DOCSLIB.ORG

126 FM12 Abstracts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. Any of the IC4 lump purchases could be of size zero. A simple condition is Talk Title TBA - Avellaneda provided that guarantees that the intermediate lump pur- chase is of size zero. This is joint work with Gennady Abstract not available at time of publication. Shaikhet and Silviu Predoiu. Marco Avellaneda Steven E. Shreve Courant Institute Carnegie Mellon University New York University Dept of Mathematical Sciences [email protected] [email protected] IC5 IC2 Optimal Order Placement in Limit Order Books Stable Diffusions With Rank-based Interactions, Abstract not available at time of publication. and Models of Large Equity Markets Xin Guo We introduce and study ergodic diffusion processes inter- University of California, Berkeley acting through their ranks. These interactions give rise to [email protected] invariant measures which are in broad agreement with sta- bility properties observed in large equity markets over long time-periods. The models we develop assign growth rates IC6 and variances that depend on both the name (identity) Quantitative Absence of Arbitrage and Equivalent and the rank (according to capitalization) of each individ- Changes of Measure ual asset. Such models are able realistically to capture critical features of the observed stability of capital distri- It is well known that absence of arbitrage is a highly desir- bution over the past century, all the while being simple able feature in mathematical models of financial markets. enough to allow for rather detailed analytical study. The In its pure form (whether as NFLVR or as the existence of methodologies used in this study touch upon the question a variant of an equivalent martingale measure R), it is qual- of triple points for systems of interacting diffusions; in par- itative and therefore robust towards equivalent changes of ticular, some choices of parameters may permit triple (or the underlying reference probability (the ”real-world” mea- higher-order) collisions to occur. We show, however, that sure P). But what happens if we look at more quantitative such multiple collisions have no effect on any of the sta- versions of absence of arbitrage, where we impose for in- bility properties of the resulting system. This is accom- stance some integrability on the density dR/dP? To which plished through a detailed analysis of collision local times. extent is such a property robust towards changes of P? We The models have connections with the analysis of Queue- discuss these questions and present some recent results. ing Networks in heavy traffic, and with competing par- The talk is based on joint work with Tahir Choulli (Uni- ticle systems in Statistical Mechanics (e.g., Sherrington- versity of Alberta, Edmonton). Kirkpatrick model for spin-glasses). Their hydrodynamic- limit behavior is governed by generalized porous medium Martin Schweizer equations with convection, whereas limits of a different ETH Math kind display phase transitions and are governed by Poisson- Zurich, Switzerland Dirichlet laws. [email protected] Ioannis Karatzas Columbia University SP1 [email protected] AWM-SIAM Sonia Kovalevsky Lecture : The Role of Characteristics in Conservation Laws IC3 Sonya Kovalevsky, in the celebrated Cauchy-Kovalevsky Simulation Schemes for Stopped Lvy Processes theorem, made clear the significance of characteristics in partial differential equations. In the field of hyperbolic Jump processes, and Lvy processes in particular, are noto- conservation laws, characteristic curves (in one space di- riously difficult to simulate. The task becomes even harder mension) and surfaces (in higher dimensions) dominate the if the process is stopped when it crosses a certain boundary, behavior of solutions. Some examples of systems exhibit FM12 Abstracts 127 interesting, one might even say pathological, characteristic scalar Banach algebra. Positive results are obtained for behavior. This talk will focus on ways that characteristics both commutative and noncommutative algebras. in systems of conservation laws give information about the systems being modeled. Ruth Curtain University of Groningen, Netherlands Barbara Lee Keyfitz [email protected] The Ohio State University Department of Mathematics bkeyfi[email protected] SP5 I.E. Block Community Lecture: Creating Reality: the Mathematics Behind Visual Effects SP2 The John Von Neumann Lecture: Liquid Crystals Abstract to follow. for Mathematicians Robert Bridson Liquid crystals form an important class of soft matter sys- University of British Columbia tems with properties intermediate between solid crystals [email protected] and isotropic fluids. They are the working substance of liq- uid crystal displays, which form the basis of a huge multi- national industry. The lecture will describe these fascinat- SP6 ing materials, and what different branches of mathematics, SIAG/FME Junior Scientist Prize: Market-Based such as partial differential equations, the calculus of vari- Aapproach to Modeling Derivatives Prices ations, multiscale analysis, scientific computation, dynam- ical systems, algebra and topology, can say about them. Most of the existing quantitative methods in Finance rely on the assumptions of the underlying mathematical mod- els. The problem of choosing the appropriate model as- John Ball sumptions is one of the cornerstones of modern Financial Oxford Centre for Nonlinear PDE Mathematical Institute Engineering. I am interested in developing modeling frame- Oxford works that facilitate the use of historical observations when [email protected] making the choice of model assumptions. It turns out that, in the markets with a large family