\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{{H}andbook of {M}athematical {F}unctions: with {F}ormulas,
  {G}raphs, and {M}athematical {T}ables}, volume~55.
\newblock Dover Publications, 1965.

\bibitem[Applebaum(2004)]{applebaum2004levy}
David Applebaum.
\newblock {L}{\'e}vy {P}rocesses: {F}rom {P}robability to {F}inance and
  {Q}uantum {G}roups.
\newblock \emph{Notices of the American Mathematical Society}, 51\penalty0
  (11):\penalty0 1336--1347, 2004.

\bibitem[Bachelier(1900)]{bachelier1900theorie}
Louis Bachelier.
\newblock \emph{{T}h{\'e}orie de la sp{\'e}culation}.
\newblock Gauthier-Villars, 1900.

\bibitem[Berkson(1980)]{berkson1980minimum}
Joseph Berkson.
\newblock {M}inimum {C}hi-square, not {M}aximum {L}ikelihood!
\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{{R}isk-Neutral {V}aluation: {P}ricing and {H}edging of
  {F}inancial {D}erivatives}.
\newblock Springer, 2004.

\bibitem[Black(1976)]{black1976pricing}
Fischer Black.
\newblock {T}he {P}ricing of {C}ommodity {C}ontracts.
\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 {T}he {P}ricing of {O}ptions and {C}orporate {L}iabilities.
\newblock \emph{The Journal of Political Economy}, pages 637--654, 1973.

\bibitem[Buckle(1995)]{buckle1995bayesian}
D.~J. Buckle.
\newblock {B}ayesian {I}nference for {S}table {D}istributions.
\newblock \emph{Journal of the American Statistical Association}, 90\penalty0
  (430):\penalty0 605--613, 1995.

\bibitem[Butler(2007)]{butler2007saddlepoint}
Ronald~W. Butler.
\newblock \emph{{S}addlepoint {A}pproximations with {A}pplications}, volume~22.
\newblock Cambridge University Press, 2007.

\bibitem[Carr et Madan(1999)]{carr1999option}
Peter~P. Carr et Dilip~B. Madan.
\newblock {O}ption {V}aluation {U}sing the {F}ast {F}ourier {T}ransform.
\newblock \emph{Journal of Computational Finance}, 2\penalty0 (4):\penalty0
  61--73, 1999.

\bibitem[Carr et~al.(1998)Carr, Chang, et Madan]{madan1998variance}
Peter~P. Carr, Eric~C. Chang, et Dilip~B. Madan.
\newblock {T}he {V}ariance {G}amma {P}rocess and {O}ption {P}ricing.
\newblock \emph{European Finance Review}, 2\penalty0 (1):\penalty0 79--105,
  1998.

\bibitem[Crowder(1986)]{crowder1986consistency}
Martin Crowder.
\newblock {O}n {C}onsistency and {I}nconsistency of {E}stimating {E}quations.
\newblock \emph{Econometric Theory}, pages 305--330, 1986.

\bibitem[Crowder(1987)]{crowder1987linear}
Martin Crowder.
\newblock {O}n {L}inear and {Q}uadratic {E}stimating {F}unctions.
\newblock \emph{Biometrika}, 74\penalty0 (3):\penalty0 591--597, 1987.

\bibitem[Daniels(1954)]{daniels1954saddlepoint}
Henry~E. Daniels.
\newblock {S}addlepoint {A}pproximations in {S}tatistics.
\newblock \emph{The Annals of Mathematical Statistics}, pages 631--650, 1954.

\bibitem[Derman(1996)]{derman1996modelrisk}
Emanuel Derman.
\newblock {M}odel {R}isk.
\newblock Technical report, Goldman Sachs, 1996.

\bibitem[Dodge(2004)]{dodge2004statistique}
Yadolah Dodge.
\newblock \emph{{S}tatistique: {D}ictionnaire Encyclop{\'e}dique}.
\newblock Springer Verlag France, 2004.

\bibitem[Epps(2007)]{epps2007pricing}
Thomas~W. Epps.
\newblock \emph{{P}ricing {D}erivative {S}ecurities}.
\newblock World Scientific Publishing Company incorporated, 2007.

