Annual Report
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Numerical Solution of Jump-Diffusion LIBOR Market Models
Finance Stochast. 7, 1–27 (2003) c Springer-Verlag 2003 Numerical solution of jump-diffusion LIBOR market models Paul Glasserman1, Nicolas Merener2 1 403 Uris Hall, Graduate School of Business, Columbia University, New York, NY 10027, USA (e-mail: [email protected]) 2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA (e-mail: [email protected]) Abstract. This paper develops, analyzes, and tests computational procedures for the numerical solution of LIBOR market models with jumps. We consider, in par- ticular, a class of models in which jumps are driven by marked point processes with intensities that depend on the LIBOR rates themselves. While this formulation of- fers some attractive modeling features, it presents a challenge for computational work. As a first step, we therefore show how to reformulate a term structure model driven by marked point processes with suitably bounded state-dependent intensities into one driven by a Poisson random measure. This facilitates the development of discretization schemes because the Poisson random measure can be simulated with- out discretization error. Jumps in LIBOR rates are then thinned from the Poisson random measure using state-dependent thinning probabilities. Because of discon- tinuities inherent to the thinning process, this procedure falls outside the scope of existing convergence results; we provide some theoretical support for our method through a result establishing first and second order convergence of schemes that accommodates thinning but imposes stronger conditions on other problem data. The bias and computational efficiency of various schemes are compared through numerical experiments. Key words: Interest rate models, Monte Carlo simulation, market models, marked point processes JEL Classification: G13, E43 Mathematics Subject Classification (1991): 60G55, 60J75, 65C05, 90A09 The authors thank Professor Steve Kou for helpful comments and discussions. -
CURRICULUM VITAE Anatoliy SWISHCHUK Department Of
CURRICULUM VITAE Anatoliy SWISHCHUK Department of Mathematics & Statistics, University of Calgary 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 Office: MS552 E-mails: [email protected] Tel: +1 (403) 220-3274 (office) home page: http://www.math.ucalgary.ca/~aswish/ Education: • Doctor of Phys. & Math. Sci. (1992, Doctorate, Institute of Mathematics, National Academy of Sciences of Ukraine (NASU), Kiev, Ukraine) • Ph.D. (1984, Institute of Mathematics, NASU, Kiev, Ukraine) • M.Sc., B.Sc. (1974-1979, Kiev State University, Faculty of Mathematics & Mechanics, Probability Theory & Mathematical Statistics Department, Kiev, Ukraine) Work Experience: • Full Professor, Department of Mathematics and Statistics, University of Calgary, Calgary, Canada (April 2012-present) • Co-Director, Mathematical and Computational Finance Laboratory, Department of Math- ematics and Statistics, University of Calgary, Calgary, Canada (October 2004-present) • Associate Professor, Department of Mathematics and Statistics, University of Calgary, Calgary, Canada (July 2006-March 2012) • Assistant Professor, Department of Mathematics and Statistics, University of Calgary, Calgary, Canada (August 2004-June 2006) • Course Director, Department of Mathematics & Statistics, York University, Toronto, ON, Canada (January 2003-June 2004) • Research Associate, Laboratory for Industrial & Applied Mathematics, Department of Mathematics & Statistics, York University, Toronto, ON, Canada (November 1, 2001-July 2004) • Professor, Probability Theory & Mathematical Statistics -
Introduction to Black's Model for Interest Rate
INTRODUCTION TO BLACK'S MODEL FOR INTEREST RATE DERIVATIVES GRAEME WEST AND LYDIA WEST, FINANCIAL MODELLING AGENCY© Contents 1. Introduction 2 2. European Bond Options2 2.1. Different volatility measures3 3. Caplets and Floorlets3 4. Caps and Floors4 4.1. A call/put on rates is a put/call on a bond4 4.2. Greeks 5 5. Stripping Black caps into caplets7 6. Swaptions 10 6.1. Valuation 11 6.2. Greeks 12 7. Why Black is useless for exotics 13 8. Exercises 13 Date: July 11, 2011. 