STATISTICAL SCIENCES FOR FINANCE | Stochastic Finance

cod. 0222400013

STOCHASTIC FINANCE

	0222400013
	DEPARTMENT OF ECONOMICS AND STATISTICS
	EQF7
	STATISTICAL SCIENCES FOR FINANCE
	2022/2023

CURRICULUM BIG DATA ANALYTICS

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2014
	SPRING SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	SECS-S/06	10	60	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	MARILENA SIBILLO T Curriculum
	MASSIMILIANO MENZIETTI Curriculum

EXAMS

	Exam	Date	Session
	FINANZA STOCASTICA	05/04/2023 - 11:30	SESSIONE ORDINARIA
	FINANZA STOCASTICA	05/04/2023 - 11:30	SESSIONE DI RECUPERO

	Objectives
	THE STOCHASTIC FINANCE COURSE, IN LINE WITH THE CORE OBJECTIVES OF THE DEGREE PROGRAM, IS DEDICATED TO THE ANALYSIS AND APPLICATION OF MATHEMATICAL MODELS USED IN FINANCE WHEN THE STOCHASTIC ELEMENT BECOMES PART OF THE QUANTITATIVE DESCRIPTION. IN PARTICULAR, STUDENTS WILL ACQUIRE THE TOOLS OF STOCHASTIC COMPUTATION AND COMPUTER IMPLEMENTATION NECESSARY TO SOLVE COMPLEX PROBLEMS RELATED TO THE FINANCIAL SECTOR. THE TEACHING FINALIZES THE FORMAL RIGOR TO AN APPLICATIVE PERSPECTIVE, EMPHASIZING THE CRITICAL DISCUSSION OF THE RESULTS. KNOWLEDGE AND UNDERSTANDING STUDENTS WILL LEARN HOW TO DEAL WITH THE STOCHASTIC ELEMENT AS A TOOL OF CONCRETE UTILITY DUE TO THE INCREASED INFORMATION CONTENT THAT A STOCHASTIC MODEL OFFERS TO THE ANALYST, COMPARED TO A DETERMINISTIC APPROACH. COMPUTER APPLICATIONS WILL PROVIDE STUDENTS WITH THE TOOLS TO PROCEED WITH ANALYSIS, ESTIMATES, FORECASTS, RELATED TO THE PROCESSES OF FINANCIAL QUANTITIES AND HUMAN SURVIVAL, THIS LAST FUNDAMENTAL IN THE FINANCIAL ANALYSIS OF LIFE INSURANCE CONTRACTS. IN SUMMARY, THE CORNERSTONES OF THE COURSE WILL CONSIST OF THE FOLLOWING POINTS: •INCLUSION OF THE STOCHASTIC ELEMENT IN THE FINANCIAL HYPOTHESES •THE FUNDAMENTAL ASSUMPTIONS TO DESCRIBE A STOCHASTIC PROCESS USEFUL IN FINANCE •THE DIFFERENTIAL APPROACH TO UNDERSTAND THE DYNAMICS OF THE DESCRIPTION OF A RANDOM QUANTITY •THE INTEREST RATE: THE DESCRIPTIONS OF ITS TREND AND ITS IMPACT THROUGH PROCESSES, THEOREMS AND EQUATIONS. •USE OF R SOFTWARE IN STOCHASTIC FINANCE: A WAY TO AMPLIFY THE SCOPE AND THE RANGE OF THE RESULTS OBTAINABLE •ESTIMATION AND SIMULATIONS OF RATE TERM STRUCTURE •SURVIVAL ANALYSIS: SPECIALIZED SOFTWARE AND PROJECTIONS FOR THE DESCRIPTION OF SURVIVAL TRENDS, FUNDAMENTAL FOR THE MANAGEMENT OF LIFE INSURANCE PORTFOLIOS. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING STUDENTS WILL ACQUIRE ANALYTICAL AND CRITICAL SKILLS THAT WILL ENABLE THEM TO: •THE HISTORICAL CONSTRUCTION AND PROJECTION OF INTEREST RATE TERM STRUCTURES IN SPECIFIED FINANCIAL MARKETS •THE HISTORICAL CONSTRUCTION AND PROJECTION OF SURVIVAL •THE PRICING OF FINANCIAL DERIVATIVES AND THE DEVELOPMENT OF OPERATIONAL STRATEGIES TRANSVERSAL SKILLS STUDENTS WILL ACQUIRE ANALYTICAL AND CRITICAL SKILLS THAT WILL ENABLE THEM TO: •DESCRIBE THE BEHAVIOR OF FINANCIAL QUANTITIES IN THE PAST BEHAVIOR AND ELABORATE FORECASTS ON THEIR FUTURE EVOLUTION •ABILITY TO SYNTHESIZE THE IMPACT OF UNCERTAINTY WITH QUANTITATIVE INDICATORS •STRUCTURE MATHEMATICAL DESCRIPTIONS FOR CONTRACTS DEPENDENT ON THE INTEREST RATE •CONFIDENTLY USE SPECIALIZED FINANCIAL SOFTWARE

