367 lines
14 KiB
Text
367 lines
14 KiB
Text
\begin{thebibliography}{63}
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\providecommand{\natexlab}[1]{#1}
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\providecommand{\url}[1]{\texttt{#1}}
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\expandafter\ifx\csname urlstyle\endcsname\relax
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\providecommand{\doi}[1]{doi: #1}\else
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\providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi
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\bibitem[Abramowitz et Stegun(1965)]{abramowitz1965handbook}
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Milton Abramowitz et Irene~A Stegun.
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\newblock \emph{Handbook of mathematical functions: with formulas, graphs, and
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mathematical tables}, volume~55.
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\newblock Dover publications, 1965.
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\bibitem[Applebaum(2004)]{applebaum2004levy}
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David Applebaum.
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\newblock L{\'e}vy processes: From probability to finance and quantum groups.
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\newblock \emph{Notices of the AMS}, 51\penalty0 (11):\penalty0 1336--1347,
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2004.
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\bibitem[Bachelier(1900)]{bachelier1900theorie}
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Louis Bachelier.
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\newblock \emph{Th{\'e}orie de la sp{\'e}culation}.
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\newblock Gauthier-Villars, 1900.
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\bibitem[Barndorff-Nielsen et~al.(2001)Barndorff-Nielsen, Mikosch, et
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Resnick]{barndorff2001levy}
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O.E.E. Barndorff-Nielsen, T.E. Mikosch, et S.I.E. Resnick.
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\newblock \emph{L{\'e}vy Processes: Theory and Applications}.
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\newblock Birkhäuser, 2001.
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\newblock ISBN 9780817641672.
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\newblock URL \url{http://books.google.ca/books?id=ExpTdTauXMwC}.
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\bibitem[Berkson(1980)]{berkson1980minimum}
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Joseph Berkson.
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\newblock Minimum chi-square, not maximum likelihood!
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\newblock \emph{The Annals of Statistics}, pages 457--487, 1980.
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\bibitem[Bingham et Kiesel(2004)]{bingham2004risk}
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Nicholas~H Bingham et R{\"u}diger Kiesel.
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\newblock \emph{Risk-neutral valuation: Pricing and hedging of financial
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derivatives}.
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\newblock Springer, 2004.
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\bibitem[Black(1976)]{black1976pricing}
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Fischer Black.
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\newblock The pricing of commodity contracts.
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\newblock \emph{Journal of financial economics}, 3\penalty0 (1):\penalty0
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167--179, 1976.
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\bibitem[Black et Scholes(1973)]{black1973pricing}
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Fischer Black et Myron Scholes.
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\newblock The pricing of options and corporate liabilities.
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\newblock \emph{The journal of political economy}, pages 637--654, 1973.
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\bibitem[Buckle(1995)]{buckle1995bayesian}
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DJ~Buckle.
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\newblock Bayesian inference for stable distributions.
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\newblock \emph{Journal of the American Statistical Association}, 90\penalty0
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(430):\penalty0 605--613, 1995.
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\bibitem[Butler(2007)]{butler2007saddlepoint}
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Ronald~W Butler.
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\newblock \emph{Saddlepoint approximations with applications}, volume~22.
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\newblock Cambridge University Press, 2007.
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\bibitem[Carr et Madan(1999)]{carr1999option}
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Peter Carr et Dilip Madan.
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\newblock Option valuation using the fast fourier transform.
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\newblock \emph{Journal of Computational Finance}, 2\penalty0 (4):\penalty0
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61--73, 1999.
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\bibitem[Crowder(1986)]{crowder1986consistency}
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Martin Crowder.
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\newblock On consistency and inconsistency of estimating equations.
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\newblock \emph{Econometric Theory}, pages 305--330, 1986.
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\bibitem[Crowder(1987)]{crowder1987linear}
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Martin Crowder.
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\newblock On linear and quadratic estimating functions.
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\newblock \emph{Biometrika}, 74\penalty0 (3):\penalty0 591--597, 1987.
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\bibitem[Daniels(1954)]{daniels1954saddlepoint}
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Henry~E Daniels.
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\newblock Saddlepoint approximations in statistics.
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\newblock \emph{The Annals of Mathematical Statistics}, pages 631--650, 1954.
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\bibitem[Derman(1996)]{derman1996modelrisk}
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Emanuel Derman.
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\newblock Model risk.
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\newblock Technical report, Goldman Sachs, 1996.
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\bibitem[Dodge(2004)]{dodge2004statistique}
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Yadolah Dodge.