1 2 GRAEME WEST AND LYDIA WEST, FINANCIAL MODELLING AGENCY© Bibliography 15 1. Introduction We consider the Black Model for futures/forwards which is the market standard for quoting prices (via implied volatilities). Black[1976] considered the problem of writing options on commodity futures and this was the first \natural" extension of the Black-Scholes model. This model also is used to price options on interest rates and interest rate sensitive instruments such as bonds. Since the Black-Scholes analysis assumes constant (or deterministic) interest rates, and so forward interest rates are realised, it is difficult initially to see how this model applies to interest rate dependent derivatives. However, if f is a forward interest rate, it can be shown that it is consistent to assume that • The discounting process can be taken to be the existing yield curve. • The forward rates are stochastic and log-normally distributed. The forward rates will be log-normally distributed in what is called the T -forward measure, where T is the pay date of the option. -
Some Mathematical Aspects of Market Impact Modeling by Alexander Schied and Alla Slynko
EMS Series of Congress Reports EMS Congress Reports publishes volumes originating from conferences or seminars focusing on any field of pure or applied mathematics. The individual volumes include an introduction into their subject and review of the contributions in this context. Articles are required to undergo a refereeing process and are accepted only if they contain a survey or significant results not published elsewhere in the literature. Previously published: Trends in Representation Theory of Algebras and Related Topics, Andrzej Skowro´nski (ed.) K-Theory and Noncommutative Geometry, Guillermo Cortiñas et al. (eds.) Classification of Algebraic Varieties, Carel Faber, Gerard van der Geer and Eduard Looijenga (eds.) Surveys in Stochastic Processes Jochen Blath Peter Imkeller Sylvie Rœlly Editors Editors: Jochen Blath Peter Imkeller Sylvie Rœlly Institut für Mathematik Institut für Mathematik Institut für Mathematik der Technische Universität Berlin Humboldt-Universität zu Berlin Universität Potsdam Straße des 17. Juni 136 Unter den Linden 6 Am Neuen Palais, 10 10623 Berlin 10099 Berlin 14469 Potsdam Germany Germany Germany [email protected] [email protected] [email protected] 2010 Mathematics Subject Classification: Primary: 60-06, Secondary 60Gxx, 60Jxx Key words: Stochastic processes, stochastic finance, stochastic analysis,statistical physics, stochastic differential equations ISBN 978-3-03719-072-2 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. -
Pricing Bermudan Swaptions on the LIBOR Market Model Using the Stochastic Grid Bundling Method
Pricing Bermudan Swaptions on the LIBOR Market Model using the Stochastic Grid Bundling Method Stef Maree,∗ Jacques du Toity Abstract We examine using the Stochastic Grid Bundling Method (SGBM) to price a Bermu- dan swaption driven by a one-factor LIBOR Market Model (LMM). Using a well- known approximation formula from the finance literature, we implement SGBM with one basis function and show that it is around six times faster than the equivalent Longstaff–Schwartz method. The two methods agree in price to one basis point, and the SGBM path estimator gives better (higher) prices than the Longstaff–Schwartz prices. A closer examination shows that inaccuracies in the approximation formula introduce a small bias into the SGBM direct estimator. 1 Introduction The LIBOR Market Model (LMM) is an interest rate market model. It owes much of its popularity to the fact that it is consistent with Black’s pricing formulas for simple interest rate derivatives such as caps and swaptions, see, for example, [3]. Under LMM all forward rates are modelled as individual processes, which typically results in a high dimensional model. Consequently when pricing more complex instruments under LMM, Monte Carlo simulation is usually used. When pricing products with early-exercise features, such as Bermudan swaptions, a method is required to determine the early-exercise policy. The most popular approach to this is the Longstaff–Schwartz Method (LSM) [8]. When time is discrete (as is usually the case in numerical schemes) Bellman’s backward induction principle says that the price of the option at any exercise time is the maximum of the spot payoff and the so-called contin- uation value. -
Approximations to the Lévy LIBOR Model By
