\begin{thebibliography}{63}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
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  \providecommand{\doi}[1]{doi: #1}\else
  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Abramowitz et Stegun(1965)]{abramowitz1965handbook}
Milton Abramowitz et Irene~A Stegun.
\newblock \emph{Handbook of mathematical functions: with formulas, graphs, and
  mathematical tables}, volume~55.
\newblock Dover publications, 1965.

\bibitem[Applebaum(2004)]{applebaum2004levy}
David Applebaum.
\newblock L{\'e}vy processes: From probability to finance and quantum groups.
\newblock \emph{Notices of the AMS}, 51\penalty0 (11):\penalty0 1336--1347,
  2004.

\bibitem[Bachelier(1900)]{bachelier1900theorie}
Louis Bachelier.
\newblock \emph{Th{\'e}orie de la sp{\'e}culation}.
\newblock Gauthier-Villars, 1900.

\bibitem[Barndorff-Nielsen et~al.(2001)Barndorff-Nielsen, Mikosch, et
  Resnick]{barndorff2001levy}
O.E.E. Barndorff-Nielsen, T.E. Mikosch, et S.I.E. Resnick.
\newblock \emph{L{\'e}vy Processes: Theory and Applications}.
\newblock Birkhäuser, 2001.
\newblock ISBN 9780817641672.
\newblock URL \url{http://books.google.ca/books?id=ExpTdTauXMwC}.

\bibitem[Berkson(1980)]{berkson1980minimum}
Joseph Berkson.
\newblock Minimum chi-square, not maximum likelihood!
\newblock \emph{The Annals of Statistics}, pages 457--487, 1980.

\bibitem[Bingham et Kiesel(2004)]{bingham2004risk}
Nicholas~H Bingham et R{\"u}diger Kiesel.
\newblock \emph{Risk-neutral valuation: Pricing and hedging of financial
  derivatives}.
\newblock Springer, 2004.

\bibitem[Black(1976)]{black1976pricing}
Fischer Black.
\newblock The pricing of commodity contracts.
\newblock \emph{Journal of financial economics}, 3\penalty0 (1):\penalty0
  167--179, 1976.

\bibitem[Black et Scholes(1973)]{black1973pricing}
Fischer Black et Myron Scholes.
\newblock The pricing of options and corporate liabilities.
\newblock \emph{The journal of political economy}, pages 637--654, 1973.

\bibitem[Buckle(1995)]{buckle1995bayesian}
DJ~Buckle.
\newblock Bayesian inference for stable distributions.
\newblock \emph{Journal of the American Statistical Association}, 90\penalty0
  (430):\penalty0 605--613, 1995.

\bibitem[Butler(2007)]{butler2007saddlepoint}
Ronald~W Butler.
\newblock \emph{Saddlepoint approximations with applications}, volume~22.
\newblock Cambridge University Press, 2007.

\bibitem[Carr et Madan(1999)]{carr1999option}
Peter Carr et Dilip Madan.
\newblock Option valuation using the fast fourier transform.
\newblock \emph{Journal of Computational Finance}, 2\penalty0 (4):\penalty0
  61--73, 1999.

\bibitem[Crowder(1986)]{crowder1986consistency}
Martin Crowder.
\newblock On consistency and inconsistency of estimating equations.
\newblock \emph{Econometric Theory}, pages 305--330, 1986.

\bibitem[Crowder(1987)]{crowder1987linear}
Martin Crowder.
\newblock On linear and quadratic estimating functions.
\newblock \emph{Biometrika}, 74\penalty0 (3):\penalty0 591--597, 1987.

\bibitem[Daniels(1954)]{daniels1954saddlepoint}
Henry~E Daniels.
\newblock Saddlepoint approximations in statistics.
\newblock \emph{The Annals of Mathematical Statistics}, pages 631--650, 1954.

\bibitem[Derman(1996)]{derman1996modelrisk}
Emanuel Derman.
\newblock Model risk.
\newblock Technical report, Goldman Sachs, 1996.

\bibitem[Dodge(2004)]{dodge2004statistique}
Yadolah Dodge.
\newblock \emph{Statistique: dictionnaire encyclop{\'e}dique}.
\newblock Springer Verlag France, 2004.

