Supplemental material for: Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options


 Catherine Bridges
 2 years ago
 Views:
Transcription
1 Sulemental material for: Dynamic jum intensities and risk remiums: evidence from S&P5 returns and otions Peter Christo ersen University of Toronto, CBS and CREATES Kris Jacobs University of Houston and Tilburg University Chayawat Ornthanalai Georgia Institute of Technology December 6, In this sulement we rovide four sets of additional results. In Section we derive continuoustime limits of our models and comare them to existing models in the literature. In Section we rovide more detail on the risk remiums in our model. In Section 3 we resent the a ne comonent GARCH model and rovide estimation results. Finally, in Section 4 we show autocorrelation lots for the models return innovations. Model comarison using continuoustime limits In this section we derive the continuoustime limits for our model. Denoting the sie of the time ste by, our log return dynamic and the variance and jum intensity rocesses can be written as follows R (t + ) = r + ( =)h (t + ) + ( y )h y (t + ) + (t + ) + y (t + ) and h (t + ) = w () + b () h (t) + a () h (t) ((t) c () h (t)) + d () (y(t) e ()) h y (t + ) = w y () + b y () h y (t) + a y () h (t) ((t) c y () h (t)) + d y () (y(t) e y ()) :
2 where (t+) N(; h (t+)) and y (t + ) J h y (t + ) ; ; : Note that we write the GARCH arameters as a function of the time interval in order to study their convergence as the time interval shrinks to ero. Before deriving the limits, we need to de ne the variance and jum intensity as er unit time (t) = h (t) =; and y (t) = h y (t) =. Similarly, we exress the normal and jum innovation (t) and y (t) as functions of the time interval by letting (t) (t) (t; ) and y(t) = y(t; ); () where (t; ) N(; ) and y(t; ) J ( y (t); () ; ()) for () = = and () = = : It is easy to rove that y(t) and y(t; ) in () are identically distributed by looking at their moment generating functions. Using this arameteriation, we can write the return dynamics as R (t + ) r = ( ) (t + ) + ( y ) y (t + ) () + (t + ) (t + ; ) + y(t + ; ): Similarly, the GARCH dynamics for the variance and jum intensity can be written as (t + ) = w () + d () y (t + ) = w y () + d y (). Convergence of the model + b () (t) + a () y(t; ) e () + b y () y (t) + a y () y(t; ) ey () (t; ) c () (t) (3) (t; ) c y () (t) (4) There are various ways to obtain continuoustime limits as the time interval shrinks to ero. We follow the aroach of Heston and Nandi () to obtain the limits for the GARCH dynamics, and of Duan, Ritchken and Sun ( 6) to obtain the limit for the Comound Poisson rocess. First, consider the limit for the variance of the Normal innovation, (t + ). We let the
3 GARCH arameters in (3) be a function of the time interval according to w () = 4 ; a () = 4 ; c () = d () = ; e () = ; b () = : Substituting the above relations into (3) and eliminating the exectations and quadratic variations that converge in robability to ero gives (t + ) (t) = + ( (t)) (t) (t; ) + y(t; ) : We now consider the convergence of (t; ) and y(t; ): Notice that as the time interval shrinks to ero we have the following convergence (t; ) =) dw (t); where W (t) is a Wiener rocess. Note that the sign in front of dw (t) does not imact its limit since the Wiener increment is symmetric. For the convergence of the Comound Poisson rocess, we use the results in Duan, Ritchken and Sun (6) y(t; ) =) X N(t) + dn(t) y(t; ) =) X N(t) + dn(t); (5) where dn(t) is a Poisson counting rocess with intensity y (t) and the X i s reresent a sequence of indeendent standard normal random variables that are indeendent of W (t) and N(t). Note that a more roer notation for y (t) is y (t ), where t indicates the left continuous convergence of the limit. However for simlicity, we dro the t notation. We further note that for small dt, X N(t) + is normally distributed with mean and variance : Letting Q(t) be distributed as N ; ; the variance dynamic of the GARCH model therefore converges weakly to d (t) = ( (t)) dt + (t)dw (t) + Q(t) dn(t) Similarly, the return dynamic converges weakly to d ln S (t) = r + ( ) (t) + ( y ) y (t) dt + (t)dw (t) + Q(t)dN(t) Next, consider the continuoustime limits of the jum intensity in (4). We let the GARCH arameters be functions of the time interval according to w y () = y y 4 y ; a y () = 4 y ; c y () = y d y () = y ; e y () = y ; by () = y : 3
