SERGIO
BIANCHI
SECSS/06
Insegnamento  Codice  Anno  Corso  Frequentare  Bacheca  

QUANTITATIVE FINANCIAL MODELLING  10592803  2023/2024  
MATEMATICA FINANZIARIA  1017164  2023/2024  
MATEMATICA FINANZIARIA  1017164  2022/2023  


QUANTITATIVE FINANCIAL MODELLING  10592803  2022/2023  
Course Syllabus Quantitative Financial Modelling I semester  Fall 2022
All course material can be found at https://classroom.google.com/c/NDg4NTIzNDk0NzA5 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)
Textbooks [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: ContinuousTime 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 subdirectory of the classroom page)
The additional materials will be available at https://classroom.google.com/c/Mzg3NjU2OTMzOTY5
Prerequisites Students should know and master:
Final and grade policy Final Exam: · Project (with class presentation) · Individual oral examination Weights:
Grading 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.
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 socalled binomial model, and in continuous time, such as the one leading to the famous BlackScholes 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 socalled Greeks) of the option price will also be focused and some financial puzzles such as the behavior of implied volatility and socalled rough volatility will be explored. Part 3. The third part of the course will be devoted to yield curve modeling. Some of the basic onefactor spotinterest rate models will be reviewed (timehomogeneous models: Vasicek, Cox Ingersoll Ross (CIR), Exponential Vasicek (EV); models with timevarying 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 HeathJarrowMorton (HJM) framework as a theoretical approach for developing a noarbitrage interestrate theory.
Expected learning objectives and skills
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 nonextendible 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 fourfive 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:
Along with the above materials, upon completion of the work, each group participant will individually send to the instructor a selfassessment sheet and an evaluation form of the other group members. The forms will be made available with the Project requirements. The information on the selfassessment 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 Note: “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.


MATEMATICA FINANZIARIA  1017164  2021/2022  
QUANTITATIVE FINANCIAL MODELLING  10592803  2021/2022  
MATEMATICA FINANZIARIA  1017164  2021/2022  
MATEMATICA FINANZIARIA  1017164  2020/2021  
MATEMATICA FINANZIARIA  1017164  2020/2021  
QUANTITATIVE FINANCIAL MODELLING  10592803  2020/2021  
MATEMATICA FINANZIARIA  1017164  2019/2020  
MATEMATICA FINANZIARIA  1017164  2019/2020  
MATEMATICA FINANZIARIA  1017164  2018/2019  
MATEMATICA FINANZIARIA  1017164  2017/2018  
MATEMATICA FINANZIARIA  1017164  2016/2017 
Giovedì 11.3013 (Studio 1.09)
Short CV Sergio Bianchi
Full professor of Mathematics for Economics, Actuarial Science and Finance at Sapienza University of Rome, Italy
Int l professor affiliate at the Department of Finance and Risk Engineering, Tandon School of Engineering, New York University (New York City, USA).
Formerly professor at University of Cassino and Southern Lazio (Italy) [19982020], the New York University (USA) [20122015], the Pontifical Gregorian University (Vatican State) [19922001] and the University of Sassari (Italy) [199798].
Research interests: fractional and multifractional stochastic processes, selfsimilarity and scaling laws, stochastic volatility models, risk assessment and models. Author of about 80 scientific publications. Reviewer for about thirty academic journals and member of the editorial board of three academic journals.
Main engagements in academic responsibilities: Chair of Department (20052009) [22 faculty members, 4 staff]; Vice Rector for Research and Benchmarking (20092012); Chair of the Master program in "Quantitative and Technical Analysis of Financial Markets" (20162018) [18 courses, 15 instructors]; Chair of the Joint facultystudent committee (2020); Member of the board of professors of the Ph.D. in Models for Economics and Finance (2018).