Ritratto di sergio.bianchi@uniroma1.it
Insegnamento Codice Anno Corso - Frequentare Bacheca

L'operazione finanziaria. Classificazione delle operazioni finanziarie. Il mercato dei capitali. Caratteristiche del mercato ideale e dei mercati reali. La definizione di arbitraggio. 


Operazioni finanziarie elementari. Il principio di equivalenza finanziaria. Operazioni di investimento e operazioni di anticipazione. Interesse e sconto. La funzione valore. Tasso di interesse e tasso di sconto periodali. Relazioni fondamentali tra le grandezze finanziarie. 

Contratti a pronti e contratti a termine. Proprietà e aspetti terminologici. Operatività a pronti e a termine. Schema della struttura a pronti. Schema della struttura a termine. Relazione tra operazioni a pronti e a termine. Principio di assenza di arbitraggio. 

Tassi periodali e tassi per periodo unitario. Tasso periodale e tasso di interesse effettivo per periodo unitario. Tasso di interesse medio per periodo unitario. Tassi equivalenti. 

Leggi finanziarie intertemporali e regimi finanziari. Regime della capitalizzazione composta. Regime della capitalizzazione semplice. Regime dello sconto commerciale. Confronto tra regimi finanziari.

Tassi nominali e forza di interesse. Tasso di interesse nominale convertibile in volte nel periodo unitario. Intensità istantanea di interesse. Tasso di sconto nominale convertibile in volte nel periodo unitario. Generalizzazione (per leggi dipendenti dalla durata). Forza di interesse. 

Scindibilità. Teoremi sulla scindibilità. Teorema di Cantelli.

Operazioni finanziarie composte. Rendite finanziarie. Classificazione. Valore capitale delle rendite finanziarie. Rendite periodiche, Valori attuali e montanti delle rendite finanziarie (con tassi periodali, tassi a pronti, tassi a termine, tassi medi). Valore attuale di una rendita a rata e tasso costanti. 

Valori attuali e montanti di rendite periodi (tutti i casi: intere, frazionate, temporanee, perpetue, immediate, differite, anticipate, posticipate).  

Problemi sulle rendite. Ricerca della rata. Ricerca del numero di annualità. Tasso interno di rendimento. Ricerca del tasso. Metodi numerici per la ricerca del tasso: metodi iterativo, per interpolazione, per approssimazioni successive, metodo di Newton. 

Indici temporali e di variabilità. Scadenza media finanziaria. Scadenza media aritmetica. Duration. Flat yield curve duration. 

Cenni di teoria dell’immunizzazione finanziaria. Duration come tempo ottimo di smobilizzo. Convexity. Shift additivi. Teorema di Fisher-Weil. Teorema di Redington

Ammortamenti e prestiti. Generalità. Piano di ammortamento. Schemi tipici. Ammortamento uniforme (italiano). Ammortamento progressivo (francese). Ammortamento a due tassi (americano). Ammortamento ad interessi anticipati (tedesco).

Introduzione alla valutazione dei principali titoli derivati (forward, futures, swap, opzioni). La valutazione neutrale al rischio (cenni).



Course Syllabus

Quantitative Financial Modelling

I semester - Fall 2022


All course material can be found at 


The password to access the material should be requested at sergio.bianchi@uniroma1.it


Instructor: prof. Sergio Bianchi (sergio.bianchi@uniroma1.it)


Office: 1.09

Office Hours: Tuesday 10 –11:30 a.m. (or by appointment) 


Office Phone: 0649766507 


Class Hours 

Tuesday 12 pm - 2 pm (Aula Matematica Memotef, first floor)

Wednesday 10 am - 12 pm (Aula Master Memotef, fifth floor)

Thursday 10 am - 12 pm (Aula Matematica Memotef, first floor)



[a] Shreve S.E., Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer Finance, 2005

[b] Shreve S.E., Stochastic Calculus for Finance II: Continuous-Time Models, 2nd edition, Springer Finance, 2004

[c] Musiela M., Rutkwoski M., Martingale Methods in Financial Modelling, Stochastic Modelling and Applied Probability, Springer, 2009

[d] Oosterlee C.W., Grzelak L.A., Mathematical Modeling and Computation in Finance (with Exercises and Python and MATLAB computer codes), World Scientific, 2020

[e] Brigo D., Mercurio F., Interest Rate Models – Theory and Practice (With Smile, Inflation and Credit), Springer, 2006


Additional Materials (in parentheses the sub-directory of the classroom page)

  • Slides used during the classes (Classes)
  • Financial time series (Data)
  • Papers focusing on specific topics covered during the course (Further readings)
  • Matlab functions and software (Software) 
  • Websites of interest (Websites)

The additional materials will be available at https://classroom.google.com/c/Mzg3NjU2OTMzOTY5



Students should know and master:

  • the topics of a basic course in Financial Mathematics (with a special concern to the simple and compound interest scheme, both in discrete and continuous time, and to the market structure)
  • the basics of probability theory and of stochastic processes theory (a short recall will be given at the beginning of the course)


Final and grade policy

Final Exam: 

·     Project (with class presentation) 

·     Individual oral examination 


  • 20% Course participation (attendance and assignments)
  • 30% Project evaluation 
  • 50% Individual oral examination 

Grading scale:

US Scale


IT Scale





































Registration Area

In Google Classroom a Registration Area is active. Students will be asked to fill a form reporting some details which will be kept in due consideration to constitute the groups for each project and adjust the focus of the lessons, to avoid going into too much obvious explanation or, conversely, taking for granted topics with which the class is less familiar. Students are asked to register within the first week of the course.

