E. Alós, O. Mazet, and D. Nualart, Stochastic calculus with respect to Gaussian processes. The Annals of Probability, pp.766-801, 2001.

E. Alós, J. A. León, and J. Vives, An anticipating Itô formula for Lévy processes. ALEA Lat, Am. J. Probab. Math. Stat, vol.4, pp.285-305, 2008.

J. Ansel and C. Stricker, Lois de martingale, densités et décomposition de Föllmer- Schweizer, Ann. Inst. H. Poincaré Probab. Statist, vol.28, issue.3, pp.375-392, 1992.

R. T. Baillie, Long memory processes and fractional integration in econometrics, Journal of Econometrics, vol.73, issue.1, pp.5-59, 1996.
DOI : 10.1016/0304-4076(95)01732-1

C. Bender, An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stochastic Process, Appl, vol.104, issue.1, pp.81-106, 2003.

C. Bender and T. Marquardt, Stochastic calculus for convoluted L??vy processes, Bernoulli, vol.14, issue.2, pp.499-518, 2008.
DOI : 10.3150/07-BEJ115

C. Bender, T. Sottinen, and E. Valkeila, Fractional Processes as Models in Stochastic Finance, Advanced mathematical methods for finance, pp.75-103, 2011.
DOI : 10.1007/978-3-642-18412-3_3

C. Bender, T. Sottinen, and E. Valkeila, Pricing by hedging and no-arbitrage beyond??semimartingales, Finance and Stochastics, vol.2, issue.2, pp.441-468, 2008.
DOI : 10.1142/3907

J. Beran, Statistics for long-memory processes, of Monographs on Statistics and Applied Probability. Chapman and Hall, 1994.

F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications. Probability and Its Applications, 2008.

T. R. Bielecki and M. Rutkowski, Credit risk: Modeling, valuation and hedging, 2002.
DOI : 10.1007/978-3-662-04821-4

F. Black and J. C. Cox, VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS, The Journal of Finance, vol.90, issue.1, pp.351-67, 1976.
DOI : 10.1111/j.1540-6261.1976.tb01891.x

F. Black and M. S. Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-54, 1973.
DOI : 10.1086/260062

F. Black and P. Karasinski, Bond and Option Pricing when Short Rates are Lognormal, Financial Analysts Journal, vol.47, issue.4, 1991.
DOI : 10.2469/faj.v47.n4.52

J. Bouchaud and D. Sornette, The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes, Journal de Physique I, vol.4, issue.6, 1994.
DOI : 10.1051/jp1:1994233

URL : https://hal.archives-ouvertes.fr/jpa-00246951

P. Brémaud, Point processes and queues: Martingale dynamics, 1981.
DOI : 10.1007/978-1-4684-9477-8

P. Carmona and L. Coutin, Fractional Brownian Motion and the Markov Property, Electronic Communications in Probability, vol.3, issue.0, pp.95-107, 1998.
DOI : 10.1214/ECP.v3-998

URL : https://hal.archives-ouvertes.fr/hal-00265452

P. Carmona, L. Coutin, and G. Montseny, Stochastic integration with respect to fractional brownian motion, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.39, issue.1, pp.27-68, 2003.
DOI : 10.1016/S0246-0203(02)01111-1

P. Cheridito, Regularizing fractional Brownian motion with a view towards stock price modelling

P. Cheridito, Mixed Fractional Brownian Motion, Bernoulli, vol.7, issue.6, pp.913-934, 2001.
DOI : 10.2307/3318626

URL : http://www.maths.soton.ac.uk/EMIS/journals/HOA/JAMSA/Volume2006/32435.pdf

P. Cheridito, Arbitrage in fractional Brownian motion models, Finance and Stochastics, vol.7, issue.4, pp.533-553, 2003.
DOI : 10.1007/s007800300101

M. Ø. Bent-jesper-christensen, J. Nielsen, and . Zhu, Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model, Journal of Empirical Finance, vol.17, issue.3, pp.460-470, 2010.
DOI : 10.1016/j.jempfin.2009.09.008

A. Chronopoulou and S. Tindel, On inference for fractional differential equations, Statistical Inference for Stochastic Processes, vol.111, issue.1, pp.29-61, 2013.
DOI : 10.1007/s004400050171

URL : https://hal.archives-ouvertes.fr/hal-00587087

E. Cinlar, Introduction to stochastic processes, 1975.

G. Mandelker, J. Clarke, and T. Jandik, Expert Financial Planning: Investment Strategies from Industry Leaders, Chapter The Efficient Markets Hypothesis, pp.126-141, 2001.