\bibitem[Epps et Pulley(1983)]{epps1983test}
Thomas~W. Epps et Lawrence~B. Pulley.
\newblock {A} {T}est for {N}ormality {B}ased on the {E}mpirical
  {C}haracteristic {F}unction.
\newblock \emph{Biometrika}, 70\penalty0 (3):\penalty0 723--726, 1983.

\bibitem[Everitt et Skrondal(2006)]{everitt2006cambridge}
Brian Everitt et Anders Skrondal.
\newblock \emph{{T}he {C}ambridge {D}ictionary of {S}tatistics}, volume~4.
\newblock Cambridge University Press, 2006.

\bibitem[Fama et French(1993)]{fama1993common}
Eugene~F. Fama et Kenneth~R. French.
\newblock {C}ommon {R}isk {F}actors in the {R}eturns on {S}tocks and {B}onds.
\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 {O}n the {E}fficiency of {E}mpirical {C}haracteristic {F}unction
  {P}rocedures.
\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 {L}arge-sample {P}roperties of {P}arameter {E}stimates for {S}trongly
  {D}ependent {S}tationary {G}aussian {T}ime {S}eries.
\newblock \emph{The Annals of Statistics}, 14\penalty0 (2):\penalty0 517--532,
  1986.

\bibitem[Gil-Pelaez(1951)]{gil1951note}
J.~Gil-Pelaez.
\newblock {N}ote on the {I}nversion {T}heorem.
\newblock \emph{Biometrika}, 38\penalty0 (3-4):\penalty0 481--482, 1951.

\bibitem[Gourieroux et Monfort(1989)]{gourieroux1989statistique}
Christian Gourieroux et Alain Monfort.
\newblock \emph{{S}tatistique 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{{G}eneralized {M}ethod of {M}oments}.
\newblock Oxford University Press, 2005.

\bibitem[Hamilton(1994)]{hamilton1994time}
James~Douglas Hamilton.
\newblock \emph{{T}ime {S}eries {A}nalysis}, volume~2.
\newblock Cambridge University Press, 1994.

\bibitem[Hansen(1982)]{hansen1982large}
Lars~Peter Hansen.
\newblock {L}arge {S}ample {P}roperties of {G}eneralized {M}ethod of {M}oments
  {E}stimators.
\newblock \emph{Econometrica}, pages 1029--1054, 1982.

\bibitem[Henze(1990)]{henze1990approximation}
Norbert Henze.
\newblock {A}n {A}pproximation to the {L}imit {D}istribution of the
  {E}pps-{P}ulley {T}est {S}tatistic for {N}ormality.
\newblock \emph{Metrika}, 37\penalty0 (1):\penalty0 7--18, 1990.

\bibitem[Heston(1993)]{heston1993closed}
Steven~L. Heston.
\newblock {A} {C}losed-{F}orm {S}olution for {O}ptions with {S}tochastic
  {V}olatility with {A}pplications to {B}ond and {C}urrency {O}ptions.
\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 {E}stimation of the {P}areto {L}aw from {U}nderreported {D}ata: {A}
  {F}urther {A}nalysis.
\newblock \emph{Journal of Econometrics}, 5\penalty0 (1):\penalty0 1--11, 1977.

\bibitem[Hogg et Craig(1978)]{hogg1978introduction}
Robert~V. Hogg et Allen Craig.
\newblock \emph{{I}ntroduction to {M}athematical {S}tatistics}.
\newblock Macmillan, 1978.

\bibitem[iti Sato(1999)]{sato1999levy}
Ken iti Sato.
\newblock \emph{{L}{\'e}vy {P}rocesses and {I}nfinitely {D}ivisible
  {D}istributions}.
\newblock Cambridge Studies in Advanced Mathematics. Cambridge University
  Press, 1999.

\bibitem[Itkin(2005)]{itkin2005pricing}
Andrey Itkin.
\newblock {P}ricing {O}ptions with {VG} {M}odel {U}sing {FFT}.
\newblock \emph{arXiv preprint physics/0503137}, 2005.

\bibitem[{Jingbo Wang} et Marsaglia(2003)]{wang2003evaluating}
Wai Wan~Tsang {Jingbo Wang} et George Marsaglia.
\newblock {E}valuating {K}olmogorov's {D}istribution.
\newblock \emph{Journal of Statistical Software}, 8\penalty0 (18):\penalty0
  1--4, 2003.