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Course Objectives

The course provides some of the most relevant theoretical tools for quantitative analysis of financial markets at the advanced master's level. Ideally, it will be structured into three parts:

Part 1. A prerequisite to dealing with the mathematical modeling of financial markets is their knowledge, hence the first part of the Course will be dedicated to an overview of the structure of financial markets, the types of contracts traded therein, and the general principles of modeling the price dynamics of financial assets. Special emphasis will be given to topics such as the Efficient Market Hypothesis and its analytical relationship to the martingale model, the financial markets microstructure, and the notion of arbitrage in market models of increasing generality. In this part of the course, students will also develop the ability to analyze, recognize and test the main stylized facts, whose parry and thrust drive much modeling of financial time series.

Part 2. In its second part, the course will cover pricing models in which price evolves both in discrete time, as in the so-called binomial model, and in continuous time, such as the one leading to the famous Black-Scholes formula. The analysis of such models is unified by the fundamental principle of no arbitrage opportunities, which allows for formulas for valuation and hedging (pricing and hedging) of various derivative securities. The role and the calculation of several measures of sensitiveness (the so-called Greeks) of the option price will also be focused and some financial puzzles such as the behavior of implied volatility and so-called rough volatility will be explored.

Part 3. The third part of the course will be devoted to yield curve modeling. Some of the basic one-factor spot-interest rate models will be reviewed (time-homogeneous models: Vasicek, Cox Ingersoll Ross (CIR), Exponential Vasicek (EV); models with time-varying coefficients: Hull and White’s extended Vasicek model, extensions of the CIR model, Black and Karasinski’s (BK) extended EV model). A hint will also be given to the Heath-Jarrow-Morton (HJM) framework as a theoretical approach for developing a no-arbitrage interest-rate theory.


Expected learning objectives and skills

  • Access, organize, and analyze with advanced quantitative methods and tools the relevant patterns exhibited by financial data.
  • Critically analyze, question, and evaluate implications of alternative and new financial models to address trading and risk management issues.
  • Develop an awareness of the implications that potential abuse of financial contracts can have in systemic risk and substantial negative spillovers on society.
  • Convey mathematical and financial models clearly, and in high-quality written form.
  • In-depth understanding of the no-arbitrage principle and of its role in asset pricing theory.
  • Acquire a robust conceptual knowledge of the fundamental issues determining the valuation and behavior of the main derivatives contracts.
  • Develop knowledge and skill sufficient for correct application and analysis of continuous-time stochastic models involving stochastic integrals and stochastic differential equations.


Assignments and Assessment 

Students will be asked to turn in three assignments at the end of each month of course. The assignments will concern the topics covered in each part of the course. For each assignment it will be settled a non-extendible deadline at the midnight of the due date. The evaluation will concern correctness, clearness, effectiveness of the individual project. The assignments will concur to determine the final mark for a share equal to 20% (see grade policy).


Group project

Provided that the number of students attending allows for this, as a part of the final exam, students will be subdivided into small groups of four-five participants. Each group will be asked to develop a project on a topic randomly chosen among those covered by the course. Each group designates a representative for all communication with the instructor. The project is articulated into three parts:

  • a short paper (no longer than six, one-sided A4 pages, Times New Roman 12 or equivalent);
  • a computer program implementing the task outlined in the project theme;
  • a PPT/PDF/LATEX presentation (no longer than 15 slides) that will be used by the group to illustrate the project to the class. The duration of each presentation is 25 minutes + 5 minutes of discussion.

Along with the above materials, upon completion of the work, each group participant will individually send to the instructor a self-assessment sheet and an evaluation form of the other group members.  The forms will be made available with the Project requirements. The information on the self-assessment sheet and the evaluation form will be strictly confidential and in no way will be disclosed to any student enrolled in the course. It is therefore recommended that evaluations be made with the utmost intellectual honesty.

The project will concur to determine the final mark for a share equal to 30% (see grade policy).



Preliminary Course Calendar 


“Theory” and “Applications” refer to Chapters/paragraphs of the suggested books; students can find “Data and software” and “Websites” in the relevant section of Google Classroom; samely, “Further readings” refer to papers, presentations, or other material that students can find in the section Further readings of Google Classroom.




Stochastic processes. Joint distribution function. Probability mass function of order k. Ensemble and time mean. Gaussian processes. Discrete-time Martingales. Total variation. Quadratic variation. Continuous-time limit of the random walk model. Standard and Fractional Brownian motion (distribution, increments, continuity, non-differentiability, martingale property, quadratic variation, law of iterated logarithm, scaling, and self-similarity). Geometric Brownian motion. GBM as a stochastic model for the value of a stock. Simulations.


Suggested additional readings:


[a] Ch. 2, 2.4, 2.5, Ch. 5, 5.1, 5.2; [b] Ch. 3


[d] Ch. 1, 1.2; Ch. 2, 2.1, 2.3, 9.1, 9.1.1


Data and software

Fraclab (Tool running in Matlab licensed by INRIA)

Scaling.m (matlab routine)

Further readings

  • Fractional Brownian motions, fractional noises and applications (B.B. Mandelbrot, J.W. Van Ness)
  • Arbitrage with fractional Brownian motion (L.C.G. Rogers)
  • Simulation of fractional Brownian motion (master’s thesis Ton Dieker)




https://project.inria.fr/fraclab/ (to download Fraclab)




Itô process. Financial interpretation of the Itô integral. Itô’s lemma. Higher-Dimensional Itô’s Lemma. Examples. Euler-Maruyama approximation method.