R. Cont, Long range dependence in financial markets, Fractals in Engineering, pp.159-180, 2005.
DOI : 10.1007/1-84628-048-6_11

R. Cont, Empirical properties of asset returns: stylized facts and statistical issues, Quantitative Finance, vol.1, issue.2, pp.223-236, 2001.
DOI : 10.1080/713665670

R. Cont and P. Tankov, Financial modelling with jump processes, Chapman & Hall/ CRC Financial Mathematics Series. Chapman & Hall/CRC, vol.2, 2004.
DOI : 10.1201/9780203485217

URL : https://hal.archives-ouvertes.fr/hal-00002693

R. Coviello, C. Di-girolami, and F. Russo, On stochastic calculus related to financial assets without semimartingales, Bulletin des Sciences Math??matiques, vol.135, issue.6-7, pp.6-7733, 2011.
DOI : 10.1016/j.bulsci.2011.06.008

URL : https://hal.archives-ouvertes.fr/inria-00564756

J. C. Cox, J. E. Ingersoll, J. , and S. A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, vol.53, issue.2, pp.385-407, 1985.
DOI : 10.2307/1911242

F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Mathematische Annalen, vol.286, issue.1, pp.463-520, 1994.
DOI : 10.1007/978-3-662-21726-9

G. Di and N. , On orthogonal polynomials and the Malliavin derivative for Lévy stochastic measures, Analyse et probabilités, pp.55-70, 2008.

G. Di, N. , and Y. A. Rozanov, Stochastic integrals and adjoint derivatives, In Stochastic analysis and applications, vol.2, pp.265-307, 2007.

D. Nunno, . Giulia, . Øksendal, . Bernt, and F. Proske, Malliavin Calculus for Lévy Processes with Applications to Finance, 2009.
DOI : 10.1007/978-3-540-78572-9

M. Dozzi, Y. Mishura, and G. Shevchenko, Asymptotic behavior of mixed power variations and statistical estimation in mixed models. ArXiv e-prints, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01095611

D. Duffie, J. Kenneth, and . Singleton, Modeling Term Structures of Defaultable Bonds, Review of Financial Studies, vol.2, issue.4, pp.687-720, 1999.
DOI : 10.1016/0304-405X(86)90066-8

E. F. Fama, The Behavior of Stock-Market Prices, The Journal of Business, vol.38, issue.1, pp.34-105, 1965.
DOI : 10.1086/294743

E. F. Fama, Efficient Capital Markets: II, The Journal of Finance, vol.44, issue.Supplement, pp.1575-1617, 1991.
DOI : 10.1016/0304-405X(88)90060-8

J. Fleming and C. Kirby, Long memory in volatility and trading volume, Journal of Banking & Finance, vol.35, issue.7, pp.1714-1726, 2011.
DOI : 10.1016/j.jbankfin.2010.11.007

R. Fox and M. S. Taqqu, Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series, The Annals of Statistics, vol.14, issue.2, pp.517-532, 1986.
DOI : 10.1214/aos/1176349936

A. Vivoli, F. Mainardi, and R. Gorenflo, Renewal processes of Mittag- Leffler and Wright type, Fract. Calc. Appl. Anal, vol.8, issue.1, pp.7-38, 2005.

C. Gouriéroux and A. Monfort, Séries temporelles et modèles dynamiques Collection Economie et statistiques avancées, 1990.

P. Guasoni, Optimal investment with transaction costs and without semimartingales, The Annals of Applied Probability, vol.12, issue.4, pp.1227-1246, 2002.
DOI : 10.1214/aoap/1037125861

P. Guasoni, NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND, Mathematical Finance, vol.5, issue.4, pp.569-582, 2006.
DOI : 10.1007/s007800050049

E. J. Hannan, The asymptotic theory of linear time-series models, Journal of Applied Probability, vol.39, issue.01, pp.130-145, 1973.
DOI : 10.1214/aoms/1177693494

D. Heath, R. Jarrow, and A. Morton, Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation, Econometrica, vol.60, issue.1, pp.77-105, 1992.
DOI : 10.2307/2951677

J. Hicks, Value and Capital: An Inquiry Into Some Fundamental Principles of Economic Theory. Clarendon paperbacks, 1946.

T. Hida and M. Hitsuda, Gaussian processes, volume 120 of Translations of Mathematical Monographs, 1993.

S. Y. Thomas, S. Ho, and . Lee, Term structure movements and pricing interest rate contingent claims, Journal of Finance, vol.41, issue.5, pp.1011-1029, 1986.