4 Substituting these into (4) and eliminating all the exectations and quadratic variations that converge in robability to ero gives y (t + ) y (t) = y y + y y (t) + y y y (t) y y (t) (t; ) + y y(t; ) : Using the results for the limits of the Normal innovation that (t; ) =) dw (t); and for the Comound Poisson rocess in (5), we obtain the following weak convergence result for the jum intensity d y (t) = y y + y y (t) + y y y (t) dt + y y (t)dw (t) + y Q(t) dn(t):. Summary We have shown that under the arametric assumtions made the continuoustime limit of our model is given by d ln S (t) = r + ( ) (t) + ( y ) y (t) dt + (t)dw (t) + Q(t)dN(t) (6) d (t) = + ( (t)) dt + (t)dw (t) + Q(t) dn(t) (7) d y (t) = y y + y y (t) + y y y (t) dt (8) + y y (t)dw (t) + y Q(t) dn(t) where W (t) is a Wiener rocess, N t is a Poisson counting rocess with intensity y (t); and Q(t) N ; reresents the stochastic jum sie that is indeendent of W (t) and N(t): We can write the above limits more comactly by using vector notation d ln S (t) = d (t) d y (t) = r + ( ) (t) + ( y ) y (t) + ( (t)) y y + y y (t) + y y y (t) dt + (t)dw (t) + Q(t)dN(t) " dt +.3 The SantaClara and Yan model () y y y # (t)dw (t) Q(t) dn(t) The model of SantaClara and Yan (, henceforth SCY) falls in the class of quadratic models. The return dynamic follows d ln S (t) = r + (t) (t) y (t) dt + (t)dw s (t) + Q(t)dN(t) 4
5 where W (t) is a Wiener rocess and N(t) is a Poisson rocess with intensity y (t): The equity remium term in the SCY model is denoted as (t) : Because the model is quadratic, the equity remium is a nonlinear function of (t) and y (t): The SCY model arametries the variance and the jum intensity as follows (t) = Z ; y (t) = Y where Z and Y are latent state variables with the following dynamics dz(t) ( = Z(t)) dy (t) y y Y (t) dt + y dw (t) dw Y (t) The three Wiener rocesses in the SCY model are arameteried with the following correlation matrix.4 Model comarison = s sy s y sy y When comaring the continuoustime limit of our model to the SCY model, the similarity is that they both allow for dynamic volatility and dynamic jum intensity. As far as modeling di erences are concerned, our model has both advantages and disadvantages comared to the SCY model. The quadratic nature of the SCY model is an imortant advantage. Our model falls in the a ne class, and in that sense it is closer to the class of continuoustime a ne SVJ models. On the other hand, the SCY model as is standard does not allow for jums in volatility C A : and jums in the jum intensity whereas our model does. If we shut down the jums in volatility and jums in jum intensity in our model, that is we set, = and y = in (7) and (8), then our model falls under the a ne jumdi usion class d ln S (t) = d (t) d y (t) = r + ( ) (t) + ( y ) y (t) dt + (t)dw (t) + Q(t)dN(t) ( (t)) y y (t) + y y y (t) dt + (t)dw (t): y y This restricted version of our model is similar to the a ne jumdi usion models studied in several aers in the continuoustime literature, but it does not nest the quadratic jumdi usion model of SCY. 5
6 Risk remium structure: comarison with existing studies The framework in this aer leads to a simle a ne seci cation of the equity remium in the variance of the normal innovation and the jum intensity. That is, log E t [ex (R t+ )] = h ;t+ + y h y;t+ where h ;t+ and y h y;t+ reresent the normal risk remium and the jum risk remium, resectively. We now show that the resulting decomosition of the equity remium is consistent with existing studies such as Pan (), Broadie, Chernov and Johannes (7) and Liu, Pan and Wang (5). Lemma Using the EMM in Proosition and the riskneutral dynamics in Proosition, the conditional equity remium for the return dynamic in (.) can be written as where h y;t+ h ;t+ + h y;t+ h y;t+ (9) e + h y;t+ and h y;t+ e + h y;t+ are the comensators to the jum comonent under the riskneutral and hysical measure resectively. h i Proof. Taking the logarithm of E St+ t S t = e r+h ;t++ yh y;t+ yields the conditional equity remium h ;t+ + y h y;t+. We are left to show that y h y;t+ = h y;t+ h y;t+: Using the EMM condition y e + e y + y e ( +y) + = ; we can write y h y;t+ = e + h y;t+ e ( +y) + h y;t+ e y + y = h y;t+ h y;t+ where the second line in the above equation follows from! h y;t+ = h y;t+ ex y + y and = + y () which was shown in Proosition Using an equilibrium model with a reresentative agent, Liu, Pan and Wang (5) also obtain exression (9) for the equity remium. They also refer to h ;t+ as the normal risk 6