[b] Ch. 4, 4.1, 4.2, 4.3, 4.4; [c] Appendices B; [e] Appendices C, C.1, C.2, C.3, C.4


[d] Ch. 1, 1.3, 1.4; Ch. 2, 2.1, 9.1.2, 9.2


Further readings

  • Robert Jarrow and Philip Protter, A short history of stochastic integration and mathematical finance: The early years, 1880–1970, Institute of Mathematical Statistics Lecture Notes – Monograph Series, 45, 75–91, (2004)
  • Hans Föllmer, On Kiyosi Itô's Work and its Impact
  • Vlad Gheorghiu, Itô calculus in a nutshell






Financial markets. Taxonomy, size, and instruments. Modeling financial markets. Assumptions. Return and risk. Efficient Market Hypothesis. A first look at arbitrage. Law of one price. Stylized facts.



[c] Ch. 1, [e] Ch. 2, from 2.1 to 2.6





Further readings

  • Fama E., Efficient capital markets: A review of theory and empirical work, The Journal of Finance 25 (2) (1970) 383-417.
  • Malkiel B.G., The Efficient Market Hypothesis and Its Critics, Journal of Economic Perspectives, 17, 1, 59–82 (2003)
  • Guillaume D.M., Dacorogna M.M., Davè R.R:, Müller U.A., Olsen R.B., Pictet O.V., From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets, Finance and Stochastics, 1, 95–129 (1997)
  • Lux T., Chapter 3 - Stochastic Behavioral Asset-Pricing Models and the Stylized Facts, in Handbook of Financial Markets: Dynamics and Evolution, 161-215 (2009)
  • Cont R., Empirical properties of asset returns: stylized facts and statistical issues, Quantitative Finance, 1(2), 223-236 (2001)
  • Rickles D., Econophysics and the Complexity of Financial Markets, Philosophy of Complex Systems, 531-565 (2011)



https://www.youtube.com/watch?v=wnCxlIQjT-s (A Random Walk Down Wall Street, B. Malkiel, Talks at Google)



Financial derivatives. Taxonomy. Forward and Futures. Standardization and mark to market. Forward (future) price (via no arbitrage argument). Hedging. Swaps. Interest Rate Swaps. Pricing. Use of swaps in hedging, speculation, and comparative advantage. Options. Taxonomy. A first example of pricing via no arbitrage argument. 



[b] Ch. 5, 5.6    [c] Ch. 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, Ch. 9, 9.4

Applications and software

[d] Ch. 3, 3.1.1


René M. Stulz, Demystifying Financial Derivatives, The Milken Institute Review, 2005





Risk-Neutral Probability Measure (or Equivalent Martingale Measure). Radon-Nikodým derivative process. Put-Call parity. Elementary Market Model. General single-period market models. Trading strategies and arbitrage-free models. Wealth process of a trading strategy.  Gain process. Discounted Stock price and value process. Discounted gain process. Arbitrage.


[a], Ch. 3, 3.1, 3.2   [b] Ch. 4, 4.5.6, Ch. 5, 5.1, 5.2, 5.3   

Applications and software

[d], Ch. 2.3, Ch. 7, 7.2


  • Buhlmann H., Delbaen F., Embrechts P., Shiryaev A., No arbitrage Change of Measure and Conditional Esscher Transforms, 1996






First fundamental Theorem of Asset Pricing. Market model with arbitrage. Stochastic volatility model. Completeness of market models. Algebraic criterion for market completeness. Second fundamental Theorem of Asset Pricing (probabilistic criterion for market completeness).



[b] Ch. 5, 5.4     [c] Ch. 2, 2.6, 2.7

Applications and software



  • Yan Zeng, Fundamental Theorem of Asset Pricing in a Nutshell: With a View toward Numéraire Change (2009)






Cox-Ross-Rubinstein (CRR) pricing model. Bernoulli process. Bernoulli Counting process. The CRR Call Option pricing formula (with Cox-Ross-Rubinstein parametrization and with Jarrow-Rudd parametrization).



[a] Ch. 1, 1.1, 1.2, 1.3, 1.4    [c] Ch. 2, 2.1, 2.2

Applications and software



  • Cox J.C., Ross S.A., Rubinstein M., Option pricing: A simplified approach, Journal of Financial Economics, 7(3), 1979, 229-263
  • Rutkwoski (slides), Binomial market model







Black-Scholes-Merton model. Assumptions for the risk-free bond, for the stock price and for the self-financing trading strategy. Martingale measure for the stock. Admissible trading strategies. Attainable contingent claims. Black-Scholes option pricing formula (based on both replicating strategy and risk-neutral measure). Terminal boundary conditions.



[b] Ch. 4, 4.5, 4.6    [c] Ch.2, 2.3, 3

Applications and software

[d] Ch. 3, 3.1.2, 3.1.3, 3.2, 3.3


  • Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy. 81 (3): 637–654
  • Ajay Shah, Black, Merton and Scholes: Their work and its consequences (1997)





The Greeks (delta, gamma, theta, rho, vega). Delta-neutral and gamma-neutral portfolios. Volatility. Implied volatility. Volatility “measures”



[b] Ch. 4, 4.5.5   [c] Ch. 7, 7.1, 7.6

Applications and software

[d] Ch. 3, 3.2.1, Ch. 4, 4.1, 4.2 4.3, Ch. 8, Ch. 9.5


  • Elisa Alòs, Maria Elvira Mancino, Tai-Ho Wang, Volatility and volatility-linked derivatives: estimation, modeling, and pricing, Decisions in Economics and Finance (2019) 42:321–349
  • Various Authors, Taxonomy of Global Risk, Uncertainty, and Volatility Measures, International Finance Discussion Papers, Board of Governors of the Federal Reserve System, 1216, 2017
  • Gatheral, J. (2006). The volatility surface: a practitioner's guide (Vol. 357). John Wiley & Sons.