THE STOCHASTIC FINANCE COURSE, IN LINE WITH THE CORE OBJECTIVES OF THE DEGREE PROGRAM, IS DEDICATED TO THE ANALYSIS AND APPLICATION OF MATHEMATICAL MODELS USED IN FINANCE WHEN THE STOCHASTIC ELEMENT BECOMES PART OF THE QUANTITATIVE DESCRIPTION. IN PARTICULAR, STUDENTS WILL ACQUIRE THE TOOLS OF STOCHASTIC COMPUTATION AND COMPUTER IMPLEMENTATION NECESSARY TO SOLVE COMPLEX PROBLEMS RELATED TO THE FINANCIAL SECTOR. THE TEACHING FINALIZES THE FORMAL RIGOR TO AN APPLICATIVE PERSPECTIVE, EMPHASIZING THE CRITICAL DISCUSSION OF THE RESULTS.
KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL LEARN HOW TO DEAL WITH THE STOCHASTIC ELEMENT AS A TOOL OF CONCRETE UTILITY DUE TO THE INCREASED INFORMATION CONTENT THAT A STOCHASTIC MODEL OFFERS TO THE ANALYST, COMPARED TO A DETERMINISTIC APPROACH. COMPUTER APPLICATIONS WILL PROVIDE STUDENTS WITH THE TOOLS TO PROCEED WITH ANALYSIS, ESTIMATES, FORECASTS, RELATED TO THE PROCESSES OF FINANCIAL QUANTITIES AND HUMAN SURVIVAL, THIS LAST FUNDAMENTAL IN THE FINANCIAL ANALYSIS OF LIFE INSURANCE CONTRACTS.
IN SUMMARY, THE CORNERSTONES OF THE COURSE WILL CONSIST OF THE FOLLOWING POINTS:
•INCLUSION OF THE STOCHASTIC ELEMENT IN THE FINANCIAL HYPOTHESES
•THE FUNDAMENTAL ASSUMPTIONS TO DESCRIBE A STOCHASTIC PROCESS USEFUL IN FINANCE
•THE DIFFERENTIAL APPROACH TO UNDERSTAND THE DYNAMICS OF THE DESCRIPTION OF A RANDOM QUANTITY
•THE INTEREST RATE: THE DESCRIPTIONS OF ITS TREND AND ITS IMPACT THROUGH PROCESSES, THEOREMS AND EQUATIONS.
•USE OF R SOFTWARE IN STOCHASTIC FINANCE: A WAY TO AMPLIFY THE SCOPE AND THE RANGE OF THE RESULTS OBTAINABLE
•ESTIMATION AND SIMULATIONS OF RATE TERM STRUCTURE
•SURVIVAL ANALYSIS: SPECIALIZED SOFTWARE AND PROJECTIONS FOR THE DESCRIPTION OF SURVIVAL TRENDS, FUNDAMENTAL FOR THE MANAGEMENT OF LIFE INSURANCE PORTFOLIOS.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL ACQUIRE ANALYTICAL AND CRITICAL SKILLS THAT WILL ENABLE THEM TO:
•THE HISTORICAL CONSTRUCTION AND PROJECTION OF INTEREST RATE TERM STRUCTURES IN SPECIFIED FINANCIAL MARKETS
•THE HISTORICAL CONSTRUCTION AND PROJECTION OF SURVIVAL
•THE PRICING OF FINANCIAL DERIVATIVES AND THE DEVELOPMENT OF OPERATIONAL STRATEGIES
TRANSVERSAL SKILLS
STUDENTS WILL ACQUIRE ANALYTICAL AND CRITICAL SKILLS THAT WILL ENABLE THEM TO:
•DESCRIBE THE BEHAVIOR OF FINANCIAL QUANTITIES IN THE PAST BEHAVIOR AND ELABORATE FORECASTS ON THEIR FUTURE EVOLUTION
•ABILITY TO SYNTHESIZE THE IMPACT OF UNCERTAINTY WITH QUANTITATIVE INDICATORS
•STRUCTURE MATHEMATICAL DESCRIPTIONS FOR CONTRACTS DEPENDENT ON THE INTEREST RATE
•CONFIDENTLY USE SPECIALIZED FINANCIAL SOFTWARE

