
Cell Biology Annual Meeting Program Shirley Tilghman, President Julie Theriot, Program Chair Karen Oegema, Local Organizer ascb.org/2015meeting Search Your Smartphone App Store for ASCB2015 Submit Your Research Committed to Excellence, Rigor, and Breadth eNeuro has joined JNeurosci in the PubMed Central database. Learn more at SfN.org DON’T MISS OUT ON ANOTHER ISSUE! SUBSCRIBE Sign up now to receive FOR FREE* the monthly print magazine. TODAY! Each issue contains feature articles on hot new trends in science, profiles of top-notch researchers, reviews of the latest tools and technologies, and much, much more. * Only available for a limited time. Not all requests qualify for a free subscription. www.the-scientist.com/subscribe The Company of Biologists is a UK based charity and not-for-profit publisher run by biologists for biologists. The Company aims to promote research and study across all branches of biology through the publication of its five journals. Development Advances in developmental biology and stem cells dev.biologists.org Journal of Cell Science The science of cells jcs.biologists.org The Journal of Experimental Biology At the forefront of comparative physiology and integrative biology jeb.biologists.org Disease Models & Mechanisms Basic research with translational impact dmm.biologists.org Biology Open Facilitating rapid peer review for accessible research bio.biologists.org In addition to publishing, The Company makes an important contribution to the scientific community, providing grants, travelling fellowships and sponsorship -
Finn Lillelund Aachmann Eivind Aadland
PLOS ONE would like to thank all those who reviewed on behalf of the journal in 2015: Finn Lillelund Aachmann Yusuf Abba Eivind Aadland Nathlee Abbai Claus Aagaard Alexander Abbas Rasmus Aagaard Syed Abbas Philip Aagaard Ash Mohammad Abbas Eivind Aakhus Muhammad Abbas Ågot Aakra Ata Abbas Rob Aalberse Z. Abbas Lauri Aaltonen Aamir Abbas Mari Aaltonen James Abbas Eric Aamodt Faisal Abbas Håvard Aanes Saleem Abbasi Nikolaos Aantonakakis Ali Abbasi Ardalan Aarabi M. Kaleem Abbasi Jiska Aardoom Siddique Abbasi Julie Aarestrup S.A Abbasi Gloster Aaron Jennifer Abbass-Dick Erika Aaron Maggie Abbassi Shawn Aaron Jessica Abbate Philip Aaronson Mauro Abbate Scott Aaronson Giovanni Abbate-Daga Henk Aarts Souheila Abbeddou Jos Aarts Olivier Abbo Ellen Aasum Susan Abbondanzo Mohd Nadhir Ab Wahab Derek Abbott Jose Abad David H. Abbott Jorge Abad Jessica Abbott Francisca Abad William Abbott Eduardo Abade Sabra Abbott Fernando Abad-Franch Daniel Abbott Fitsum Abadi Andrew Abbott Javier Abadia Peter Abbott Valerie Abadie Gavin Abbott Tatjana Abaffy Giovanni Abbruzzese Grace Abakpa Sophie Abby Xesus Abalo Ekram Abd El Wahab Inmaculada Aban Ahmed Abd El Wahed Daniel Abankwa Aini Ismafairus Abd Hamid Jenny Abanto M Abdalla Federico Abascal Walid Abdallah Aniekan Abasiattai F Abdallah Zaid Abassi Mohamed Abdel Hakeem Solomon Abay Bahaa-Eldin Abdel Rahim Mohamed Abdelbary Keiko Abe Mohamed Abdel-Daim Takeru Abe Hesham Abdeldayem Nobuhito Abe Sonia Abdelhak Toshiaki Abe Asmaa Abdelhamid Hiroshi Abe Maha Abdelhaq Kensaku Abe Nasser Abdel-Latif Keietsu Abe Ahmad -
12Th International Ceramics Congress June 6-11, 2010