Interest rates models. Simple spot rate. Continuously compounded spot rate. Simple forward rate. Continuously compounded forward rate. Instantaneous forward rate. Forward curve. Short rate. Forward vs. future rates. Forward Rate Agreement (FRA). Term structure (or yield curve). Bootstrapping. Stochastic models for bond prices. arbitrage-free family of bond prices.



[b] Ch. 9, 9.4    [c] Ch. 9, 9.1, 9.5. 9.6

Applications and software

[d] Ch.11


Lesniewski A.,  Interest Rate and Credit Models (slides)






Short-rate models. Affine models. Stylized facts on yield curve. Vasiček model. Cox-Ingersoll-Ross (CIR) model. Dothan model. Ho-Lee model. Hull-White extension of Vasiček model. Hull-White extension of CIR model. Instantaneous forward rate models (Heat-Jarrrow-Morton, HJM, framework). HJM forward rate specification. Theorem HJM.



[b] Ch.10, 10.1, 10.2, 10.3     [c] Ch. 7, 7.4, Ch.9, 9.6, Ch.10, 10.1, 10.2, Ch. 11, 11.1    [e] Ch. 3, 3.1, 3.2, 3.3, 3.4, Ch. 5

Applications and software

[d] Ch.8, 8.1, 8.2, 8.3, Ch. 9, 9.3, 9.4, Ch.11


  • Chan K.C., Karolyi G.A., Longstaff F.A., Sanders. A.B., An Empirical Comparison of Alternative Models of the Short-Term Interest Rate, The Journal of Finance, 47(3), 1992, 1209-1227








Project presentation and discussion




Lunedì 11.30-13, Giovedì 11.30-13 (Studio 1.09)

Short CV Sergio Bianchi

Full professor of Mathematics for Economics, Actuarial Science and Finance at Sapienza University of Rome, Italy
International Affiliate Professor, Department of Finance and Risk Engineering, Tandon School of Engineering, New York University (NY)

Previous Positions
· 01/09/2014 - 31/08/2015 Industry Professor at Polytechnic Institute of the New York University, School of Engineering, Department of Finance and Risk Engineering
· 01/04/2006 15/01/2020 Full Professor at University of Cassino Dept. Economics and Law
· 01/10/2001 - 30/03/2006 Associate Professor at University of Cassino Dept. Economia e Territorio
· 30/06/1998 - 01/10/2001 Assistant Professor at University of Cassino Dept. Economia e Territorio
· 01/09/1997 31/10/1998 Contract Professor of Financial Mathematics at University of Sassari (Italy)
· 01/07/1998 30/06/2001 Invited Professor of Elements of Calculus I and II at Pontificia Università Gregoriana
· 01/09/1991 30/06/1998 Contract Professor of Elements of Calculus I at Pontificia Università Gregoriana

Visiting Positions
· 2012-2019. Invited Visiting Professor at New York University, Tandon School of Engineering, Department of Finance and Risk Engineering
· 2016 Invited Visiting Professor with Erasmus+ at Department of Mathematics/Institute of Mathematics and Informatics, Szent István University, Godollo (Hungary)

Editorial Activities
· 23/04/2021 - to date, Guest Editor for Fractal and Fractional
· 25/07/2017 - 31/05/2018, Guest Editor for Risk and Decision Analysis
· 2019/20 Guest Editor for Mathematical Methods for Economics and Finance
· 2017/18 Guest Editor for Risk and Decision Analysis
· Member of the Editorial Board of Risk and Decision Analysis
· Member of the Advisory Board of Mathematical Methods in Economics and Finance
· Reviewer for
Applied Economics Applied Economics Letters Applied Soft Computing Arabian Journal of Geosciences Chaos Chaos, Solitons and Fractals Empirical Economics Finance Research Letters Fluctuation and Noise Letters Impresa Ambiente Management Insurance: Mathematics and Economics Mathematical Methods in Economics and Finance Mathematical and Statistical Methods for Actuarial Sciences and Finance Mathematical Reviews (American Mathematical Society) Nonlinear Dynamics & Econometrics Physica A Pure Mathematics and Applications Quantitative Finance Rendiconti per gli Studi Economici Quantitativi Risk And Decision Analysis WSEAS, World Scientific and Engineering Academy and Society Miur PRIN University of Padua

Scientific Boards
· 2018 to date, Member of the Board of Professors (Ph.D. in Modelli per l Economia e la Finanza), Sapienza University of Rome
· 01/12/2016 to date, Member of the Editorial Board of Risk and Decision Analysis
· 01/04/2016 - 07/03/2018 Coordinator of the 1° Level Master in "Quantitative and Technical Analysis of Financial Markets" (315 class hours, 18 courses, 60 CFU, 15 professors, 2 staff) at University of Cassino and Southern Lazio (Italy)
· 11/2009 08/2014 Head of the Technical Board for the evaluation of Spin-Off of University of Cassino
· 11/2009 08/2014 Member of the Board of Professors (Ph.D. in Economics), University of Cassino
· 11/2009 08/2014 Member of the Scientific Council of the I.S.M.E.F., Istituto Mediterraneo di Formazione per le Professionalità Nautiche onlus, Formia (Italy)
· 2008 to date Member of the Scientific Committee of the biennial conference Mathematical and Statistical Methods for Actuarial Sciences and Finance (University of Venice, University of Salerno, Dauphine Université Paris)
· 2006-2009. Member of the Board of Professors (Ph.D. in Quantitative Methods for Economics and Land), University of Cassino
· 2005. Member of the Board of Professors (Ph.D. in Institutions and Methods of Analysis of land systems), University of Cassino