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\newblock \emph{Statistique: dictionnaire encyclop{\'e}dique}.
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\newblock Springer Verlag France, 2004.
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\bibitem[Epps(2007)]{epps2007pricing}
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Thomas~W Epps.
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\newblock \emph{Pricing derivative securities}.
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\newblock World Scientific Publishing Company Incorporated, 2007.
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\bibitem[Epps et Pulley(1983)]{epps1983test}
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Thomas~W Epps et Lawrence~B Pulley.
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\newblock A test for normality based on the empirical characteristic function.
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\newblock \emph{Biometrika}, 70\penalty0 (3):\penalty0 723--726, 1983.
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\bibitem[Everitt et Skrondal(2006)]{everitt2006cambridge}
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Brian Everitt et Anders Skrondal.
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\newblock \emph{The Cambridge dictionary of statistics}, volume~4.
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\newblock Cambridge University Press Cambridge, 2006.
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\bibitem[Fama et French(1993)]{fama1993common}
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Eugene~F Fama et Kenneth~R French.
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\newblock Common risk factors in the returns on stocks and bonds.
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\newblock \emph{Journal of financial economics}, 33\penalty0 (1):\penalty0
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3--56, 1993.
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\bibitem[Feuerverger et McDunnough(1981)]{feuerverger1981efficiency}
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Andrey Feuerverger et Philip McDunnough.
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\newblock On the efficiency of empirical characteristic function procedures.
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\newblock \emph{Journal of the Royal Statistical Society. Series B
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(Methodological)}, pages 20--27, 1981.
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\bibitem[Fox et Taqqu(1986)]{fox1986large}
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Robert Fox et Murad~S Taqqu.
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\newblock Large-sample properties of parameter estimates for strongly dependent
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stationary gaussian time series.
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\newblock \emph{The Annals of Statistics}, 14\penalty0 (2):\penalty0 517--532,
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1986.
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\bibitem[Gil-Pelaez(1951)]{gil1951note}
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J~Gil-Pelaez.
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\newblock Note on the inversion theorem.
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\newblock \emph{Biometrika}, 38\penalty0 (3-4):\penalty0 481--482, 1951.
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\bibitem[Gourieroux et Monfort(1989)]{gourieroux1989statistique}
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Christian Gourieroux et Alain Monfort.
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\newblock \emph{Statistique et mod{\`e}les {\'e}conom{\'e}triques: Notions
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g{\'e}n{\'e}rales, estimation, pr{\'e}vision, algorithmes}, volume~1.
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\newblock Economica, 1989.
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\bibitem[Hall(2005)]{hall2005generalized}
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Alastair~R Hall.
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\newblock \emph{Generalized method of moments}.
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\newblock Oxford University Press Oxford, 2005.
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\bibitem[Hamilton(1994)]{hamilton1994time}
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James~Douglas Hamilton.
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\newblock \emph{Time series analysis}, volume~2.
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\newblock Cambridge Univ Press, 1994.
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\bibitem[Hansen(1982)]{hansen1982large}
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Lars~Peter Hansen.
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\newblock Large sample properties of generalized method of moments estimators.
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\newblock \emph{Econometrica: Journal of the Econometric Society}, pages
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1029--1054, 1982.
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\bibitem[Henze(1990)]{henze1990approximation}
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N~Henze.
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\newblock An approximation to the limit distribution of the epps-pulley test
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statistic for normality.
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\newblock \emph{Metrika}, 37\penalty0 (1):\penalty0 7--18, 1990.
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\bibitem[Heston(1993)]{heston1993closed}
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Steven~L Heston.
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\newblock A closed-form solution for options with stochastic volatility with
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applications to bond and currency options.
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\newblock \emph{Review of financial studies}, 6\penalty0 (2):\penalty0
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327--343, 1993.
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\bibitem[Hinkley et Revankar(1977)]{hinkley1977estimation}
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David~V Hinkley et Nagesh~S Revankar.
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\newblock Estimation of the pareto law from underreported data: A further
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analysis.
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\newblock \emph{Journal of Econometrics}, 5\penalty0 (1):\penalty0 1--11, 1977.
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\bibitem[Hogg et Craig(1978)]{hogg1978introduction}
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R.V. Hogg et A.T. Craig.
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\newblock \emph{Introduction to mathematical statistics}.
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\newblock Macmillan, 1978.
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\newblock ISBN 9780029789902.
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\newblock URL \url{http://books.google.ca/books?id=OZYQAQAAIAAJ}.