7 remium and y h y;t+ = h y;t+ h y;t+ as the jum risk remium. 3 The a ne comonent GARCH model Christo ersen, Jacobs, Ornthanalai and Wang (8) develo an a ne comonent GARCH model, and demonstrate its suerior otion ricing erformance relative to the benchmark a ne HestonNandi GARCH(,) rocess. The richer volatility dynamics enable the comonent model to cature atterns in longmaturity as well as in shortmaturity otions. The return dynamic of the comonent GARCH is identical to that of the GARCH(,) model. It is given by R t+ ln(s t+ =S t ) = r + ( =) h t+ + t+ () where t+ N (; h t+ ). The variance dynamic of the comonent GARCH model however consists of two comonents: the shortrun comonent h t+ ; and the longrun comonent q t+ h t+ = q t+ + (h t q t ) + t h t h t h t t q t+ =! + q t + ' t h t h t h t : t () To rice otions, we need the riskneutralied version of the comonent GARCH model. The riskneutral comonent GARCH dynamic is given by R t+ ln(s t+ =S t ) = r + h t+ = q t+ + (h t q t ) + h t t h t q t+ =! + q t + ' h t t h t h t+ + t+ (3) t h t t h t ; and where the riskneutral arameters are de ned as = + + ' ; = + + ', and i = i + ; for i = ; : We have estimated the comonent GARCH using the data set used in our aer. Table S contains the estimation results. Panel A shows the MLE estimates on returns only, and Panel B shows the MLE estimates obtained using returns and otions jointly. Comaring the Otion IVRMSE of 5.5% in Panel A with the results in Table of the aer, we see that the comonent GARCH model outerforms the DVCJ and CVDJ models, 7
8 but it is outerformed by the DVDJ and DVSDJ models. The comonent GARCH model in which both comonents are Gaussian is thus better than the single factor DVCJ and CVDJ models but worse than the twofactor DVCJ and CVDJ models. The comonent GARCH model also erforms better than the twofactor Gaussian model in Table. For the case of the joint estimation, the total loglikelihood for the comonent GARCH model in Panel B of Table S is 38,77, which is better than the GARCH and twofactor GARCH model in Table 6, but worse than the three jum models, DVCJ, DVDJ and DVSDJ. Therefore, the new jum models erform well relative to the comonent GARCH model in this case too. 4 Autocorrelations of returns and innovations In this section we resent the autocorrelations of the return data, and comare them to the autocorrelations from the model innovations. The return seci cation is R t+ r + h;t+ + ( y ) h y;t+ + t+ + y t+ : (4) Figure S lots the autocorrelation function of daily S&P5 return, R t+, for 969, along with the autocorrelation of the daily total residual from our models, de ned as t+ + y t+ = R t+ r h;t+ ( y ) h y;t+ : (5) Figure S also shows twostandarddeviation Bartlett bands. The to left anel in Figure S shows that the daily S&P5 returns dislay no systematic timeseries atterns. The rst autocorrelation is ositive, erhas caturing illiquidity in the cash index that we use. The other ve anels in Figure S show that not surrisingly the residuals in the models we estimate largely retain the autocorrelation atterns from the raw returns. 8
9 References Broadie, M., Chernov, M., Johannes, M., 7. Model seci cation and risk remia: evidence from futures otions. Journal of Finance 6, Christo ersen, P., Jacobs, K., Ornthanalai, C., Wang, Y., 8. Otion valuation with longrun and shortrun volatility comonents. Journal of Financial Economics 9, Duan, J.C., Ritchken, P., Sun, Z., 6. Aroximating GARCHjum models, jumdi usion rocesses, and otion ricing. Mathematical Finance 6, 5. Heston, S., Nandi, S.,. A closedform GARCH otion ricing model. Review of Financial Studies 3, Liu, J., Pan, J., Wang, T., 5. An equilibrium model of rareevent remia and its imlication for otion smirks. Review of Financial Studies 8, Pan, J.,. The jumrisk remia imlicit in otions: evidence from an integrated timeseries study. Journal of Financial Economics 63, 3 5. SantaClara, P., Yan, S.,. Crashes, volatility, and the equity remium: lessons from S&P5 otions. Review of Economics and Statistics 9,
10 Samle Autocorrelation Samle Autocorrelation Samle Autocorrelation Figure S: Autocorrelation functions for S&P5 returns and model residuals Data GARCH (,) DVCJ CVDJ DVDJ DVSDJ Lag Lag Notes to Figure: We lot the autocorrelation function (ACF) for the daily S&P5 return, R t+ in the to left anel and the ACF of the model residuals, t+ + y t+ in the other ve anels. We use daily returns for 969.
11 Table S: MLE and joint MLE with comonent GARCH model Panel A: Returns MLE (9699) Panel B: Joint otions & returns MLE (9959) Parameters Parameters λ.6e+ λ.e+ (9.E) (5.35E3) 8.3E7.4E6 (6.65E8) (6.8E) β 7.5E β 7.34E (.8E) (8.E8).39E E6 (.36E7) (7.6E8) 4.53E+.66E+ (7.68E+) (3.36E+) (7.64E+) (5.7E+).E E6 (.E7) (4.47E8) 9.9E 9.86E (8.E4).95E4 Proerties Proerties Persistence.9977 Longrun risk remium 4.6% Percent of annual variance % Average annual volatility 9.6% Average annual volatility 4.97% Percent of annual variance % Loglikelihood 4,457 Total loglikelihood 38,77 Otion IVRMSE 5.5 Otions loglikelihood 4,49 Return loglikelihood 33,784 Notes to Table: We estimate a comonent GARCH model (see Christoffersen el al. (8)) using MLE on returns and joint MLE on Otions and Returns. Panel A reorts MLE on daily S&P 5 daily returns from June 969 to December 9. Panel B resent results jointly fitting daily S&P5 returns and weekly outofthe money S&P 5 otions with maturity of 5 days or less using data from January 996 to October 9. Under Proerties we reort relevant characteristics imlied by the model from each estimation methdology.