H. Scott and . Holan, Long-memory time series theory and methods, J. Amer. Statist. Assoc, vol.103, issue.484, pp.1715-1716, 2008.

J. R. Hosking, Fractional differencing, Biometrika, vol.68, issue.1, pp.165-176, 1981.
DOI : 10.1093/biomet/68.1.165

Y. Hu, D. Nualart, W. Xiao, and W. Zhang, Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation, Acta Math. Sci. Ser. B Engl. Ed, issue.5, pp.311851-1859, 2011.

J. Hull, M. Predescu, and A. White, The relationship between credit default swap spreads, bond yields, and credit rating announcements, Journal of Banking & Finance, vol.28, issue.11, pp.2789-2811, 2004.
DOI : 10.1016/j.jbankfin.2004.06.010

J. Hull and A. White, Pricing Interest-Rate-Derivative Securities, Review of Financial Studies, vol.6, issue.4, pp.573-92, 1990.
DOI : 10.1016/0304-405X(77)90016-2

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Mathematical Library, 1989.

R. A. Jarrow, D. Lando, and S. M. Turnbull, A Markov Model for the Term Structure of Credit Risk Spreads, Review of Financial Studies, vol.September, issue.2, pp.481-523, 1997.
DOI : 10.3905/jfi.1993.408084

A. Robert, S. M. Jarrow, and . Turnbull, Pricing derivatives on financial securities subject to credit risk, Journal of Finance, vol.50, issue.1, pp.53-85, 1995.

J. Mccarthy, C. Pantalone, and H. Li, Investigating Long Memory in Yield Spreads, The Journal of Fixed Income, vol.19, issue.1, pp.73-81, 2009.
DOI : 10.3905/JFI.2009.19.1.073

I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, 1991.
DOI : 10.1007/978-1-4684-0302-2

D. Lando, On cox processes and credit risky securities, Review of Derivatives Research, vol.2, issue.2, pp.99-120, 1998.
DOI : 10.1007/BF01531332

N. Laskin, Fractional Poisson process, Communications in Nonlinear Science and Numerical Simulation, vol.8, issue.3-4, pp.3-4, 2003.
DOI : 10.1016/S1007-5704(03)00037-6

D. Li, Constructing a Credit Curve, Credit Risk Special Report, 1998.

I. N. Lobato and C. Velasco, Long memory in stock-market trading volume, J. Bus. Econ. Stat, vol.18, pp.410-427, 2000.

F. Mainardi, R. Gorenflo, and E. Scalas, A fractional generalization of the Poisson processes, Vietnam Journal of Mathematics, vol.32, pp.53-64, 2004.

P. Malliavin and A. Thalmaier, Stochastic calculus of variations in mathematical finance, 2006.

A. Benoit-mandelbrot, L. Fisher, and . Calvet, A multifractal model of asset returns, 1164.

B. Benoit and . Mandelbrot, When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models, The Review of Economics and Statistics, vol.53, issue.3, pp.225-261, 1971.

B. Benoit, J. W. Mandelbrot, and . Van-ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev, vol.10, pp.422-437, 1968.

T. Marquardt, Fractional L??vy processes with an application to long memory moving average processes, Bernoulli, vol.12, issue.6, pp.1099-1126, 2006.
DOI : 10.3150/bj/1165269152

C. Robert and . Merton, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, vol.29, issue.2, pp.449-70, 1974.

P. A. Meyer, Un Cours sur les Int??grales Stochastiques, Lecture Notes in Math, vol.511, pp.245-400, 1976.
DOI : 10.1007/978-3-540-45530-1_11

S. Yuliya and . Mishura, Stochastic calculus for fractional Brownian motion and related processes, Lecture Notes in Mathematics, 1929.