\bibitem[Epps(2007)]{epps2007pricing}
Thomas~W Epps.
\newblock \emph{Pricing derivative securities}.
\newblock World Scientific Publishing Company Incorporated, 2007.

\bibitem[Epps et Pulley(1983)]{epps1983test}
Thomas~W Epps et Lawrence~B Pulley.
\newblock A test for normality based on the empirical characteristic function.
\newblock \emph{Biometrika}, 70\penalty0 (3):\penalty0 723--726, 1983.

\bibitem[Everitt et Skrondal(2006)]{everitt2006cambridge}
Brian Everitt et Anders Skrondal.
\newblock \emph{The Cambridge dictionary of statistics}, volume~4.
\newblock Cambridge University Press Cambridge, 2006.

\bibitem[Fama et French(1993)]{fama1993common}
Eugene~F Fama et Kenneth~R French.
\newblock Common risk factors in the returns on stocks and bonds.
\newblock \emph{Journal of financial economics}, 33\penalty0 (1):\penalty0
  3--56, 1993.

\bibitem[Feuerverger et McDunnough(1981)]{feuerverger1981efficiency}
Andrey Feuerverger et Philip McDunnough.
\newblock On the efficiency of empirical characteristic function procedures.
\newblock \emph{Journal of the Royal Statistical Society. Series B
  (Methodological)}, pages 20--27, 1981.

\bibitem[Fox et Taqqu(1986)]{fox1986large}
Robert Fox et Murad~S Taqqu.
\newblock Large-sample properties of parameter estimates for strongly dependent
  stationary gaussian time series.
\newblock \emph{The Annals of Statistics}, 14\penalty0 (2):\penalty0 517--532,
  1986.

\bibitem[Gil-Pelaez(1951)]{gil1951note}
J~Gil-Pelaez.
\newblock Note on the inversion theorem.
\newblock \emph{Biometrika}, 38\penalty0 (3-4):\penalty0 481--482, 1951.

\bibitem[Gourieroux et Monfort(1989)]{gourieroux1989statistique}
Christian Gourieroux et Alain Monfort.
\newblock \emph{Statistique et mod{\`e}les {\'e}conom{\'e}triques: Notions
  g{\'e}n{\'e}rales, estimation, pr{\'e}vision, algorithmes}, volume~1.
\newblock Economica, 1989.

\bibitem[Hall(2005)]{hall2005generalized}
Alastair~R Hall.
\newblock \emph{Generalized method of moments}.
\newblock Oxford University Press Oxford, 2005.

\bibitem[Hamilton(1994)]{hamilton1994time}
James~Douglas Hamilton.
\newblock \emph{Time series analysis}, volume~2.
\newblock Cambridge Univ Press, 1994.

\bibitem[Hansen(1982)]{hansen1982large}
Lars~Peter Hansen.
\newblock Large sample properties of generalized method of moments estimators.
\newblock \emph{Econometrica: Journal of the Econometric Society}, pages
  1029--1054, 1982.

\bibitem[Henze(1990)]{henze1990approximation}
N~Henze.
\newblock An approximation to the limit distribution of the epps-pulley test
  statistic for normality.
\newblock \emph{Metrika}, 37\penalty0 (1):\penalty0 7--18, 1990.

\bibitem[Heston(1993)]{heston1993closed}
Steven~L Heston.
\newblock A closed-form solution for options with stochastic volatility with
  applications to bond and currency options.
\newblock \emph{Review of financial studies}, 6\penalty0 (2):\penalty0
  327--343, 1993.

\bibitem[Hinkley et Revankar(1977)]{hinkley1977estimation}
David~V Hinkley et Nagesh~S Revankar.
\newblock Estimation of the pareto law from underreported data: A further
  analysis.
\newblock \emph{Journal of Econometrics}, 5\penalty0 (1):\penalty0 1--11, 1977.

\bibitem[Hogg et Craig(1978)]{hogg1978introduction}
R.V. Hogg et A.T. Craig.
\newblock \emph{Introduction to mathematical statistics}.
\newblock Macmillan, 1978.
\newblock ISBN 9780029789902.
\newblock URL \url{http://books.google.ca/books?id=OZYQAQAAIAAJ}.

\bibitem[Itkin(2005)]{itkin2005pricing}
Andrey Itkin.
\newblock Pricing options with vg model using fft.
\newblock \emph{arXiv preprint physics/0503137}, 2005.