Institutional Responsibilities
· 2009-2014, Rector s Delegate for Research and Benchmarking, University of Cassino
· 2007-2009, Representative of the Heads of Department in the Academic Senate of the University of Cassino
· 2005-2009, Chair of Department Istituzioni, Metodi Quantitativi e Territorio (22 faculty members, 4 staff), University of Cassino
· 2004-2005, Member of the Committee for the Evaluation of the Research, University of Cassino
· 2004-2005, Member of the Recruitment Committee of the Faculty of Economics, University of Cassino
· 2004-2005, Member of the Educational Program Committee 2005/06, Faculty of Economics, University of Cassino
· 2003-2005, Scientific Coordinator of the Computer Laboratory of the Department Economia e Territorio , University of Cassino
· 2003-2004, Head of the Educational Program Committee 2004/05, Faculty of Economics, University of Cassino
· 1999-2001, Member of the Educational Program Committee of the Master in Economics and Business Administration, Faculty of Economics, University of Cassino

Research interests
Applied Mathematical Finance - Stochastic processes: multifractional processes, self-similar processes, long run memory models

Main scientific publications

Refereed Journal Articles

- BIANCHI S., FREZZA M., PIANESE A. (2021), Forecasting Value-at-Risk in turbulent stock markets via the local regularity of the price process, Computational Management Science, https://doi.org/10.1007/s10287-021-00412-w
- BIANCHI S., PIANESE A., FREZZA M., PALAZZO A.M. (2020), Stochastic dominance in the outer distributions of the -efficiency domain, forthcoming in Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer
- FREZZA M., BIANCHI S., PIANESE A. (2020), Fractal analysis of market (in)efficiency during the COVID-19, Finance Research Letters, Available online 19 November 2020, 101851
- TAPIERO C.S., VALLOIS P., BIANCHI S. (2020), The Origins of Randomness: Granularity, Information and Speed of Convergence (2020), Mathematical Methods in Economics and Finance, special issue on "Fractional and multifractional models and methods in finance", 13/14, 1, 2018/2019, 75-96
- BIANCHI S. (2020), Matematica e cognizione giurisdizionale, Diritto Pubblico Europeo, Rassegna online, n.2, ISSN: 2421-0528
- BIANCHI S., LI, Q. (2020), A new estimator of the self-similarity exponent through the Empirical Likelihood Ratio Test, Journal of Statistical Computation and Simulation, 90(11), 1982-2001, ISSN: 0094-9655
- BIANCHI S., PIANESE A., FREZZA M. (2020), A distribution-based method to gauge market liquidity through scale invariance between investment horizons, Applied Stochastic Models in Business and Industry, https://doi.org/10.1002/asmb.2531
- PIANESE A., ATTIAS A., BIANCHI S., VARGA Z. (2020), Demographic Dynamics for Population Systems with Migration and its Effect on the Pay-As-You-Go Pension Systems, Insurance: Mathematics and Economics, 92, 115-127
- BIANCHI S., (2018), Special Issue: Fractional Calculus and Its Applications, Introduction, Risk and Decision Analysis, 7(1-2):1-3, ISSN: 1569-7371
- BIANCHI S., PALAZZO, A.M., PIANESE A. (2018), Fast and unbiased estimator of the time-dependent Hurst exponent, Chaos, 28, 031102, ISSN: 1054-1500
- BIANCHI S., FREZZA M. (2018), Liquidity, Efficiency and the 2007-2008 Global Financial Crisis, Annals of Economics and Finance, 10(2), ISSN 1529-7373
- BIANCHI S., PIANESE A. (2018), Time-Varying Hurst-Hölder Exponents and the Dynamics of (In)Efficiency in Stock Markets, Chaos Solitons and Fractals, 109, 64-75, ISSN: 0960-0779
- BIANCHI S., FREZZA M. (2017), Fractal stock markets: International evidence of dynamical (in)efficiency, Chaos, 27, 071102
- BIANCHI S., PANTANELLA A., PIANESE A. (2015), Efficient Markets and Behavioral Finance: A comprehensive Multifractional Model. Advances in Complex Systems, vol. 18, ISSN: 0219-5259
-BIANCHI S., A. PIANESE (2014), Multifractional Processes in Finance, Risk and Decision Analysis, Vol. 5, Number 1, 1-22, ISSN:1569-7371
- BIANCHI S., PANTANELLA A., PIANESE A. (2013) Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity, Quantitative Finance, 13(8), 1317-1330
- BIANCHI S., A.M. PALAZZO, A. PANTANELLA, A. PIANESE (2013), Self-Similarity Parameter Estimation for k-dimensional Processes, International Journal of Computer Theory and Engineering, 5, 302-306, ISSN: 1793-8201
- ANGRISANI M, ATTIAS A, BIANCHI S., VARGA Z (2012), Sustainability of a Pay-As-You-Go Pension System by Dynamic Immigration Control, Applied Mathematics and Computation, 219, 2442-2452, ISSN: 0096-3003
- BIANCHI S, PANTANELLA A., PIANESE A (2012), Modeling and simulation of currency exchange rates using MPRE, International Journal of Modeling and Optimization, 2(3), 309-314 ISSN: 2010-3697
- BIANCHI S., PANTANELLA A. (2011), Pointwise Regularity Exponents and well-behaved residuals in Stock Markets, International Journal of Trade, Economics and Finance, 2, 1, 52-60
- BIANCHI S., PANTANELLA A. (2010) Pointwise Regularity Exponents and Market Cross-Correlations, International Review of Business Research Papers, 6(2), 39-51, ISSN: 1834-5883
- BIANCHI S., DE BELLIS I., PIANESE A. (2010), Fractal properties of some European electricity markets. International Journal of Financial Markets and Derivatives, 1(4), 395-421, ISSN: 1756-7130
- BIANCHI S., TRUDDA A (2008). Global asset return in pension funds: a dynamical risk analysis. Mathematical Methods in Economics and Finance, 3(2), 1-16, ISSN: 1971-6419
- BIANCHI S., PIANESE A (2008). Multifractional properties of stock indices decomposed by filtering their pointwise Hoelder regularity. International Journal of Theoretical and Applied Finance, vol. 11(6); p. 567-595, ISSN: 0219-0249
- BIANCHI S., PIANESE A (2007). Modeling Stock Price Movements: Multifractality or Multifractionality?. Quantitative Finance, vol. 7; p. 301-319, ISSN: 1469-7688
- ANGRISANI M, ATTIAS A, BIANCHI S., VARGA Z (2006). Demographic dynamics for the pay-as-you-go pension system. Pure Mathematics and Applications, vol. 15; p. 357-374, ISSN: 1218-4586
- BIANCHI S., PIANESE A (2006). Multiscaling in the distribution of the exchange rates. WSEAS Transaction on Mathematics, vol. 6; p. 354-360, ISSN: 1109-2769
- BIANCHI S. (2005). Pathwise Identification of the Memory Function of the Multifractional Brownian Motion with Application to Finance. International Journal of Theoretical and Applied Finance, vol. 8; p. 255-281, ISSN: 0219-0249
- BIANCHI S. (2005). A Cautionary Note on the Detection of Multifractal Scaling in Finance and Economics. Applied Economics Letters, vol. 12; p. 775-780, ISSN: 1350-4851
- BIANCHI S. (2004). A New Distribution-Based Test of Self-Similarity. Fractals-Complex Geometry Patterns and Scaling in Nature and Society, vol. 3; p. 331-346, ISSN: 0218-348X
- BIANCHI S. (1999). Testing Self-Affinity of Stock Returns. Rendiconti per gli Studi Economici Quantitativi; p. 26-43, ISSN: 1591-9773
- BIANCHI S. (1995). Fasi stabili e caotiche del mercato borsistico italiano: una procedura di discriminazione. Rivista Milanese di Economia, vol. 56; p. 101-119, ISSN: 0392-9728