J. F. Muzy, J. Delour, and E. Bacry, Modelling fluctuations of financial time series: from cascade process to stochastic volatility model, The European Physical Journal B, vol.17, issue.3, pp.537-548, 2000.
DOI : 10.1007/s100510070131

C. Necula, Option Pricing in a Fractional Brownian Motion Environment, SSRN Electronic Journal, 2004.
DOI : 10.2139/ssrn.1286833

I. Nourdin, Selected aspects of fractional Brownian motion, Bocconi & Springer Series, vol.4
DOI : 10.1007/978-88-470-2823-4

URL : https://hal.archives-ouvertes.fr/hal-01314412

D. Nualart, The Malliavin Calculus and Related Topics, 1995.
DOI : 10.1007/978-1-4757-2437-0

D. Nualart and W. Schoutens, Chaotic and predictable representations for Lévy processes. Stochastic Process, Appl, vol.90, issue.1, pp.109-122, 2000.

G. , D. Nunno, and S. Sjursen, On chaos representation and orthogonal polynomials for the doubly stochastic Poisson process. Seminar on Stochastic Analysis, Random Fields and Applications VII, Progress in Probability, vol.67, pp.23-54, 2013.

E. Edgar and . Peters, Fractal Market Analysis, 1994.

E. E. Peters, Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility, Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility, 1996.

B. L. Rao, Statistical inference for fractional diffusion processes Wiley Series in Probability and Statistics, 2010.

E. Philip and . Protter, Stochastic integration and differential equations, Applications of Mathematics, vol.21, 2004.

R. A. Zuber, R. S. Johnson, and J. M. Gandar, A re-examination of the market segmentation theory as a pedagogical model, Journal of Financial Education, vol.36, pp.1-37, 2010.

L. C. Rogers, Arbitrage with Fractional Brownian Motion, Mathematical Finance, vol.7, issue.1, pp.95-105, 1997.
DOI : 10.1111/1467-9965.00025

F. Russo and P. Vallois, Forward, backward and symmetric stochastic integration . Probability Theory and Related Fields, pp.403-421, 1993.

A. Paul and . Samuelson, Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, vol.6, pp.41-49, 1965.

K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, 1999.

K. Sato, Additive processes and stochastic integrals, Illinois J. Math, vol.50, issue.1-4, pp.825-851, 2006.

P. J. Schönbucher, Credit derivatives pricing models: Models, pricing and implementation, 2003.

A. N. Shiryaev, On arbitrage and replication for fractal models, 1998.

D. L. Snyder, Random point processes, 1975.

L. Josep, F. Solé, and . Utzet, A family of martingales generated by a process with independent increments, Theory of Stochastic Processes, pp.139-144, 2008.

T. Sottinen and E. Valkeila, On arbitrage and replication in the fractional Black???Scholes pricing model, Proc. of the Steklov Inst. of Math, pp.93-107, 2003.
DOI : 10.1007/BF02401743

H. Tikanmäki and Y. Mishura, Fractional L??vy Processes as a Result of Compact Interval Integral Transformation, Stochastic Analysis and Applications, vol.29, issue.6, pp.1081-1101, 2011.
DOI : 10.1007/978-3-540-75873-0

B. Dilip, H. Madan, and . Unal, Pricing the risks of default, Review of Derivatives Research, vol.2, pp.121-160, 1998.

G. Unal and A. Dinler, Exact linearization of one dimensional It?? equations driven by??fBm: Analytical and numerical solutions, Nonlinear Dynamics, vol.10, issue.2, pp.251-259, 2008.
DOI : 10.1007/978-3-642-14394-6

O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics, vol.5, issue.2, pp.177-188, 1977.
DOI : 10.1016/0304-405X(77)90016-2

W. Willinger, V. Paxson, R. H. Riedi, and M. S. Taqqu, Long-range dependence and data network traffic, Theory and applications of long-range dependence, pp.373-407, 2003.

W. Xiao, W. Zhang, and X. Zhang, Maximum-likelihood estimators in the mixed fractional Brownian motion, Statistics, vol.45, issue.1, pp.73-85, 2011.
DOI : 10.1016/j.spa.2007.05.004

A. Yablonski, The Malliavin Calculus for Processes with Conditionally Independent Increments, Stochastic Analysis and Applications, pp.641-678, 2007.
DOI : 10.1007/978-3-540-70847-6_30

W. Zhao, Research on Fractional Option Pricing Model Under Real Brownian Motion Environment, 2009 First International Conference on Information Science and Engineering, pp.5047-5050, 2009.
DOI : 10.1109/ICISE.2009.954