Dynamic Jump Intensities and Risk Premiums in Crude Oil Futures and Options Markets
Dynamic Jump Intensities and Risk Premiums in Crude Oil Futures and Options Markets Peter Christoffersen University of Toronto, CBS, and CREATES Kris Jacobs University of Houston and Tilburg University
More informationThe fast Fourier transform method for the valuation of European style options inthemoney (ITM), atthemoney (ATM) and outofthemoney (OTM)
Comutational and Alied Mathematics Journal 15; 1(1: 16 Published online January, 15 (htt://www.aascit.org/ournal/cam he fast Fourier transform method for the valuation of Euroean style otions inthemoney
More informationF inding the optimal, or valuemaximizing, capital
Estimating RiskAdjusted Costs of Financial Distress by Heitor Almeida, University of Illinois at UrbanaChamaign, and Thomas Philion, New York University 1 F inding the otimal, or valuemaximizing, caital
More informationEffect Sizes Based on Means
CHAPTER 4 Effect Sizes Based on Means Introduction Raw (unstardized) mean difference D Stardized mean difference, d g Resonse ratios INTRODUCTION When the studies reort means stard deviations, the referred
More information1 Gambler s Ruin Problem
Coyright c 2009 by Karl Sigman 1 Gambler s Ruin Problem Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial fortune of $i and then on each successive gamble either wins
More informationPresales, Leverage Decisions and Risk Shifting
Presales, Leverage Decisions and Risk Shifting Su Han Chan Professor Carey Business School Johns Hokins University, USA schan@jhu.edu Fang Fang AssociateProfessor School of Public Economics and Administration
More informationFour Derivations of the BlackScholes Formula by Fabrice Douglas Rouah www.frouah.com www.volopta.com
Four Derivations of the BlackScholes Formula by Fabrice Douglas Rouah www.frouah.com www.volota.com In this note we derive in four searate ways the wellknown result of Black and Scholes that under certain
More informationA Study on HestonNandi GARCH Option Pricing Model
2011 3rd International Conference on Information and Financial Engineering IPEDR vol.12 (2011) (2011) IACSIT Press, Singapore A Study on HestonNandi GARCH Option Pricing Model Suk Joon Byun KAIST Business
More informationEconomics 241B Hypothesis Testing: Large Sample Inference
Economics 241B Hyothesis Testing: Large Samle Inference Statistical inference in largesamle theory is base on test statistics whose istributions are nown uner the truth of the null hyothesis. Derivation
More informationAn inventory control system for spare parts at a refinery: An empirical comparison of different reorder point methods
An inventory control system for sare arts at a refinery: An emirical comarison of different reorder oint methods Eric Porras a*, Rommert Dekker b a Instituto Tecnológico y de Estudios Sueriores de Monterrey,
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More informationA MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
9 th ASCE Secialty Conference on Probabilistic Mechanics and Structural Reliability PMC2004 Abstract A MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
More informationAn important observation in supply chain management, known as the bullwhip effect,
Quantifying the Bullwhi Effect in a Simle Suly Chain: The Imact of Forecasting, Lead Times, and Information Frank Chen Zvi Drezner Jennifer K. Ryan David SimchiLevi Decision Sciences Deartment, National
More informationApplications of Regret Theory to Asset Pricing
Alications of Regret Theory to Asset Pricing Anna Dodonova * Henry B. Tiie College of Business, University of Iowa Iowa City, Iowa 522421000 Tel.: +13193379958 Email address: annadodonova@uiowa.edu
More informationTworesource stochastic capacity planning employing a Bayesian methodology
Journal of the Oerational Research Society (23) 54, 1198 128 r 23 Oerational Research Society Ltd. All rights reserved. 165682/3 $25. www.algravejournals.com/jors Tworesource stochastic caacity lanning
More informationRisk in Revenue Management and Dynamic Pricing
OPERATIONS RESEARCH Vol. 56, No. 2, March Aril 2008,. 326 343 issn 0030364X eissn 15265463 08 5602 0326 informs doi 10.1287/ore.1070.0438 2008 INFORMS Risk in Revenue Management and Dynamic Pricing Yuri
More informationEstimating the Degree of Expert s Agency Problem: The Case of Medical Malpractice Lawyers
Estimating the Degree of Exert s Agency Problem: The Case of Medical Malractice Lawyers Yasutora Watanabe Northwestern University March 2007 Very Preliminary and Incomlete  Comments Welcome! Abstract
More informationMultiperiod Portfolio Optimization with General Transaction Costs
Multieriod Portfolio Otimization with General Transaction Costs Victor DeMiguel Deartment of Management Science and Oerations, London Business School, London NW1 4SA, UK, avmiguel@london.edu Xiaoling Mei
More informationA Simple Model of Pricing, Markups and Market. Power Under Demand Fluctuations
A Simle Model of Pricing, Markus and Market Power Under Demand Fluctuations Stanley S. Reynolds Deartment of Economics; University of Arizona; Tucson, AZ 85721 Bart J. Wilson Economic Science Laboratory;
More informationThe predictability of security returns with simple technical trading rules
Journal of Emirical Finance 5 1998 347 359 The redictability of security returns with simle technical trading rules Ramazan Gençay Deartment of Economics, UniÕersity of Windsor, 401 Sunset, Windsor, Ont.,
More informationEstimating the Degree of Expert s Agency Problem: The Case of Medical Malpractice Lawyers
Estimating the Degree of Exert s Agency Problem: The Case of Medical Malractice Lawyers Yasutora Watanabe Northwestern University March 2007 Abstract I emirically study the exert s agency roblem in the
More informationAn actuarial approach to pricing Mortgage Insurance considering simultaneously mortgage default and prepayment