Approximations to the Lévy LIBOR Model by Hassana Al-Hassan ([email protected]) Supervised by: Dr. Sure Mataramvura Co-Supervised by: Emeritus Professor Ronnie Becker Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town, South Africa A thesis submitted for the degree of Master of Science University of Cape Town May 27, 2014 The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non- commercial research purposes only. Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University of Cape Town Plagiarism Declaration “I, Hassana AL-Hassan, know the meaning of plagiarism and declare that all of the work in the thesis, save for that which is properly acknowledged, is my own”. SIGNED Hassana Al-Hassan, May 27, 2014 i Declaration of Authorship I, Hassana AL-Hassan, declare that this thesis titled, “The LIBOR Market Model Versus the Levy LIBOR Market Model” and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other quali- fication at this University or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly attributed. -
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. -
5, 2018 Room 210, Run Run Shaw Bldg., HKU
July 3 - 5, 2018 Room 210, Run Run Shaw Bldg., HKU Program and Abstracts Institute of Mathematical Research Department of Mathematics Speakers: Jiro Akahori Ritsumeikan University Guangyue Han The University of Hong Kong Yaozhong Hu University of Alberta Davar Khoshnevisan University of Utah Arturo Kohatsu-Higa Ritsumeikan University Jin Ma University of Southern California Kihun Nam Monash University Lluís Quer-Sardanyons Universitat Autònoma Barcelona Xiaoming Song Drexel University Samy Tindel Purdue University Ciprian Tudor Université Paris 1 Tai-Ho Wang Barach College, City University of New York Jing Wu Sun Yat-Sen University Panqiu Xia University of Kansas George Yuan Soochow University & BBD Inc. Jianfeng Zhang University of Southern California Xicheng Zhang Wuhan University Organizing Committee: Guangyue Han, Jian Song, Jeff Yao (The University of Hong Kong), Xiaoming Song (Drexel University) Contact: Jian Song ([email protected]), Xiaoming Song ([email protected]) July 3 - 5, 2018 Room 210, Run Run Shaw Bldg., HKU Time / Date July 3 (Tue) July 4 (Wed) July 5 (Thur) Arturo Davar 9:30 – 10:30 Jin Ma Kohatsu-Higa Khoshnevisan 10:30 – 10:50 Tea Break 10:50 – 11:50 Xicheng Zhang George Yuan Samy Tindel Lunch Break 14:00 – 15:00 Yaozhong Hu Jianfeng Zhang Jiro Akahori Lluís 15:10 – 16:10 Tai-Ho Wang Jing Wu Quer-Sardanyons 16:10 – 16:30 Tea Break 16:30 – 17:30 Kihun Nam Ciprian Tudor Xiaoming Song 17:30 – 18:30 Guangyue Han Panqiu Xia Jul 3, 2018 9:30 – 10:30 Jin Ma, University of Southern California Time Consistent Conditional Expectation -
Interest Rate Models: Paradigm Shifts in Recent Years
Interest Rate Models: Paradigm shifts in recent years Damiano Brigo Q-SCI, Managing Director and Global Head DerivativeFitch, 101 Finsbury Pavement, London Columbia University Seminar, New York, November 5, 2007 This presentation is based on the book "Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit" by D. Brigo and F. Mercurio, Springer-Verlag, 2001 (2nd ed. 2006) http://www.damianobrigo.it/book.html Damiano Brigo, Q-SCI, DerivativeFitch, London Columbia University Seminar, November 5, 2007 Overview ² No arbitrage and derivatives pricing. ² Modeling suggested by no-arbitrage discounting. 1977: Endogenous short-rate term structure models ² Reproducing the initial market interest-rate curve exactly. 1990: Exogenous short rate models ² A general framework for no-arbitrage rates dynamics. 1990: HJM - modeling instantaneous forward rates ² Moving closer to the market and consistency with market formulas 1997: Fwd market-rates models calibration and diagnostics power ² 2002: Volatility smile extensions of Forward market-rates models Interest rate models: Paradigms shifts in recent years 1 Damiano Brigo, Q-SCI, DerivativeFitch, London Columbia University Seminar, November 5, 2007 No arbitrage and Risk neutral valuation Recall shortly the risk-neutral valuation paradigm of Harrison and Pliska's (1983), characterizing no-arbitrage theory: A future stochastic payo®, built on an underlying fundamental ¯nancial asset, paid at a future time T and satisfying some technical conditions, has as unique price at current time t -
Volume 52, Number 3, 2016 ISSN 0246-0203