\bibitem[Kotz et~al.(2001)Kotz, Kozubowski, et Podg{\'o}rski]{kotz2001laplace}
Samuel Kotz, Tomasz~J. Kozubowski, et Krzystof Podg{\'o}rski.
\newblock \emph{{T}he {L}aplace {D}istribution and {G}eneralizations: {A}
  {R}evisit with {A}pplications to {C}ommunications, {E}conomics,
  {E}ngineering, and {F}inance}.
\newblock Progress in Mathematics Series. Birkh{\"a}user, 2001.

\bibitem[Koutrouvelis(1980)]{KOUTROUVELIS01011980}
Ioannis~A. Koutrouvelis.
\newblock {{A} {G}oodness-{O}f-{F}it {T}est of {S}imple {H}ypotheses {B}ased on
  the {E}mpirical {C}haracteristic {F}unction}.
\newblock \emph{{B}iometrika}, 67\penalty0 (1):\penalty0 238--240, 1980.

\bibitem[Kozubowski et Podg{\'o}rski(1999)]{kozubowski1999class}
Tomasz~J. Kozubowski et Krzysztof Podg{\'o}rski.
\newblock {A} {C}lass of {A}symmetric {D}istributions.
\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 {A}symmetric {L}aplace {L}aws and {M}odeling {F}inancial {D}ata.
\newblock \emph{{M}athematical and {C}omputer {M}odeling}, 34\penalty0
  (9):\penalty0 1003--1021, 2001.

\bibitem[Kyprianou(2007)]{kyprianou2007introductory}
Andreas~E. Kyprianou.
\newblock \emph{{I}ntroductory {L}ectures on {F}luctuations of {L}{\'e}vy
  {P}rocesses with {A}pplications}.
\newblock Springer, 2007.

\bibitem[Lugannani et Rice(1980)]{lugannani1980saddle}
Robert Lugannani et Stephen Rice.
\newblock {S}addle {P}oint {A}pproximation for the {D}istribution of the {S}um
  of {I}ndependent {R}andom {V}ariables.
\newblock \emph{Advances in Applied Probability}, pages 475--490, 1980.

\bibitem[Lukacs(1960)]{lukacs1960characteristic}
Eugene Lukacs.
\newblock \emph{{C}haracteristic {F}unctions}, volume~4.
\newblock Griffin London, 1960.

\bibitem[Luong et Thompson(1987)]{luong1987minimum}
Andrew Luong et Mary~E. Thompson.
\newblock {M}inimum-{D}istance {M}ethods {B}ased on {Q}uadratic {D}istances for
  {T}ransforms.
\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 {T}he {V}ariance {G}amma {M}odel for {S}hare {M}arket {R}eturns.
\newblock \emph{Journal of Business}, pages 511--524, 1990.

\bibitem[Mandelbrot(1963)]{mandelbrot1963variation}
Benoit Mandelbrot.
\newblock {T}he {V}ariation of {C}ertain {S}peculative {P}rices.
\newblock \emph{Journal of Business}, pages 394--419, 1963.

\bibitem[Merton(1976)]{merton1976option}
Robert~C. Merton.
\newblock {O}ption {P}ricing when {U}nderlying {S}tock {R}eturns {A}re
  {D}iscontinuous.
\newblock \emph{Journal of Financial Economics}, 3\penalty0 (1):\penalty0
  125--144, 1976.

\bibitem[Mikosch et~al.(2001)Mikosch, Resnick, et
  Barndorff-Nielsen]{barndorff2001levy}
Thomas Mikosch, Sidney~I. Resnick, et Ole~E. Barndorff-Nielsen.
\newblock \emph{{L}{\'e}vy {P}rocesses: {T}heory and {A}pplications}.
\newblock Birkh{\"a}user, 2001.

\bibitem[Mitchell(1916)]{mitchell1916critique}
Wesley~C. Mitchell.
\newblock {A} {C}ritique of {I}ndex {N}umbers of the {P}rices of {S}tocks.
\newblock \emph{The Journal of Political Economy}, pages 625--693, 1916.