An actuarial aroach to ricing Mortgage Insurance considering simultaneously mortgage default and reayment Jesús Alan Elizondo Flores Comisión Nacional Bancaria y de Valores aelizondo@cnbv.gob.mx Valeria
More informationJoint Production and Financing Decisions: Modeling and Analysis
Joint Production and Financing Decisions: Modeling and Analysis Xiaodong Xu John R. Birge Deartment of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208,
More informationRisk and Return. Sample chapter. e r t u i o p a s d f CHAPTER CONTENTS LEARNING OBJECTIVES. Chapter 7
Chater 7 Risk and Return LEARNING OBJECTIVES After studying this chater you should be able to: e r t u i o a s d f understand how return and risk are defined and measured understand the concet of risk
More informationA Note on the Stock Market Trend Analysis Using MarkovSwitching EGARCH Models
( 251 ) Note A Note on the Stock Market Trend Analysis Using MarkovSwitching EGARCH Models MITSUI, Hidetoshi* 1) 1 Introduction The stock marketʼs fluctuations follow a continuous trend whether or not
More informationOption Valuation Using Daily Data: Pricing Kernels, GARCH and SV Models
Option Valuation Using Daily Data: Pricing Kernels, GARCH and SV Models Peter Christoffersen Rotman School of Management, University of Toronto, Copenhagen Business School, and CREATES, University of Aarhus
More informationOn the predictive content of the PPI on CPI inflation: the case of Mexico
On the redictive content of the PPI on inflation: the case of Mexico José Sidaoui, Carlos Caistrán, Daniel Chiquiar and Manuel RamosFrancia 1 1. Introduction It would be natural to exect that shocks to
More informationPOISSON PROCESSES. Chapter 2. 2.1 Introduction. 2.1.1 Arrival processes
Chater 2 POISSON PROCESSES 2.1 Introduction A Poisson rocess is a simle and widely used stochastic rocess for modeling the times at which arrivals enter a system. It is in many ways the continuoustime
More informationAn Introduction to Risk Parity Hossein Kazemi
An Introduction to Risk Parity Hossein Kazemi In the aftermath of the financial crisis, investors and asset allocators have started the usual ritual of rethinking the way they aroached asset allocation
More informationThe Heston Model. Hui Gong, UCL http://www.homepages.ucl.ac.uk/ ucahgon/ May 6, 2014
Hui Gong, UCL http://www.homepages.ucl.ac.uk/ ucahgon/ May 6, 2014 Generalized SV models Vanilla Call Option via Heston Itô s lemma for variance process EulerMaruyama scheme Implement in Excel&VBA 1.
More informationTHE WELFARE IMPLICATIONS OF COSTLY MONITORING IN THE CREDIT MARKET: A NOTE
The Economic Journal, 110 (Aril ), 576±580.. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 50 Main Street, Malden, MA 02148, USA. THE WELFARE IMPLICATIONS OF COSTLY MONITORING
More informationPopulation Genetics I
Poulation Genetics I The material resented here considers a single diloid genetic locus, ith to alleles A and a; their relative frequencies in the oulation ill be denoted as and q (ith q 1 ). HardyWeinberg
More informationCharacterizing and Modeling Network Traffic Variability
Characterizing and Modeling etwork Traffic Variability Sarat Pothuri, David W. Petr, Sohel Khan Information and Telecommunication Technology Center Electrical Engineering and Comuter Science Deartment,
More informationImplementation of Statistic Process Control in a Painting Sector of a Automotive Manufacturer
4 th International Conference on Industrial Engineering and Industrial Management IV Congreso de Ingeniería de Organización Donostia an ebastián, etember 8 th  th Imlementation of tatistic Process Control
More informationDynamics of Open Source Movements
Dynamics of Oen Source Movements Susan Athey y and Glenn Ellison z January 2006 Abstract This aer considers a dynamic model of the evolution of oen source software rojects, focusing on the evolution of
More informationConsumer Price Index Dynamics in a Small Open Economy: A Structural Time Series Model for Luxembourg
Aka and Pieretii, International Journal of Alied Economics, 5(, March 2008, 3 Consumer Price Index Dynamics in a Small Oen Economy: A Structural Time Series Model for Luxembourg Bédia F. Aka * and P.
More informationA Multivariate Statistical Analysis of Stock Trends. Abstract
A Multivariate Statistical Analysis of Stock Trends Aril Kerby Alma College Alma, MI James Lawrence Miami University Oxford, OH Abstract Is there a method to redict the stock market? What factors determine
More informationA joint initiative of LudwigMaximilians University s Center for Economic Studies and the Ifo Institute for Economic Research
A joint initiative of LudwigMaximilians University s Center for Economic Studies and the Ifo Institute for Economic Research Area Conference on Alied Microeconomics  2 March 20 CESifo Conference Centre,
More informationManaging specific risk in property portfolios
Managing secific risk in roerty ortfolios Andrew Baum, PhD University of Reading, UK Peter Struemell OPC, London, UK Contact author: Andrew Baum Deartment of Real Estate and Planning University of Reading
More informationExploring TimeVarying Jump Intensities: Evidence from S&P500 Returns and Options
29s34 Exploring TimeVarying Jump Intensities: Evidence from S&P5 Returns and Options Peter Christoffersen, Kris Jacobs, Chayawat Ornthanalai Série Scientifique Scientific Series Montréal Août 29 29 Peter
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2013, Mr. Ruey S. Tsay Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2013, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (40 points) Answer briefly the following questions. 1. Describe
More information6.042/18.062J Mathematics for Computer Science December 12, 2006 Tom Leighton and Ronitt Rubinfeld. Random Walks