Volume 52, Number 3, 2016 ISSN 0246-0203 Martingale defocusing and transience of a self-interacting random walk Y. Peres, B. Schapira and P. Sousi 1009–1022 Excited random walk with periodic cookies G. Kozma, T. Orenshtein and I. Shinkar 1023–1049 Harmonic measure in the presence of a spectral gap ....I. Benjamini and A. Yadin 1050–1060 How vertex reinforced jump process arises naturally ......................X. Zeng 1061–1075 Persistence of some additive functionals of Sinai’s walk ...............A. Devulder 1076–1105 Random directed forest and the Brownian web ......R. Roy, K. Saha and A. Sarkar 1106–1143 Slowdown in branching Brownian motion with inhomogeneous variance ..............................................P. Maillard and O. Zeitouni 1144–1160 Maximal displacement of critical branching symmetric stable processes ..................................................S. P. Lalley and Y. Shao 1161–1177 On the asymptotic behavior of the density of the supremum of Lévy processes ............................................L. Chaumont and J. Małecki 1178–1195 Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation ......................................J.Ma,Z.Ren,N.TouziandJ.Zhang 1196–1216 Inviscid limits for a stochastically forced shell model of turbulent flow .....................................S. Friedlander, N. Glatt-Holtz and V. Vicol 1217–1247 Estimate for Pt D for the stochastic Burgers equation G. Da Prato and A. Debussche 1248–1258 Skorokhod embeddings via stochastic flows on the space of Gaussian measures ................................................................R. Eldan 1259–1280 Liouville heat kernel: Regularity and bounds P. Maillard, R. Rhodes, V. Vargas and O. Zeitouni 1281–1320 Total length of the genealogical tree for quadratic stationary continuous-state branching processes .......................................H. Bi and J.-F. Delmas 1321–1350 Weak shape theorem in first passage percolation with infinite passage times ........................................................R. -
Essays in Quantitative Finance Karlsson, Patrik
Essays in Quantitative Finance Karlsson, Patrik 2016 Document Version: Publisher's PDF, also known as Version of record Link to publication Citation for published version (APA): Karlsson, P. (2016). Essays in Quantitative Finance. Total number of authors: 1 General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 Patrik Karlsson Essays in Quantitative Finance Karlsson Essays in Quantitative Patrik Essays in Quantitative Finance Patrik Karlsson 9 789177 Lund Lund University Economic 530602 Department of Economics ISBN 978-91-7753-060-2 Studies ISSN 0460-0029 199 Number 199 Essays in Quantitative Finance Patrik Karlsson DOCTORAL DISSERTATION by due permission of the School of Economics and Management, Lund University, Sweden. -
Reducing Volatility for a Linear and Stable Growth in a Cryptocurrency
EXAMENSARBETE INOM DATATEKNIK, GRUNDNIVÅ, 15 HP STOCKHOLM, SVERIGE 2021 Reducing volatility for a linear and stable growth in a cryptocurrency Encourage spending, while providing a stable store of value over time in a decentralized network GUSTAF SJÖLINDER CARL-BERNHARD HALLBERG KTH SKOLAN FÖR KEMI, BIOTEKNOLOGI OCH HÄLSA Reducing volatility for a linear and stable growth in a cryptocurrency Encourage spending, while providing a stable store of value over time in a decentralized network Reducering av volatilitet för en linjär och stabil tillväxt i en kryptovaluta Uppmana användning, samt tillhandahålla ett värdebevarande över tid i ett decentraliserat nätverk Gustaf Sjölinder Carl-Bernhard Hallberg Degree Project in Computer Engineering First cycle,15 ECTS Stockholm, Sverige 2021 Supervisor at KTH: Luca Marzano Examiner: Ibrahim Orhan TRITA-CBH-GRU-2021:047 KTH The School of Technology and Health 141 52 Huddinge, Sverige Sammanfattning Internet gav människor möjlighet att utbyta information digitalt och har förändrat hur vi kommunicerar. Blockkedjeteknik och kryptovalutor har gett människan ett nytt sätt att utbyta värde på internet. Med ny teknologi kommer möjligheter, men kan även medföra problem. Ett problem som uppstått med kryptovalutor är deras volatilitet, vilket betyder att valutan upplever stora prissvängningar. Detta har gjort dessa valutor till objekt för spekulation och investering, och därmed gått ifrån sin funktion som valuta. För att en valuta ska anses som ett bra betalmedel, bör den inte ha hög volatilitet. Detta är inte bara begränsat till kryptovalutor, då till exempel Venezuelas nationella valuta Bolivar är en fiatvaluta med historiskt hög volatilitet som förlorat sin köpkraft på grund av hyperinflation under de senaste åren.