\bibitem[Kotz et~al.(2001)Kotz, Kozubowski, et Podg{\'o}rski]{kotz2001laplace}
S.~Kotz, T.J. Kozubowski, et K.~Podg{\'o}rski.
\newblock \emph{The Laplace Distribution and Generalizations: A Revisit With
  Applications to Communications, Exonomics, Engineering, and Finance}.
\newblock Progress in Mathematics Series. Birkh{\"a}user, 2001.
\newblock ISBN 9780817641665.
\newblock URL \url{http://books.google.ca/books?id=cb8B07hwULUC}.

\bibitem[Koutrouvelis(1980)]{KOUTROUVELIS01011980}
I.~A. Koutrouvelis.
\newblock A goodness-of-fit test of simple hypotheses based on the empirical
  characteristic function.
\newblock \emph{Biometrika}, 67\penalty0 (1):\penalty0 238--240, 1980.
\newblock \doi{10.1093/biomet/67.1.238}.
\newblock URL \url{http://biomet.oxfordjournals.org/content/67/1/238.abstract}.

\bibitem[Kozubowski et Podg{\'o}rski(1999)]{kozubowski1999class}
Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
\newblock A class of asymmetric distributions.
\newblock \emph{Actuarial Research Clearing House}, 1:\penalty0 113--134, 1999.

\bibitem[Kozubowski et Podg{\'o}rski(2001)]{kozubowski2001asymmetric}
Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
\newblock Asymmetric laplace laws and modeling financial data.
\newblock \emph{Mathematical and computer modelling}, 34\penalty0 (9):\penalty0
  1003--1021, 2001.

\bibitem[Kyprianou(2007)]{kyprianou2007introductory}
Andreas~E Kyprianou.
\newblock \emph{Introductory lectures on fluctuations of L{\'e}vy processes
  with applications}.
\newblock Springer, 2007.

\bibitem[Lugannani et Rice(1980)]{lugannani1980saddle}
Robert Lugannani et Stephen Rice.
\newblock Saddle point approximation for the distribution of the sum of
  independent random variables.
\newblock \emph{Advances in applied probability}, pages 475--490, 1980.

\bibitem[Lukacs(1960)]{lukacs1960characteristic}
Eugene Lukacs.
\newblock \emph{Characteristic functions}, volume~4.
\newblock Griffin London, 1960.

\bibitem[Luong et Thompson(1987)]{luong1987minimum}
A~Luong et ME~Thompson.
\newblock Minimum-distance methods based on quadratic distances for transforms.
\newblock \emph{Canadian Journal of Statistics}, 15\penalty0 (3):\penalty0
  239--251, 1987.

\bibitem[Madan et Seneta(1990)]{madan1990variance}
Dilip~B Madan et Eugene Seneta.
\newblock The variance gamma (vg) model for share market returns.
\newblock \emph{Journal of business}, pages 511--524, 1990.

\bibitem[Madan et~al.(1998)Madan, Carr, et Chang]{madan1998variance}
Dilip~B Madan, Peter~P Carr, et Eric~C Chang.
\newblock The variance gamma process and option pricing.
\newblock \emph{European Finance Review}, 2\penalty0 (1):\penalty0 79--105,
  1998.

\bibitem[Mandelbrot(1963)]{mandelbrot1963variation}
B.~Mandelbrot.
\newblock The variation of certain speculative prices.
\newblock \emph{Journal of business}, pages 394--419, 1963.

\bibitem[Merton(1976)]{merton1976option}
Robert~C Merton.
\newblock Option pricing when underlying stock returns are discontinuous.
\newblock \emph{Journal of financial economics}, 3\penalty0 (1):\penalty0
  125--144, 1976.

\bibitem[Mitchell(1916)]{mitchell1916critique}
Wesley~C Mitchell.
\newblock A critique of index numbers of the prices of stocks.
\newblock \emph{The Journal of Political Economy}, pages 625--693, 1916.

\bibitem[Newey et McFadden(1994)]{newey1994large}
Whitney~K Newey et Daniel McFadden.
\newblock Large sample estimation and hypothesis testing.
\newblock \emph{Handbook of econometrics}, 4:\penalty0 2111--2245, 1994.