6.042/8.062J Mathematics for Comuter Science December 2, 2006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Random Walks Gambler s Ruin Today we re going to talk about onedimensional random walks. In
More informationLecture 21 and 22: The Prime Number Theorem
Lecture and : The Prime Number Theorem (New lecture, not in Tet) The location of rime numbers is a central question in number theory. Around 88, Legendre offered eerimental evidence that the number π()
More informationOption Valuation Using Intraday Data
Option Valuation Using Intraday Data Peter Christoffersen Rotman School of Management, University of Toronto, Copenhagen Business School, and CREATES, University of Aarhus 2nd Lecture on Thursday 1 Model
More informationLecture Note of Bus 41202, Spring 2012: Stochastic Diffusion & Option Pricing
Lecture Note of Bus 41202, Spring 2012: Stochastic Diffusion & Option Pricing Key concept: Ito s lemma Stock Options: A contract giving its holder the right, but not obligation, to trade shares of a common
More informationSoftmax Model as Generalization upon Logistic Discrimination Suffers from Overfitting
Journal of Data Science 12(2014),563574 Softmax Model as Generalization uon Logistic Discrimination Suffers from Overfitting F. Mohammadi Basatini 1 and Rahim Chiniardaz 2 1 Deartment of Statistics, Shoushtar
More informationTHE HEBREW UNIVERSITY OF JERUSALEM
האוניברסיטה העברית בירושלים THE HEBREW UNIVERSITY OF JERUSALEM FIRM SPECIFIC AND MACRO HERDING BY PROFESSIONAL AND AMATEUR INVESTORS AND THEIR EFFECTS ON MARKET By ITZHAK VENEZIA, AMRUT NASHIKKAR, and
More informationThe Economics of the Cloud: Price Competition and Congestion
Submitted to Oerations Research manuscrit (Please, rovide the manuscrit number!) Authors are encouraged to submit new aers to INFORMS journals by means of a style file temlate, which includes the journal
More informationThe Changing Wage Return to an Undergraduate Education
DISCUSSION PAPER SERIES IZA DP No. 1549 The Changing Wage Return to an Undergraduate Education Nigel C. O'Leary Peter J. Sloane March 2005 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study
More informationThe Portfolio Characteristics and Investment Performance of Bank Loan Mutual Funds
The Portfolio Characteristics and Investment Performance of Bank Loan Mutual Funds Zakri Bello, Ph.. Central Connecticut State University 1615 Stanley St. New Britain, CT 06050 belloz@ccsu.edu 8608323262
More informationLarge firms and heterogeneity: the structure of trade and industry under oligopoly
Large firms and heterogeneity: the structure of trade and industry under oligooly Eddy Bekkers University of Linz Joseh Francois University of Linz & CEPR (London) ABSTRACT: We develo a model of trade
More informationPoint Location. Preprocess a planar, polygonal subdivision for point location queries. p = (18, 11)
Point Location Prerocess a lanar, olygonal subdivision for oint location ueries. = (18, 11) Inut is a subdivision S of comlexity n, say, number of edges. uild a data structure on S so that for a uery oint
More informationMethods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical Records
EDM Forum EDM Forum Community egems (Generating Evidence & Methods to imrove atient outcomes) Publish 122013 Methods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical
More informationA Modified Measure of Covert Network Performance
A Modified Measure of Covert Network Performance LYNNE L DOTY Marist College Deartment of Mathematics Poughkeesie, NY UNITED STATES lynnedoty@maristedu Abstract: In a covert network the need for secrecy
More informationThe Effect of Global Financial Crisis on Trade Elasticities: Evidence from BRIICS Countries and Turkey
The Effect of Global Financial Crisis on Trade Elasticities: Evidence from BRIICS Countries and Turkey Natalya Ketenci Yeditee University, Istanbul Abstract: The effect of the global financial crisis on
More informationSimulink Implementation of a CDMA Smart Antenna System
Simulink Imlementation of a CDMA Smart Antenna System MOSTAFA HEFNAWI Deartment of Electrical and Comuter Engineering Royal Military College of Canada Kingston, Ontario, K7K 7B4 CANADA Abstract:  The
More informationBias in the Estimation of Mean Reversion in ContinuousTime Lévy Processes
Bias in the Estimation of Mean Reversion in ContinuousTime Lévy Processes Yong Bao a, Aman Ullah b, Yun Wang c, and Jun Yu d a Purdue University, IN, USA b University of California, Riverside, CA, USA
More informationSeparating Trading and Banking: Consequences for Financial Stability
Searating Trading and Banking: Consequences for Financial Stability Hendrik Hakenes University of Bonn, Max Planck Institute Bonn, and CEPR Isabel Schnabel Johannes Gutenberg University Mainz, Max Planck
More informationComparing Dissimilarity Measures for Symbolic Data Analysis
Comaring Dissimilarity Measures for Symbolic Data Analysis Donato MALERBA, Floriana ESPOSITO, Vincenzo GIOVIALE and Valentina TAMMA Diartimento di Informatica, University of Bari Via Orabona 4 76 Bari,
More informationComputational Finance The Martingale Measure and Pricing of Derivatives
1 The Martingale Measure 1 Comutational Finance The Martingale Measure and Pricing of Derivatives 1 The Martingale Measure The Martingale measure or the Risk Neutral robabilities are a fundamental concet
More informationThe Online Freezetag Problem
The Online Freezetag Problem Mikael Hammar, Bengt J. Nilsson, and Mia Persson Atus Technologies AB, IDEON, SE3 70 Lund, Sweden mikael.hammar@atus.com School of Technology and Society, Malmö University,
More informationPressure Drop in Air Piping Systems Series of Technical White Papers from Ohio Medical Corporation
Pressure Dro in Air Piing Systems Series of Technical White Paers from Ohio Medical Cororation Ohio Medical Cororation Lakeside Drive Gurnee, IL 600 Phone: (800) 4480770 Fax: (847) 855604 info@ohiomedical.com