FINAL ANNOUNCEMENT Montecatini Terme, Tuscany, Italy 12th International Ceramics Congress June 6-11, 2010 5th Forum on New Materials June 13-18, 2010 CIMTEC2010 www.cimtec-congress.org CIMTEC 2010 JUNE 6 JUNE 7 JUNE 8 JUNE 9 JUNE 10 JUNE 11 Flowsheet A.M. P.M. A.M. P.M. A.M. P.M. A.M. P.M. A.M. P.M. A.M. P.M. REGISTRATION SYMPOSIUM CA CA CA CA CA CA CA CA SYMPOSIUM CB CB CB CB CB CB CB CB Focused Session CB-11 CB-11 CB-11 CB-11 CB-11 CB-11 CB-11 CB-11 Focused Session CB-12 CB-12 CB-12 CB-12 CB-12 CB-12 SYMPOSIUM CC CC CC CC SYMPOSIUM CD CD CD CD CD SYMPOSIUM CE CE CE CE CE CE CE CE SYMPOSIUM CF CF CF CF CF CF CF CF SYMPOSIUM CG CG CG CG CG CG CG CG SYMPOSIUM CH CH CH CH CH CH CH CH Focused Session CH-6 CH-6 CH-6 CH-6 CH-6 CH-6 CH-6 SYMPOSIUM CI CI CI CI CI CI CI CI SYMPOSIUM CJ CJ CJ CJ CJ CJ CJ CJ SYMPOSIUM CK CK CK CK CK CK CK CK SYMPOSIUM CL CL CL CL CL CL CONFERENCE CM CM CM CM CM CM CM CM PLENARY SESSION CONFERENCE CN CN CN CN CN CN CN INTERNATIONAL CERAMICS CONGRESS POSTER MOUNTING th POSTER DISCUSSION 12 SOCIALS OPENING CONCERT TOUR TO FLORENCE TOUR TO PISA CONFERENCE DINNER Invitation to attend SUMMARY th The 12 edition of the 12th International Ceramics Congress - Flowsheet .......................................................... -
Also in This Issue Gated Communities in Poland Report from Prussian
BALTIC A quarterly scholarly journal and news magazine. December 2012. Vol. V:3–4. 1 From the Centre for Baltic and East European Studies (CBEES) Book review: WO Södertörn University, Stockholm Naimark’s “Genocide” R LDS December 2012. Vol. V:3–4. BALTIC WORLDSbalticworlds.com Gated communities in Poland Modernizing marginal Russia Report from Prussian Posen Wolves in myth and reality Cities in the Baltic also in this issue Illustration: KG Nilson RUSSIAN HUMAN RIGHTS FIGHTERS / DISSIDENCE IN VILNIUS / BERLIN FASHION / KRAKÓW STREET ART / ANDREI PLEşU & JÜRGEN KOCKA short takes Encounter between East and West Painting “RUSSIAN CULTURE IN philosophy of language COVER ARTIST KG Nilson is EXILE (1921–1953)” was the and artistic expressionism a renowned Swedish paint- theme of a two-day confer- in the young, exiled Roman er who for several years ence at the Courtauld Insti- Jakobson. was a professor at the tute in London (November Robert Chandler, poet Royal Swedish Academy 2–3, 2012). The conference and translator of the likes of of Fine Arts. His studios are invitation was adorned with Alexander Pushkin, Nikolai in Stockholm (in the same an illustration for an article Leskov, Vasily Gross- apartment where Anders in Baltic Worlds (IV:3), writ- man, Andrei Platonov, and Zorn used to reside) and ten by Karl Schlögel, about Varlam Shalamov, gave in Bästekille, on Sweden’s Russian emigration to an address in which he southern Baltic shore. ≈ Berlin and the West. Karin showed how the question Sunvisson’s illustration is that Chernyshevsky once republished here. posed and Lenin tried to Conference organizer answer, Shto delat? (What Natalia Murray took the op- is to be done?), was kept portunity to launch a book, alive, albeit in an ironic way, The Unsung Hero of the in Russian émigré literary Russian Avant-Garde: The circles – in this case by Life and Times of Nikolay the writer Nadezhda Teffi Punin, on a key figure in (1872–1952).