Refereed Book Articles

- BIANCHI, S., FERRANTE, F., RECINTO, G., INTERLANDI, M., INTRISANO, C., VISTOCCO, D. MAIELLO, F., MICHELI, A.P. (2017), Analisi delle ricadute PET sul territorio della Provincia di Frosinone e relativa individuazione del fabbisogno formativo. Nuove figure professionali nell ambito della Programmazione comunitaria 2014 2020, Aracne Editrice, ISBN: 978-88-548-9882-0
- BIANCHI S., PIANESE A. (2014). Asset price modeling: from Fractional to Multifractional Processes. In: A. Bensoussan, D. Guegan, E., C. Tapiero. Future Perspectives in Risk Models and Finance. p. 247-286, New York: Springer, ISBN: 978-3-319-07523-5
- BIANCHI S., A. PIANESE (2008). Scaling Laws in Stock Markets. An analysis of prices and volumes. In: PERNA, CIRA, SIBILLO, MARILENA EDS. Mathematical and Statistical Methods in Finance. p. 35-42, Springer, ISBN/ISSN: 978-88-470-0703-1
- BIANCHI S., A PIANESE (2005). Reconciling Multifractal and Multifractional Processes in Financial Modeling. In: THEODORE SIMOS AND GEORGE MAROULIS. Advances in computational methods in sciences and engineering 2005. Selected papers from the international conference of computational methods in sciences and engineering 2005 (ICCMSE 2005). p. 1268-1281, LEIDEN: Brill, ISBN/ISSN: ISBN 90-6764-441-2
- BIANCHI S., MICOCCI M (1999). "La geometria frattale: l'applicazione all'analisi finanziaria". In: AA.VV.. Complementi di Matematica Finanziaria. Modelli applicativi per la scelta degli investimenti. ROMA: Ed. CISU