	Prerequisites
	COURSES IN MATHEMATICAL METHODS FOR ECONOMICS, FINANCIAL MATHEMATICS (I MODULE OF THE QUANTITATIVE METHODS COURSE) AND STATISTICS ARE RECOMMENDED.

	Contents
	THE STOCHASTIC FINANCE COURSE CONSISTS OF TWO MODULES: MODULE I - STOCHASTIC MODELS FOR FINANCE - 30 HOURS OF THEORETICAL LESSONS WITH APPLICATIONS. CHARACTERIZATION OF STOCHASTIC PROCESSES IN FINANCE. DISCRETE PROCESSES. CONTINUOUS PROCESSES. BROWNIAN MOTION. DIFFERENTIAL APPROACH. ITO’S LEMMA. INTEREST RATE SENSITIVE CONTRACTS: GENERAL EQUATION. THE MODELS OF VASICEK AND COX, INGERSOLL AND ROSS. THE BLACK AND SCHOLES FORMULA. DEFAULT RISK: THE POISSON PROCESS. MODULE II - COMPUTER APPLICATIONS TO STOCHASTIC PROCESSES FOR FINANCE - 30 HOURS OF LECTURE IN COMPUTER LAB. INTRODUCTION TO R SOFTWARE. GENERATIONS OF RANDOM VARIABLES. CREDIT VALUE ADJUSTMENT AND CREDIT DERIVATIVES. MONTE CARLO SIMULATIONS. BROWNIAN GEOMETRIC MOTION. STOCHASTIC PROCESSES FOR THE EVOLUTION OF INTEREST RATES: ESTIMATION AND SIMULATION OF TERM STRUCTURE: VASICEK AND COX INGERSOLL AND ROSS MODELS (5 HOURS EMPIRICAL APPLICATIONS IN LABORATORY). INTEREST RATE ESTIMATION: PRACTICAL CASES AND COMPARATIVE METHODOLOGIES (SMFI5 PACKAGE) (5 HOURS EMPIRICAL APPLICATIONS IN LAB). STANDARD AND EXOTIC FINANCIAL OPTIONS: BLACK & SCHOLES MODEL AND BINOMIAL MODEL. DELTA HEDGING (5 HOURS EMPIRICAL APPLICATIONS IN THE LAB). DERIVATIVE TRANSACTIONS. PACKAGES: FOPTIONS AND FEXOTICS (5 HOURS EMPIRICAL APPLICATIONS IN LABORATORY). SURVIVAL ANALYSIS AND ACTUARIAL VALUATIONS OF LIFE INSURANCE CONTRACTS. PACKAGES: DEMOGRAPHY, STMOMO, LIFECONTINGENCIES. PROJECTIONS WITH LEE CARTER MODEL AND EXTENSIONS, CBD MODEL AND EXTENSIONS (10 HOURS EMPIRICAL APPLICATIONS IN THE LABORATORY). THE DETAILED COURSE SCHEDULE IS AVAILABLE ON THE TEACHERS’ WEBSITE.