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\bibitem[Itkin(2005)]{itkin2005pricing}
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Andrey Itkin.
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\newblock Pricing options with vg model using fft.
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\newblock \emph{arXiv preprint physics/0503137}, 2005.
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\bibitem[Kotz et~al.(2001)Kotz, Kozubowski, et Podg{\'o}rski]{kotz2001laplace}
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S.~Kotz, T.J. Kozubowski, et K.~Podg{\'o}rski.
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\newblock \emph{The Laplace Distribution and Generalizations: A Revisit With
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Applications to Communications, Exonomics, Engineering, and Finance}.
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\newblock Progress in Mathematics Series. Birkh{\"a}user, 2001.
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\newblock ISBN 9780817641665.
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\newblock URL \url{http://books.google.ca/books?id=cb8B07hwULUC}.
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\bibitem[Koutrouvelis(1980)]{KOUTROUVELIS01011980}
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I.~A. Koutrouvelis.
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\newblock A goodness-of-fit test of simple hypotheses based on the empirical
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characteristic function.
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\newblock \emph{Biometrika}, 67\penalty0 (1):\penalty0 238--240, 1980.
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\newblock \doi{10.1093/biomet/67.1.238}.
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\newblock URL \url{http://biomet.oxfordjournals.org/content/67/1/238.abstract}.
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\bibitem[Kozubowski et Podg{\'o}rski(1999)]{kozubowski1999class}
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Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
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\newblock A class of asymmetric distributions.
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\newblock \emph{Actuarial Research Clearing House}, 1:\penalty0 113--134, 1999.
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\bibitem[Kozubowski et Podg{\'o}rski(2001)]{kozubowski2001asymmetric}
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Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
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\newblock Asymmetric laplace laws and modeling financial data.
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\newblock \emph{Mathematical and computer modelling}, 34\penalty0 (9):\penalty0
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1003--1021, 2001.
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\bibitem[Kyprianou(2007)]{kyprianou2007introductory}
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Andreas~E Kyprianou.
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\newblock \emph{Introductory lectures on fluctuations of L{\'e}vy processes
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with applications}.
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\newblock Springer, 2007.
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\bibitem[Lugannani et Rice(1980)]{lugannani1980saddle}
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Robert Lugannani et Stephen Rice.
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\newblock Saddle point approximation for the distribution of the sum of
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independent random variables.
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\newblock \emph{Advances in applied probability}, pages 475--490, 1980.
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\bibitem[Lukacs(1960)]{lukacs1960characteristic}
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Eugene Lukacs.
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\newblock \emph{Characteristic functions}, volume~4.
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\newblock Griffin London, 1960.
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\bibitem[Luong et Thompson(1987)]{luong1987minimum}
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A~Luong et ME~Thompson.
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\newblock Minimum-distance methods based on quadratic distances for transforms.
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\newblock \emph{Canadian Journal of Statistics}, 15\penalty0 (3):\penalty0
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239--251, 1987.
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\bibitem[Madan et Seneta(1990)]{madan1990variance}
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Dilip~B Madan et Eugene Seneta.
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\newblock The variance gamma (vg) model for share market returns.
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\newblock \emph{Journal of business}, pages 511--524, 1990.
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\bibitem[Madan et~al.(1998)Madan, Carr, et Chang]{madan1998variance}
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Dilip~B Madan, Peter~P Carr, et Eric~C Chang.
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\newblock The variance gamma process and option pricing.
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\newblock \emph{European Finance Review}, 2\penalty0 (1):\penalty0 79--105,
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1998.
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\bibitem[Mandelbrot(1963)]{mandelbrot1963variation}
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B.~Mandelbrot.
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\newblock The variation of certain speculative prices.
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\newblock \emph{Journal of business}, pages 394--419, 1963.
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\bibitem[Merton(1976)]{merton1976option}
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Robert~C Merton.
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\newblock Option pricing when underlying stock returns are discontinuous.
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\newblock \emph{Journal of financial economics}, 3\penalty0 (1):\penalty0
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125--144, 1976.
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\bibitem[Mitchell(1916)]{mitchell1916critique}
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Wesley~C Mitchell.
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\newblock A critique of index numbers of the prices of stocks.
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\newblock \emph{The Journal of Political Economy}, pages 625--693, 1916.
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\bibitem[Newey et McFadden(1994)]{newey1994large}
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Whitney~K Newey et Daniel McFadden.
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\newblock Large sample estimation and hypothesis testing.
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\newblock \emph{Handbook of econometrics}, 4:\penalty0 2111--2245, 1994.