of liquid derivative con- tracts, it is rather hard to construct a model that exploits SP3 the information contained in the historical prices of these Past President’s Address: Reflections on SIAM, derivatives. In fact, constructing such models requires the Publishing, and the Opportunities Before Us use of the so-called Market-Based Approach. The idea of this approach is to treat the liquid derivatives as generic Upon taking up the post of president I had, of course, for- financial assets and prescribe the joint evolution of their mulated my priorities for SIAM. This talk provides a good prices in such a way that any future arbitrage-free combi- occasion to revisit some of those. One area turned out nation of prices is possible. In this presentation, I will out- to play a vastly larger role than I would have anticipated, line the main difficulties associated with the construction of namely mathematical publishing and many issues associ- market-based models and will present a general methodol- ated with it, ethical, technological, economic, political, and ogy that bypasses these difficulties. Finally, I will illustrate scientific. The future of scholarly publishing is far from the theory by describing (both mathematically and numer- clear, but one thing seems certain: big changes are needed ically) a family of market-based models for the European and will be coming. We, as mathematicians, are major call options of multiple strikes and maturities. stakeholders. We should also be major agents in guiding these changes. I will present some of my observations and Sergey Nadtochiy thoughts as we confront the opportunities before us. Oxford University Oxford-Man Institute Douglas N. Arnold [email protected] School of Mathematics University of Minnesota [email protected] JP1 Systemic Risk SP4 What is systemic risk, how do we model it, how to we an- W. T. and Idalia Reid Prize Lecture: Large Alge- alyze it, and what are the implications of the analysis? I braic Properties of Riccati Equations. will address these issues both in a larger historical context and within current research mathematical finance. The key In the eighties there was considerable interest in the alge- property of systems subject to systemic risk is their inter- braic properties of the following Riccati equation connectivity and the way individual risk can become over- all, systemic risk when it is diversified by inter-connectivity. A∗X + XA XBB∗X + C∗C =0, (1) I will discuss theoretical issues that come up with mean- − field and other models and will also show results of numer- where A, B, C A, a Banach algebra with identity, and ical simulations. the involution operation∈ . Conditions are sought to ensure that the above equation∗ has a solution in A.Theresults George C. Papanicolaou were disappointing and the problem was forgotten until Stanford University this century when engineers studied the class of spatially Department of Mathematics distributed systems.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • The Mean-Reverting 4/2 Stochastic Volatility Model: Properties and Financial Applications
    Western University Scholarship@Western Electronic Thesis and Dissertation Repository 2-3-2021 10:00 AM The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications Zhenxian Gong, The University of Western Ontario Supervisor: Escobar-Anel, Marcos, The University of Western Ontario A thesis submitted in partial fulfillment of the equirr ements for the Doctor of Philosophy degree in Statistics and Actuarial Sciences © Zhenxian Gong 2021 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Applied Statistics Commons, Other Applied Mathematics Commons, Probability Commons, and the Statistical Models Commons Recommended Citation Gong, Zhenxian, "The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications" (2021). Electronic Thesis and Dissertation Repository. 7686. https://ir.lib.uwo.ca/etd/7686 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. Abstract In this thesis, we target commodity and volatility index markets, and develop a novel stochastic volatility model that incorporates mean-reverting property and 4/2 stochastic volatility process. Commodities and volatility indexes have been shown to be mean-reverting. The 4/2 stochastic volatility process integrates two processes that have contrary behaviors. As a result, not only is the 4/2 stochastic volatility process able to reproduce “smile” and “skew”, but also model the asset price time series very well even in the most extreme situation like financial crisis where the assets’ prices become highly volatile.
    [Show full text]
  • Regime-Switching Stochastic Volatility Model: Estimation and Calibration
    Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options Stéphane Goutte, Amine Ismail, Huyên Pham To cite this version: Stéphane Goutte, Amine Ismail, Huyên Pham. Regime-switching Stochastic Volatility Model : Esti- mation and Calibration to VIX options. 2017. hal-01212018v2 HAL Id: hal-01212018 https://hal.archives-ouvertes.fr/hal-01212018v2 Preprint submitted on 1 May 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options Stéphane GOUTTE1,2,∗, Amine ISMAIL3,5 and Huyên PHAM3,4 1Université Paris 8, LED , 2 rue de la Liberté, 93526 Saint-Denis Cedex, France. 2 PSB, Paris School of Business, 59 rue Nationale 75013 Paris, France. 3 Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Universités Paris 7 Diderot. 4CREST-ENSAE 5Natixis, 47 Quai d’Austerlitz, 75013 Paris. Abstract We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynam- ics with the instantaneous variance driven by a Cox-Ingersoll-Ross (CIR) process and each parameter modulated by a hidden Markov chain.
    [Show full text]