Contents

THE STOCHASTIC FINANCE COURSE CONSISTS OF TWO MODULES:
MODULE I - STOCHASTIC MODELS FOR FINANCE - 30 HOURS OF THEORETICAL LESSONS WITH APPLICATIONS.
CHARACTERIZATION OF STOCHASTIC PROCESSES IN FINANCE. DISCRETE PROCESSES. CONTINUOUS PROCESSES. BROWNIAN MOTION. DIFFERENTIAL APPROACH. ITO’S LEMMA. INTEREST RATE SENSITIVE CONTRACTS: GENERAL EQUATION. THE MODELS OF VASICEK AND COX, INGERSOLL AND ROSS. THE BLACK AND SCHOLES FORMULA. DEFAULT RISK: THE POISSON PROCESS.
MODULE II - COMPUTER APPLICATIONS TO STOCHASTIC PROCESSES FOR FINANCE - 30 HOURS OF LECTURE IN COMPUTER LAB.
INTRODUCTION TO R SOFTWARE. GENERATIONS OF RANDOM VARIABLES. CREDIT VALUE ADJUSTMENT AND CREDIT DERIVATIVES. MONTE CARLO SIMULATIONS. BROWNIAN GEOMETRIC MOTION. STOCHASTIC PROCESSES FOR THE EVOLUTION OF INTEREST RATES: ESTIMATION AND SIMULATION OF TERM STRUCTURE: VASICEK AND COX INGERSOLL AND ROSS MODELS (5 HOURS EMPIRICAL APPLICATIONS IN LABORATORY). INTEREST RATE ESTIMATION: PRACTICAL CASES AND COMPARATIVE METHODOLOGIES (SMFI5 PACKAGE) (5 HOURS EMPIRICAL APPLICATIONS IN LAB). STANDARD AND EXOTIC FINANCIAL OPTIONS: BLACK & SCHOLES MODEL AND BINOMIAL MODEL. DELTA HEDGING (5 HOURS EMPIRICAL APPLICATIONS IN THE LAB). DERIVATIVE TRANSACTIONS. PACKAGES: FOPTIONS AND FEXOTICS (5 HOURS EMPIRICAL APPLICATIONS IN LABORATORY). SURVIVAL ANALYSIS AND ACTUARIAL VALUATIONS OF LIFE INSURANCE CONTRACTS. PACKAGES: DEMOGRAPHY, STMOMO, LIFECONTINGENCIES. PROJECTIONS WITH LEE CARTER MODEL AND EXTENSIONS, CBD MODEL AND EXTENSIONS (10 HOURS EMPIRICAL APPLICATIONS IN THE LABORATORY).
THE DETAILED COURSE SCHEDULE IS AVAILABLE ON THE TEACHERS’ WEBSITE.

	Teaching Methods
	THE COURSE OF STOCHASTIC FINANCE CONSISTS OF 60 HOURS OF DIDACTICS, 30 OF WHICH WILL BE IN A COMPUTER LAB. THE LECTURES WILL BE FRONTAL AND CARRIED OUT WITH CONSTANT ATTENTION TO THE THEORETICAL APPROACH OF THE TOPICS, TO THE APPLICATIONS AND THE INTERPRETATION OF THE RESULTS OBTAINED.

	Verification of learning
	THE VERIFICATION OF LEARNING IS ORIENTED TO STIMULATE THE STUDY AND UNDERSTANDING OF THE TOPICS COVERED DURING THE COURSE BY THE STUDENTS, WITH PARTICULAR ATTENTION TO THE ABILITY TO APPLY THE MODELS TO CONCRETE SITUATIONS. MODULE I: THE STUDENT'S FINAL ASSESSMENT WILL CONSIST OF A WRITTEN AND AN ORAL TEST. THE MODULE WILL BE CONSIDERED PASSED IF BOTH THE WRITTEN TEST AND THE ORAL TEST WILL HAVE OBTAINED AN EVALUATION AT LEAST SUFFICIENT (GREATER THAN OR EQUAL TO 18/30). IN ADDITION TO THE SESSIONS SCHEDULED IN THE CALENDAR, THERE WILL BE A WRITTEN AND ORAL TEST AT THE END OF THE MODULE. EACH TEST WILL BE GRADED IN THIRTIETHS AND THE FINAL GRADE WILL BE THE AVERAGE OF THE GRADES OBTAINED ON THE TWO TESTS. THE MAXIMUM GRADE IS 30/30 WITH HONORS. THE WRITTEN TEST WILL HAVE A STRONG APPLICATIVE AND PRACTICAL CHARACTERIZATION. THE ORAL TEST WILL BE OF THEORETICAL CHARACTER. MODULE II: THE FINAL EXAM CONSISTS OF A PROJECT WORK TO BE PRESENTED IN THE FORM OF A WRITTEN PAPER AND TO BE DISCUSSED ORALLY. THE EVALUATION IS MADE IN THIRTIETHS AND IS SUFFICIENT IF PASSED WITH AT LEAST 18/30. THE MAXIMUM GRADE IS 30/30 WITH HONORS. THIS WORK WILL BE ORIENTED TO VERIFY THE ABILITY TO IMPLEMENT THE TOOLS ACQUIRED DURING THE MODULE, IN THE CONTEXT OF A APPLICATIVE CASE TO BE SOLVED. THE FINAL EVALUATION IN THE WHOLE EXAM WILL BE THE AVERAGE OF THE EVALUATIONS REPORTED IN EACH OF THE TWO MODULES.