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\bibitem[Newey et West(1987)]{newey1987hypothesis}
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Whitney~K Newey et Kenneth~D West.
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\newblock Hypothesis testing with efficient method of moments estimation.
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\newblock \emph{International Economic Review}, 28\penalty0 (3):\penalty0
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777--787, 1987.
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\bibitem[Praetz(1972)]{praetz1972distribution}
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Peter~D Praetz.
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\newblock The distribution of share price changes.
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\newblock \emph{Journal of business}, pages 49--55, 1972.
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\bibitem[Press(1967)]{press1967compound}
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S~James Press.
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\newblock A compound events model for security prices.
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\newblock \emph{Journal of Business}, pages 317--335, 1967.
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\bibitem[Sato(1999)]{sato1999levy}
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K.~Sato.
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\newblock \emph{L{\'e}vy Processes and Infinitely Divisible Distributions}.
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\newblock Cambridge Studies in Advanced Mathematics. Cambridge University
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Press, 1999.
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\newblock ISBN 9780521553025.
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\newblock URL \url{http://books.google.ca/books?id=CwT5BNG0-owC}.
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\bibitem[Schoutens(2003)]{schoutens2003levy}
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Wim Schoutens.
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\newblock \emph{L{\'e}vy processes in Finance}.
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\newblock Wiley, 2003.
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\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
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David Scott et Christine~Yang Dong.
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\newblock \emph{VarianceGamma: The Variance Gamma Distribution}, 2012.
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\newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}.
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\newblock R package version 0.3-1.
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\bibitem[Seneta(2004)]{seneta2004fitting}
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Eugene Seneta.
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\newblock Fitting the variance-gamma model to financial data.
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\newblock \emph{Journal of Applied Probability}, pages 177--187, 2004.
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\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
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Samuel~Sanford Shapiro et Martin~B Wilk.
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\newblock An analysis of variance test for normality (complete samples).
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\newblock \emph{Biometrika}, 52\penalty0 (3/4):\penalty0 591--611, 1965.
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\bibitem[Shephard(1991)]{shephard1991characteristic}
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Neil~G Shephard.
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\newblock From characteristic function to distribution function: a simple
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framework for the theory.
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\newblock \emph{Econometric Theory}, 7\penalty0 (04):\penalty0 519--529, 1991.
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\bibitem[Spiegel et Liu(1999)]{spiegel1999schaum}
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Murray~R Spiegel et John Liu.
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\newblock \emph{Schaum's mathematical handbook of formulas and tables}, volume
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1000.
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\newblock McGraw-Hill, 1999.
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\bibitem[Stuart et Ord(1987)]{stuart1987kendall}
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Alan Stuart et J~Keith Ord.
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\newblock \emph{Kendall’s advanced theory of statistics, Vol. 1}.
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\newblock Oxford University Press, New York, 1987.
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\bibitem[Teschl(2004)]{teschl2004topics}
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Gerald Teschl.
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\newblock Topics in real and functional analysis.
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\newblock \emph{unpublished, available online at
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\url{http://www.mat.univie.ac.at/\~gerald}}, 2004.
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\bibitem[Walter()]{walterlevy}
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Christian Walter.
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\newblock Levy-stability-under-addition and fractal structure of markets:
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imlications for the actuaries and emphasized axamination of matif national
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contract.
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\bibitem[Wang et~al.(2003)Wang, Tsang, et Marsaglia]{wang2003evaluating}
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Jingbo Wang, Wai~Wan Tsang, et George Marsaglia.
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\newblock Evaluating kolmogorov's distribution.
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\newblock \emph{Journal of Statistical Software}, 8\penalty0 (18):\penalty0
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1--4, 2003.
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\bibitem[Wendel(1961)]{wendel1961non}
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JG~Wendel.
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\newblock The non-absolute convergence of gil-pelaez'inversion integral.
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\newblock \emph{The Annals of Mathematical Statistics}, 32\penalty0
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(1):\penalty0 338--339, 1961.
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\bibitem[Wolfowitz(1957)]{wolfowitz1957minimum}
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Jacob Wolfowitz.
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\newblock The minimum distance method.
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\newblock \emph{The Annals of Mathematical Statistics}, pages 75--88, 1957.
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\bibitem[Wooldridge(2001)]{wooldridge2001econometric}
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Jeffrey~M Wooldridge.
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\newblock \emph{Econometric analysis of cross section and panel data}.
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\newblock MIT press, 2001.
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\end{thebibliography}
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