Refereed Conference Proceedings
- Bianchi S., Pianese A., Frezza M., A distribution-based method to gauge market liquidity through scale invariance between investment horizons, CFE-CM Statistics 2019, University of London and Birbeck, 14-16 December 2019
- Bianchi S., Pianese A., Palazzo A., Pantanella A., Assessing market (in)efficiency, Colloque MAF 2016, Paris Dauphine, March 30-31 and April 1, 2016, Paris (France)
- BIANCHI S., GÁMEZ, M., PIANESE A. (2016), Liquidity and Self-Similarity in the Distributions of the log price variations, Proceedings of the 7th Annual Financial Market Liquidity Conference, 17th-18th November 2016, Budapest (Hungary), p.14
- BIANCHI S. (2012), Market Efficiency and Behavioral Finance: A Unifying Stochastic Model of Stock Prices, (Invited Plenary Lecture), Proceedings of the American Conference on Applied Mathematics, Harvard, Cambridge, MA, USA, January 25-27, 2012, p.15-16 (ISBN:9781618040640)
- BIANCHI S., A. PANTANELLA, A. PIANESE (2012). Local Estimation of Stock Market Efficiency, Proceedings of the American Conference on Applied Mathematics , Harvard, Cambridge, MA, USA, January 25-27, 2012, 349-355 (ISBN:9781618040640)
- BIANCHI S., A. PANTANELLA, A. PIANESE (2011), "Efficient Market Hypothesis and Behavioural Finance: reconciling the opposites through multifractional processes with random exponent", 8th Applied Financial Economics (AFE) Conference, 30 June 02 July 2011, Samos Island, Greece, 501-510, ISBN: 978-9-6046-6086-5
- BIANCHI S., A.M. PALAZZO, A. PANTANELLA, A. PIANESE (2011), Self-Similarity Parameter Estimation for k-dimensional Processes, 4th IEEE International Conference on Computer Science and Information Technology, 10-12 June 2011, Chengdu, China, ISBN: 978-1-61284-836-5
- BIANCHI S., PANTANELLA A.Efficiency, Overreaction and Underreaction in Stock Markets. A Parsimonious Model of the Three Sided-Coin, ICFTE 2011, Shanghai (China), 11-13 May 2011, IEEE Catalog Number: CFP1103J-PRT, ISBN: 978-1-4244-9508-5, 617-622
- BIANCHI S., PANTANELLA A. Stock Returns Declustering Under Time Dependent Hölder Exponent, ICEME 2010, Hong Kong (China), 28-30 December 2010, IEEE CN: CFP1072L-PRT, ISBN: 978-1-4244-8965-7, 14-21
- BIANCHI S., PANTANELLA A., PIANESE A., Modeling and simulation of currency exchange rates using MPRE, 2010 International Conference on Modeling, Simulation and Control (ICMSC 2010) Cairo Egypt, November 2-4, IEEE Catalog Number: CFP1053L-PRT, ISBN: 978-1-4244-8823-0
- BIANCHI S., PANTANELLA A. (forthcoming) Pointwise Regularity Exponents and Market Cross-Correlations, 12th International Business Research Conference, Dubai (EAU), 7-8 april 2010
- ANGRISANI M, ATTIAS A, BIANCHI S., VARGA Z (2010). Dynamic analysis of the effect of immigration on the demographic background of the pay-as-you-go pension system. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Ravello, 7-9 April 2010
- BIANCHI S., TRUDDA A. Global Asset Return in Pension Funds: a dynamical risk analysis. In: Mathematical and Statistical Methods for Actuarial Sciences and Finance. Venice, 26-28 March 2008
- BIANCHI S., DE BELLIS I, PIANESE A (2009). Stochastic Modelling of the Italian Electricity Market: some empirical evidences. In: Proceedings of the 6th International Conference on Applied Financial Economics. Samos Island (Gr), 2-4/07/2009, SAMOS ISLAND: INEAG, vol. 1, p. 315-325, ISBN/ISSN: 978-960-466-044-5/1790-3912
- BIANCHI S., PANTANELLA A, PIANESE A (2009). Financial Portfolio Selection in a Nonstationary Gaussian Framework. In: THE ROLE OF THE UNIVERSITY IN THE ANALYSIS OF CURRENT ECONOMIC CRISIS. Spiru Haret University, May 28th, 2009, BUCHAREST: România de Mâine Publishing House, vol. 1, p. 619-627, ISBN/ISSN: 978-973-163-460-9
- BIANCHI S. (2006). ESTIMATION AND FILTERING OF MULTIFRACTIONAL GAUSSIAN PROCESSES (Invited plenary lecture). In: 10th WSEAS International Conference on Applied Mathematics. Dallas (Texas), 1-3 november 2006
- BIANCHI S., A. PIANESE (2005). Decomposition of financial time series into stationary subsequences under hypothesis of multifractionality. In: International Conference for the Management of risk factors in economically relevant human activities. Viterbo, September 1st-3rd, 2005
- BIANCHI S. (2004). "Pathwise Identification of the Memory Function of a Multifractional Market Model". In: Stochastic Finance 2004 International Conference, Lisbona
- BIANCHI S. (2003). Multifractality in Stock Markets: an empirical analysis. In: Quantitative Methods in Finance 2003 Conference, 10th 13th December 2003, Manly, Sydney (Australia)
- BIANCHI S. (2003). Testing Self-Similarity of Stochastic Processes. In: XXIX Conference on Stochastic Processes and their Applications, August 3-9, 2003, Angra dos Reis (Brasile)
- BIANCHI S. (2003). Empirical Evidence of Time-Dependent Memory in Stock Markets. In: 2003 Latin American Meeting of the Econometric Society, Panama City (Panama), 28-30 August 2003, p. 1-14
- BIANCHI S. (2001). A Distribution-Based Method for Evaluating Uniscaling in Finance . In: CeNDEF Workshop Papers. Amsterdam, January 2001, AMSTERDAM: Universiteit van Amsterdam, Center for Nonlinear Dynamics, vol. 4A.3.
- BIANCHI S. (2001). Self-Affine Stochastic Processes: a Distribution-Based Estimation via the Smirnov Statistic. In: 11th INFORMS Applied Probability Society Conference, New York (USA)