More informationUniversiteitUtrecht. Department. of Mathematics. Optimal a priori error bounds for the. RayleighRitz method
UniversiteitUtrecht * Deartment of Mathematics Otimal a riori error bounds for the RayleighRitz method by Gerard L.G. Sleijen, Jaser van den Eshof, and Paul Smit Prerint nr. 1160 Setember, 2000 OPTIMAL
More informationTHIS paper uses option prices to estimate the risk of the
CRASHES, VOLATILITY, AND THE EQUITY PREMIUM: LESSONS FROM S&P 500 OPTIONS Pedro SantaClara and Shu Yan* Abstract We use a novel pricing model to imply time series of diffusive volatility and jump intensity
More informationARMA, GARCH and Related Option Pricing Method
ARMA, GARCH and Related Option Pricing Method Author: Yiyang Yang Advisor: Pr. Xiaolin Li, Pr. Zari Rachev Department of Applied Mathematics and Statistics State University of New York at Stony Brook September
More informationAn Empirical Analysis of the Effect of Credit Rating on Trade Credit
011 International Conference on Financial Management and Economics IPED vol.11 (011) (011) ICSIT Press, Singaore n Emirical nalysis of the Effect of Credit ating on Trade Credit JianHsin Chou¹ MeiChing
More informationLarge firms and heterogeneity: the structure of trade and industry under oligopoly
Large firms and heterogeneity: the structure of trade and industry under oligooly Eddy Bekkers University of Linz Joseh Francois University of Linz & CEPR (London) ABSTRACT: We develo a model with endogeneity
More informationBUBBLES AND CRASHES. By Dilip Abreu and Markus K. Brunnermeier 1
Econometrica, Vol. 71, No. 1 (January, 23), 173 24 BUBBLES AND CRASHES By Dili Abreu and Markus K. Brunnermeier 1 We resent a model in which an asset bubble can ersist desite the resence of rational arbitrageurs.
More informationPiracy and Network Externality An Analysis for the Monopolized Software Industry
Piracy and Network Externality An Analysis for the Monoolized Software Industry Ming Chung Chang Deartment of Economics and Graduate Institute of Industrial Economics mcchang@mgt.ncu.edu.tw Chiu Fen Lin
More informationMethods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical Records
(Generating Evidence & Methods to imrove atient outcomes) Volume 1 Issue 3 Methods for CER, PCOR, and QI Using EHR Data in a Learning Health System Article 6 1212013 Methods for Estimating Kidney Disease
More informationValuing Stock Options: The BlackScholesMerton Model. Chapter 13
Valuing Stock Options: The BlackScholesMerton Model Chapter 13 Fundamentals of Futures and Options Markets, 8th Ed, Ch 13, Copyright John C. Hull 2013 1 The BlackScholesMerton Random Walk Assumption
More informationReal Business Cycle Models
Real Business Cycle Models Lecture 2 Nicola Viegi April 2015 Basic RBC Model Claim: Stochastic General Equlibrium Model Is Enough to Explain The Business cycle Behaviour of the Economy Money is of little
More informationChE 120B Lumped Parameter Models for Heat Transfer and the Blot Number
ChE 0B Lumed Parameter Models for Heat Transfer and the Blot Number Imagine a slab that has one dimension, of thickness d, that is much smaller than the other two dimensions; we also assume that the slab
More informationNEWSVENDOR PROBLEM WITH PRICING: PROPERTIES, ALGORITHMS, AND SIMULATION
Proceedings of the 2005 Winter Simulation Conference M. E. Kuhl, N. M. Steiger, F. B. rmstrong, and J.. Joines, eds. NEWSVENDOR PROBLEM WITH PRICING: PROPERTIES, LGORITHMS, ND SIMULTION Roger L. Zhan ISE
More informationInterbank Market and Central Bank Policy
Federal Reserve Bank of New York Staff Reorts Interbank Market and Central Bank Policy JungHyun Ahn Vincent Bignon Régis Breton Antoine Martin Staff Reort No. 763 January 206 This aer resents reliminary
More informationModels for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices
Models for S&P5 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices Peter Christo ersen Kris Jacobs Karim Mimouni Desautels Faculty of Management, McGill University July 31, 27
More informationAlpha Channel Estimation in High Resolution Images and Image Sequences
In IEEE Comuter Society Conference on Comuter Vision and Pattern Recognition (CVPR 2001), Volume I, ages 1063 68, auai Hawaii, 11th 13th Dec 2001 Alha Channel Estimation in High Resolution Images and Image
More informationThe Economics of the Cloud: Price Competition and Congestion
Submitted to Oerations Research manuscrit The Economics of the Cloud: Price Cometition and Congestion Jonatha Anselmi Basque Center for Alied Mathematics, jonatha.anselmi@gmail.com Danilo Ardagna Di. di
More informationFluent Software Training TRN99003. Solver Settings. Fluent Inc. 2/23/01
Solver Settings E1 Using the Solver Setting Solver Parameters Convergence Definition Monitoring Stability Accelerating Convergence Accuracy Grid Indeendence Adation Aendix: Background Finite Volume Method
More informationTopic 5: Stochastic Growth and Real Business Cycles
Topic 5: Stochastic Growth and Real Business Cycles Yulei Luo SEF of HKU October 1, 2015 Luo, Y. (SEF of HKU) Macro Theory October 1, 2015 1 / 45 Lag Operators The lag operator (L) is de ned as Similar
More informationIEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 2011 757. LoadBalancing Spectrum Decision for Cognitive Radio Networks
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 757 LoadBalancing Sectrum Decision for Cognitive Radio Networks LiChun Wang, Fellow, IEEE, ChungWei Wang, Student Member, IEEE,
More informationHYPOTHESIS TESTING FOR THE PROCESS CAPABILITY RATIO. A thesis presented to. the faculty of
HYPOTHESIS TESTING FOR THE PROESS APABILITY RATIO A thesis resented to the faculty of the Russ ollege of Engineering and Technology of Ohio University In artial fulfillment of the requirement for the degree
More informationPrinciples of Hydrology. Hydrograph components include rising limb, recession limb, peak, direct runoff, and baseflow.