Verification of learning

THE VERIFICATION OF LEARNING IS ORIENTED TO STIMULATE THE STUDY AND UNDERSTANDING OF THE TOPICS COVERED DURING THE COURSE BY THE STUDENTS, WITH PARTICULAR ATTENTION TO THE ABILITY TO APPLY THE MODELS TO CONCRETE SITUATIONS.
MODULE I: THE STUDENT'S FINAL ASSESSMENT WILL CONSIST OF A WRITTEN AND AN ORAL TEST. THE MODULE WILL BE CONSIDERED PASSED IF BOTH THE WRITTEN TEST AND THE ORAL TEST WILL HAVE OBTAINED AN EVALUATION AT LEAST SUFFICIENT (GREATER THAN OR EQUAL TO 18/30). IN ADDITION TO THE SESSIONS SCHEDULED IN THE CALENDAR, THERE WILL BE A WRITTEN AND ORAL TEST AT THE END OF THE MODULE.
EACH TEST WILL BE GRADED IN THIRTIETHS AND THE FINAL GRADE WILL BE THE AVERAGE OF THE GRADES OBTAINED ON THE TWO TESTS. THE MAXIMUM GRADE IS 30/30 WITH HONORS.
THE WRITTEN TEST WILL HAVE A STRONG APPLICATIVE AND PRACTICAL CHARACTERIZATION. THE ORAL TEST WILL BE OF THEORETICAL CHARACTER.
MODULE II: THE FINAL EXAM CONSISTS OF A PROJECT WORK TO BE PRESENTED IN THE FORM OF A WRITTEN PAPER AND TO BE DISCUSSED ORALLY. THE EVALUATION IS MADE IN THIRTIETHS AND IS SUFFICIENT IF PASSED WITH AT LEAST 18/30. THE MAXIMUM GRADE IS 30/30 WITH HONORS.
THIS WORK WILL BE ORIENTED TO VERIFY THE ABILITY TO IMPLEMENT THE TOOLS ACQUIRED DURING THE MODULE, IN THE CONTEXT OF A APPLICATIVE CASE TO BE SOLVED.
THE FINAL EVALUATION IN THE WHOLE EXAM WILL BE THE AVERAGE OF THE EVALUATIONS REPORTED IN EACH OF THE TWO MODULES.

	Texts
	MODULE I: S. M. ROSS, 2012, AN ELEMENTARY INTRODUCTION TO MATHEMATICAL FINANCE, CAMBRIDGE UNIVERSITY PRESS P. WILLMOT, 2007, PAUL WILLMOT INTRODUCES QUANTITATIVE FINANCE, THE WILEY FINANCE SERIES MODULO II: M. J. CRAWLEY, 2007, THE R BOOK, JOHN WILEY & SONS, EDS (AVAILABLE ONLINE) A. CLIFFORD, 2015, ANALYZING FINANCIAL DATA AND IMPLEMENTING FINANCIAL MODELS USING R, SPRINGER B. REMILLARD, 2013, STATISTICAL METHODS FOR FINANCIAL ENGINEERING, CRC PRESS, TAYLOR FRANCIS GROUP

Texts

MODULE I: S. M. ROSS, 2012, AN ELEMENTARY INTRODUCTION TO MATHEMATICAL FINANCE, CAMBRIDGE UNIVERSITY PRESS
P. WILLMOT, 2007, PAUL WILLMOT INTRODUCES QUANTITATIVE FINANCE, THE WILEY FINANCE SERIES
MODULO II: M. J. CRAWLEY, 2007, THE R BOOK, JOHN WILEY & SONS, EDS (AVAILABLE ONLINE)
A. CLIFFORD, 2015, ANALYZING FINANCIAL DATA AND IMPLEMENTING FINANCIAL MODELS USING R, SPRINGER
B. REMILLARD, 2013, STATISTICAL METHODS FOR FINANCIAL ENGINEERING, CRC PRESS, TAYLOR FRANCIS GROUP

Lessons Timetable

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