\bibitem[Newey et West(1987)]{newey1987hypothesis}
Whitney~K Newey et Kenneth~D West.
\newblock Hypothesis testing with efficient method of moments estimation.
\newblock \emph{International Economic Review}, 28\penalty0 (3):\penalty0
  777--787, 1987.

\bibitem[Praetz(1972)]{praetz1972distribution}
Peter~D Praetz.
\newblock The distribution of share price changes.
\newblock \emph{Journal of business}, pages 49--55, 1972.

\bibitem[Press(1967)]{press1967compound}
S~James Press.
\newblock A compound events model for security prices.
\newblock \emph{Journal of Business}, pages 317--335, 1967.

\bibitem[Sato(1999)]{sato1999levy}
K.~Sato.
\newblock \emph{L{\'e}vy Processes and Infinitely Divisible Distributions}.
\newblock Cambridge Studies in Advanced Mathematics. Cambridge University
  Press, 1999.
\newblock ISBN 9780521553025.
\newblock URL \url{http://books.google.ca/books?id=CwT5BNG0-owC}.

\bibitem[Schoutens(2003)]{schoutens2003levy}
Wim Schoutens.
\newblock \emph{L{\'e}vy processes in Finance}.
\newblock Wiley, 2003.

\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
David Scott et Christine~Yang Dong.
\newblock \emph{VarianceGamma: The Variance Gamma Distribution}, 2012.
\newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}.
\newblock R package version 0.3-1.

\bibitem[Seneta(2004)]{seneta2004fitting}
Eugene Seneta.
\newblock Fitting the variance-gamma model to financial data.
\newblock \emph{Journal of Applied Probability}, pages 177--187, 2004.

\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
Samuel~Sanford Shapiro et Martin~B Wilk.
\newblock An analysis of variance test for normality (complete samples).
\newblock \emph{Biometrika}, 52\penalty0 (3/4):\penalty0 591--611, 1965.

\bibitem[Shephard(1991)]{shephard1991characteristic}
Neil~G Shephard.
\newblock From characteristic function to distribution function: a simple
  framework for the theory.
\newblock \emph{Econometric Theory}, 7\penalty0 (04):\penalty0 519--529, 1991.

\bibitem[Spiegel et Liu(1999)]{spiegel1999schaum}
Murray~R Spiegel et John Liu.
\newblock \emph{Schaum's mathematical handbook of formulas and tables}, volume
  1000.
\newblock McGraw-Hill, 1999.

\bibitem[Stuart et Ord(1987)]{stuart1987kendall}
Alan Stuart et J~Keith Ord.
\newblock \emph{Kendall’s advanced theory of statistics, Vol. 1}.
\newblock Oxford University Press, New York, 1987.

\bibitem[Teschl(2004)]{teschl2004topics}
Gerald Teschl.
\newblock Topics in real and functional analysis.
\newblock \emph{unpublished, available online at
  \url{http://www.mat.univie.ac.at/\~gerald}}, 2004.

\bibitem[Walter()]{walterlevy}
Christian Walter.
\newblock Levy-stability-under-addition and fractal structure of markets:
  imlications for the actuaries and emphasized axamination of matif national
  contract.

\bibitem[Wang et~al.(2003)Wang, Tsang, et Marsaglia]{wang2003evaluating}
Jingbo Wang, Wai~Wan Tsang, et George Marsaglia.
\newblock Evaluating kolmogorov's distribution.
\newblock \emph{Journal of Statistical Software}, 8\penalty0 (18):\penalty0
  1--4, 2003.

\bibitem[Wendel(1961)]{wendel1961non}
JG~Wendel.
\newblock The non-absolute convergence of gil-pelaez'inversion integral.
\newblock \emph{The Annals of Mathematical Statistics}, 32\penalty0
  (1):\penalty0 338--339, 1961.

\bibitem[Wolfowitz(1957)]{wolfowitz1957minimum}
Jacob Wolfowitz.
\newblock The minimum distance method.
\newblock \emph{The Annals of Mathematical Statistics}, pages 75--88, 1957.

\bibitem[Wooldridge(2001)]{wooldridge2001econometric}
Jeffrey~M Wooldridge.
\newblock \emph{Econometric analysis of cross section and panel data}.
\newblock MIT press, 2001.

\end{thebibliography}