Princiles of Hydrology Unit Hydrograh Runoff hydrograh usually consists of a fairly regular lower ortion that changes slowly throughout the year and a raidly fluctuating comonent that reresents the immediate
More informationStability Improvements of Robot Control by Periodic Variation of the Gain Parameters
Proceedings of the th World Congress in Mechanism and Machine Science ril ~4, 4, ianin, China China Machinery Press, edited by ian Huang. 868 Stability Imrovements of Robot Control by Periodic Variation
More informationIEEM 101: Inventory control
IEEM 101: Inventory control Outline of this series of lectures: 1. Definition of inventory. Examles of where inventory can imrove things in a system 3. Deterministic Inventory Models 3.1. Continuous review:
More informationMaximum Likelihood Estimation
Math 541: Statistical Theory II Lecturer: Songfeng Zheng Maximum Likelihood Estimation 1 Maximum Likelihood Estimation Maximum likelihood is a relatively simple method of constructing an estimator for
More informationApproximate Guarding of Monotone and Rectilinear Polygons
Aroximate Guarding of Monotone and Rectilinear Polygons Erik Krohn Bengt J. Nilsson Abstract We show that vertex guarding a monotone olygon is NPhard and construct a constant factor aroximation algorithm
More informationMultipleProject Financing with Informed Trading * Salvatore Cantale IMD International. Dmitry Lukin New Economic School. Abstract
The ournal of Entrereneurial Finance Volume 6 Number ring 08 Coyright 0 cademy of Entrereneurial Finance nc. ll rights reserved. N: 559570 MultileProject Financing with nformed Trading * alvatore Cantale
More informationChapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
More informationOPTIMAL EXCHANGE BETTING STRATEGY FOR WINDRAWLOSS MARKETS
OPTIA EXCHANGE ETTING STRATEGY FOR WINDRAWOSS ARKETS Darren O Shaughnessy a,b a Ranking Software, elbourne b Corresonding author: darren@rankingsoftware.com Abstract Since the etfair betting exchange
More informationSTATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND
STATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND Giorgio Sciascia *, Sandro Scalise *, Harald Ernst * and Rodolfo Mura + * DLR (German Aerosace Centre) Institute for Communications
More informationDiscrete Stochastic Approximation with Application to Resource Allocation
Discrete Stochastic Aroximation with Alication to Resource Allocation Stacy D. Hill An otimization roblem involves fi nding the best value of an obective function or fi gure of merit the value that otimizes
More informationLargeScale IP Traceback in HighSpeed Internet: Practical Techniques and Theoretical Foundation
LargeScale IP Traceback in HighSeed Internet: Practical Techniques and Theoretical Foundation Jun Li Minho Sung Jun (Jim) Xu College of Comuting Georgia Institute of Technology {junli,mhsung,jx}@cc.gatech.edu
More informationDAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON
DAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON Rosario Esínola, Javier Contreras, Francisco J. Nogales and Antonio J. Conejo E.T.S. de Ingenieros Industriales, Universidad
More informationBlackScholes Equation for Option Pricing
BlackScholes Equation for Option Pricing By Ivan Karmazin, Jiacong Li 1. Introduction In early 1970s, Black, Scholes and Merton achieved a major breakthrough in pricing of European stock options and there
More informationThe risk of using the Q heterogeneity estimator for software engineering experiments
Dieste, O., Fernández, E., GarcíaMartínez, R., Juristo, N. 11. The risk of using the Q heterogeneity estimator for software engineering exeriments. The risk of using the Q heterogeneity estimator for
More informationPRICING OF FOREIGN CURRENCY OPTIONS IN THE SERBIAN MARKET
ECONOMIC ANNALS, Volume LIV, No. 180, January March 2009 UDC: 3.33 ISSN: 00133264 COMMUNICATIONS Irena Janković* DOI:10.2298/EKA0980091J PRICING OF FOREIGN CURRENCY OPTIONS IN THE SERBIAN MARKET ABSTRACT:
More informationOn Software Piracy when Piracy is Costly
Deartment of Economics Working aer No. 0309 htt://nt.fas.nus.edu.sg/ecs/ub/w/w0309.df n Software iracy when iracy is Costly Sougata oddar August 003 Abstract: The ervasiveness of the illegal coying of
More informationAn optimal batch size for a JIT manufacturing system
Comuters & Industrial Engineering 4 (00) 17±136 www.elsevier.com/locate/dsw n otimal batch size for a JIT manufacturing system Lutfar R. Khan a, *, Ruhul. Sarker b a School of Communications and Informatics,
More informationCFRI 3,4. Zhengwei Wang PBC School of Finance, Tsinghua University, Beijing, China and SEBA, Beijing Normal University, Beijing, China
The current issue and full text archive of this journal is available at www.emeraldinsight.com/20441398.htm CFRI 3,4 322 constraints and cororate caital structure: a model Wuxiang Zhu School of Economics
More information