Non-refereed Proceedings
- BIANCHI S., TRUDDA A (2008). Investment risk in Pension Funds: a dynamical approach. In: Atti del XXXII Convegno AMASES. Trento, 1-4 Settembre 2008
- BIANCHI S., A. PIANESE (2005). On a new technique for VAR estimation. In: XII Convegno di Teoria del Rischio. Università degli Studi del Molise, Campobasso, 16 giugno 2005, ROMA: Aracne, p. 101-115, ISBN/ISSN: 88-548-0637-4
- BIANCHI S., A. PIANESE (2005). Evidence of Multifractionality in the Dow Jones Index. In: 8th Italian-Spanish Meeting in Financial Mathematics. Verbania, June 30-July 1, 2005
- BIANCHI S., A. PIANESE (2005). Evaluation of Value at Risk by pointwise regularity of the price process. In: XXIX Convegno A.M.A.S.E.S.,. Palermo, 12-15 Settembre 2005
- BIANCHI S. (2004). "Pointwise Identification of the Multifractional Memory Function". In: Atti del Convegno Metodi Matematici e Statistici per l Analisi dei Dati Assicurativi e Finanziari, Edizioni CUSL, Salerno
- BIANCHI S. (2001). "Su una strategia di trading in un mercato multifrattale". In: Atti dell'VIII Convegno di Teoria del rischio. Campobasso, 14/06/2001, CAMPOBASSO: Uniservice, vol. 1, p. 27-35
- BIANCHI S. (2000). Sulla Nozione di Rischio nei Processi Autoaffini . In: Atti del VII Convegno di Teoria del Rischio. Campobasso, 9 giugno 2000, CAMPOBASSO: Uniservice, vol. 1, p. 25-32
- BIANCHI S. (1999). Efficienza, Arbitraggio e Liquidità: verso una nuova nozione di rischio finanziario? . In: Atti della Giornata di Studio "Nuovi Indirizzi Scientifici e Didattici nella Teoria del Rischio", Università del Molise, Campobasso 1999. Campobasso, 23/06/1999, CAMPOBASSO: Uniservice, vol. 1, p. 45-57
- BIANCHI S. (1999). On Estimating the Time-Changing Dependence in Economic and Financial Time Series ,. In: Atti del XXIII Convegno AMASES
- BIANCHI S. (1998). Su una classe di stimatori del parametro di autosimilarità delle distribuzioni di processi gaussiani correlati. In: XXII CONVEGNO AMASES. Genova, 1998
- BIANCHI S. (1997). Autocorrelazione delle serie finanziarie e non robustezza del range standardizzato. In: Atti della Giornata di Studio "Aspetti scientifici e didattici della teoria del rischio". Università degli Studi del Molise, Campobasso, 18/06/1997, CAMPOBASSO: Uniservice, vol. 1, p. 31-44
- BIANCHI S. (1997). Moto browniano multifrazionario e dinamiche finanziarie. In: XXI CONVEGNO AMASES. ROMA, 1997
- BIANCHI S. (1996). Un processo localmente stazionario per le dinamiche economiche. In: XX CONVEGNO AMASES. Urbino, 1996
- BIANCHI S. (1995). FMH: una verifica sul mercato italiano,. In: XIX Convegno AMASES. Pugnochiuso di Vieste

Main op-eds and public appearances
- Matematica e cognizione giurisprudenziale in Processi cognitivi e cognizione giurisdizionale , Università degli Studi di Cassino e del Lazio Meridionale, 13 dicembre 2019
- Lezione La Fisica della Finanza, Capirla per non subirla , Liceo Classifco Vitruvio Pollione , Formia, 10 dicembre 2019
- Lezione La Fisica della Finanza , Liceo Scientifico G. Pellecchia , Cassino, 18/02/2019
- Lezione La Fisica della Finanza , Convegno Educazione Finanziaria, la conoscenza rende liberi , FIDAPA, Formia, 17/11/2018
- Editorial 1° Maggio. Festa del lavoro (che manca e mancherà) , L Inchiesta, 01/05/2018
- Tavola rotonda Analisi delle ricadute PET sul territorio della Provincia di Frosinone e relativa individuazione del fabbisogno formativo. Nuove figure professionali nell ambito della Programmazione comunitaria 2014 2020 , Dipartimento di Economia e Giurisprudenza, Università degli Studi di Cassino e del Lazio Meridionale, 16/11/2017
- Interview SPY Finanza. I guai delle banche che la Germania vuol nascondere , released to the online newspaper Ilsussidiario.net, August 13th 2013 (http://www.ilsussidiario.net/News/Economia-e-Finanza/2013/8/13/SPY-FINAN...)
- Swap su tassi di interesse: l operazione del Comune di Cassino , Economia e Finanza: I derivati Cassino, Public conference, 25 marzo 2013, Biblioteca Comunale di Cassino P. Malatesta
- L'impatto dell'Università e della ricerca sulla creazione di opportunità e di prospettive occupazionali per i giovani , Public Conference «I giovani ed il lavoro: le possibili risposte ad una emergenza sociale», Comune di Cassino, Sala Restagno, 22 dicembre 2012
- La crisi: le cause e le ricette sbagliate. Come uscirne , Public conference, Sala comunale di Arce, 24/11/2012
- Interview FINANZA/ Altro che Tobin Tax, prima fermiamo i grandi speculatori (come fa Hollande) , released to the online newspaper Ilsussidiario.net, 16/11/2012
- Interview STANDARD & POOR'S/ Così la condanna australiana mette i brividi ai mostri sacri della finanza , released to the online newspaper Ilsussidiario.net, 6/11/2012
- Editorial Siamo MES proprio male , L'Inchiesta, 19/10/2012
- How the big banks have made millions with the spread , http://www.Ilsussidiario.net, 16/10/2012
- Così le grandi banche han fatto i miliardi con lo spread , http://www.Ilsussidiario.net, 15/10/2012
- Perché l Italia non fallirà, ma gli italiani probabilmente sì , L'Inchiesta, 11/10/2012
- Editorial Toccare il fondo per risollevarsi , L Inchiesta, 10/07/2012
- La bancarotta del capitale e la nuova società, nel laboratorio di Marx per uscire dalla crisi (by Paolo Ciofi). Book presentation and discussion, 25/05/2012
- Altri Lidi (by Sergio Sollima), Book presentation and discussion, 15/04/2012
- Crisi e ideologia neoliberista Book presentation and discussion, 30/03/2012
- Editorial Quanto ci costerà il debito degli USA? , L Inchiesta, 28/12/2011
- Editorial L effetto della crisi europea paralizza anche le reazioni dell economia locale , L Inchiesta, 28/11/2011
- Il mondo di domani. Cronaca della crisi globale tra presente e futuro , joint conference with Giulietto Chiesa, 9/11/2011
- Editorial L Italia nello scenario di crisi mondiale: si scrive debito, si legge rischio di default , Voce Camerale, 09/2011
- Mai ci fu pietà. La banda della Magliana dal 1977 a oggi (by Angela Camuso), Book presentation and discussion, 02/07/2010