\bibitem[Newey et McFadden(1994)]{newey1994large}
Whitney~K. Newey et Daniel McFadden.
\newblock {L}arge {S}ample {E}stimation and {H}ypothesis {T}esting.
\newblock \emph{Handbook of Econometrics}, 4:\penalty0 2111--2245, 1994.

\bibitem[Newey et West(1987)]{newey1987hypothesis}
Whitney~K. Newey et Kenneth~D. West.
\newblock {H}ypothesis {T}esting with {E}fficient {M}ethod of {M}oments
  {E}stimation.
\newblock \emph{International Economic Review}, 28\penalty0 (3):\penalty0
  777--787, 1987.

\bibitem[Praetz(1972)]{praetz1972distribution}
Peter~D. Praetz.
\newblock {T}he {D}istribution of {S}hare {P}rice {C}hanges.
\newblock \emph{Journal of Business}, pages 49--55, 1972.

\bibitem[Press(1967)]{press1967compound}
S.~James Press.
\newblock {A} {C}ompound {E}vents {M}odel for {S}ecurity {P}rices.
\newblock \emph{Journal of Business}, pages 317--335, 1967.

\bibitem[Schoutens(2003)]{schoutens2003levy}
Wim Schoutens.
\newblock \emph{{L}{\'e}vy {P}rocesses in {F}inance}.
\newblock Wiley, 2003.

\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
David Scott et Christine~Yang Dong.
\newblock \emph{{{v}ariancegamma: {T}he {V}ariance {G}amma {D}istribution}},
  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 {F}itting the {V}ariance {G}amma {M}odel to {F}inancial {D}ata.
\newblock \emph{Journal of Applied Probability}, pages 177--187, 2004.

\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
Samuel~Sanford Shapiro et Martin~B. Wilk.
\newblock {A}n {A}nalysis of {V}ariance {T}est for {N}ormality ({C}omplete
  {S}amples).
\newblock \emph{Biometrika}, 52\penalty0 (3/4):\penalty0 591--611, 1965.

\bibitem[Shephard(1991)]{shephard1991characteristic}
Neil~G. Shephard.
\newblock {F}rom {C}haracteristic {F}unction to {D}istribution {F}unction: {A}
  {S}imple {F}ramework for the {T}heory.
\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{{S}chaum's {M}athematical {H}andbook of {F}ormulas and
  {T}ables}, volume 1000.
\newblock McGraw-Hill, 1999.

\bibitem[Stuart et Ord(1987)]{stuart1987kendall}
Alan Stuart et J.~Keith Ord.
\newblock \emph{{K}endall{\rq}s {A}dvanced {T}heory of {S}tatistics, {V}ol. 1}.
\newblock Oxford University Press, 1987.

\bibitem[Teschl(2004)]{teschl2004topics}
Gerald Teschl.
\newblock {T}opics in {R}eal and {F}unctional {A}nalysis.
\newblock 2004.
\newblock URL \url{http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html}.

\bibitem[Walter(1995)]{walterlevy}
Christian Walter.
\newblock {L}{\'e}vy-{S}tability {U}nder {A}ddition and {F}ractal {S}tructure
  of {M}arkets: {I}mplications for the {A}ctuaries and {E}mphasized
  {E}xamination of {MATIF} {N}ational {C}ontract.
\newblock In \emph{Proceedings of the 5th AFIR colloquium}. International
  Actuarial Association, 1995.

\bibitem[Wendel(1961)]{wendel1961non}
J.~G. Wendel.
\newblock {T}he {N}on-{A}bsolute {C}onvergence of {G}il-{P}elaez' {I}nversion
  {I}ntegral.
\newblock \emph{The Annals of Mathematical Statistics}, 32\penalty0
  (1):\penalty0 338--339, 1961.

\bibitem[Wolfowitz(1957)]{wolfowitz1957minimum}
Jacob Wolfowitz.
\newblock {T}he {M}inimum {D}istance {M}ethod.
\newblock \emph{The Annals of Mathematical Statistics}, pages 75--88, 1957.

\bibitem[Wooldridge(2001)]{wooldridge2001econometric}
Jeffrey~M. Wooldridge.
\newblock \emph{{E}conometric {A}nalysis of {C}ross {S}ection and {P}anel
  {D}ata}.
\newblock MIT press, 2001.

\end{thebibliography}