Professore Associato

Giuseppe Alesii

corporate finance, financial management, real options, financial structure, derivatives, asset pricing
05 Finanza Aziendale
SECS-P/09 - Finanza aziendale
Mathematics and Applications

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Models and Algorithms for Financial Management

Course Objectives

Introduction to finance problems from a micro and macro economics perspective and from a financial accounting point of view. Applications of computer science and quantitative abilities to financial modelling

Course Content

Fixed income securities valuation under the assumption of certainty: interest rates risk sensitivity:
- (a) Macaulay duration
- (b) term structure of interest rates, spot, forward and short rates;
- (c) Fisher Weil duration.
Shares valutation under the assumption of certainty, dividend discount model:
- (a) Myron Gordon's dividend growth model;
- (b) Modigliani Miller 1961, growth model;
- (c) fundamental indexes and dividend discount models, cross sectionals and longitudinal evidences;
Capital Budgeting, choosing real investments in an industrial firmunder the assumption of certainty:
- (a) criteria:
  - i. Payback Period,
  - ii. Internal Rate of Return,
  - iii. Net Present Value,
  - iv. Profitability Index,
  - v. Economic Value Added (as an extension of Modigliani Miller 1961);
- (b) methods:
  - Uniform Annuity Series for investment projects with different horizons;
  - i. capital rationing, uni e multiperiod cases, linear programming applied to multiperiod cases, geometric approach and Excel Solver Tool application;
  - ii. optimal harvesting, Faustmann problem individual and repeated cycles problems solutions.
- (c) comparative statics and dynamic optimization: Richard Bellman's Dynamic Programming in a deterministic frameworkl:
  - i. continuous and discrete control variables
  - ii. application to the choice and optimal dynamic management of investment project for renewable and exhaustible resources.
An hands on introduction to stochastic processes most used in derivatives valuation modelling:
- (a) time series modelling: additive shocks, multiplicative shocks.
  - i. MA(1), AR(1) representations
  - ii. from sufficient statistics of a normal distribution to those of the corresponding log normal;
- (b) Wiener process as a limit case of a random walk
- (c) Ito process as a generalization of a Wiener process
- (d) Geometric Brownian Motion:
  - i. univariate GBM;
    - A. Ito's lemma application: log transform process parameters derivation, Arithmetic Brownian Motion
    - B. Monte Carlo simulation of Pde solution and of its Euler approximation
    - C. parameters empirical estimate;
    - D. binomial approximation through moment matching conditions: Cox, Ross, Rubinstein 1979
    - E. Brownian Bridge, concept and Monte Carlo Simulation;
- (e) Ornstein Uhlenbeck:
  - - i. original version with arithmetic shocks;
    - ii. Ito's lemma application: derivation of Schwartz 1997 version, geometric with spring effects on logarithms;
    - iii. OU process parameters estimates;
    - iv. Monte Carlo simulation of processes sub i. and ii.
    - v. Binomial approximation Sick 1995

Martingale Pricing for derivative securities:
- (a) american options valuation: drift change and backward induction in the following models
  - i. Cox, Ross, Rubinstein 1979
  - ii. Sick 1995
Real Options
- (a) parallelism with decision tree analysis
- (b) martingale pricing viability for an irregular uncertainty resolution, multiperiod securities markets di Harrison e Kreps 1979
- (c) differences and analogies between real and financial options
- (d) most frequent real options, Mickey mouse examples
  - i. option to wait;
  - ii. option to expand/contract
  - iii. option to mothball/restart
  - iv. option to switch use
  - v. option to abandon
  - vi. option to default
  - vii. operating default
  - viii. financial default
    - asset substitution moral hazard
    - underinvestment moral hazard
    - put call parity interpretation of bond holders equity holders wealth transfer
- (e) different approaches to real options valuations:
- (f) the general real options model of Kulatilaka-Trigeorgis:
  - i. mickey mouse example
  - ii. taxonomy of operating modes of an industrial plant Markov Chain states analogies;
  - iii. binomial lattice Cox, Ross, Rubinstein 1979, Mickey Mouse example.
Least Squares Monte Carlo, Longstaff, Schwartz 2001 RFS:
- (a) general introduction to the model and comparison with Tsitsiklis Van Roy model;
- (b) american/bermudean put option valuation, example of Moreno Navas 2003 MF:
- (c) LSMC for the Kulatilaka Trigeorgis general real options model, Gamba 2011 JMF

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

have a thorough and deep knowledge of capital budgeting / securities pricing models under certainty and portfolio selection and basic asset pricing models. Moreover, she/he must be knowledgeable with the general themes of finance.
be able to use her/his programming skills in simple Excel spreadsheets and/or in high programming languages such as Gauss or MatLab, not only for financial models and algorithms dealt with at lesson but also for other similar problems.
have acquired general skills in the field of algorithms and applied programming for financial modelling which enable him/her to make educated choices in a problem solving practice framework. The student should be able to retrieve financial data, compute main descriptive statistics, estimate parameters of main asset pricing models (Information procurement and analysis). The student should be able to apply integer and non integer linear programming and numerical non linear optimization algorithms in both capital budgeting and asset pricing (algorithm choice).
be capable to give a presentation both in front of a general practitioners' audience and a more academic one about the models dealt within the course.
have acquired a method of study both thanks to a wide knowledge of the main streams in which financial modelling is evolving, theoretical continued learning, and a confident practice with respect to the main high level programming languages, GAUSS and MatLab, which are continually evolving, best practice continued learning.

Prerequisites and Learning Activities

Pre-Assessment Formal prerequisites are:

Actual prerequisites are not assessed at the beginning of the course and they are considered as a given when tuning the teaching approach of finance topics. A good programming ability is required for the following applications: A) any spreadsheet, e.g. Excel, Calc; B) any matrix oriented language, e.g. MatLab, Gauss, Ox, Octave, Scilab. In the computer lab classes, Gauss will be used. Univariate and multivariate calculus is applied in most of the models. A solid background in probability theory is required.

Assessment Methods and Criteria

Pre Assessment

A preliminary assessment of prerequisite skills is not performed in this course.

Formative Assessment

The formative assessment of this course teaching and learning process is performed through class participation during lessons:

A) students may be asked to answer questions about topics dealt with at lesson; students may ask instructor questions during lessons both about the very topic dealt with at lesson and about correlated topics they are particularly interested in.
B) summary of previous week lessons: a student is randomly selected to sum up topics dealt with in the previous sessions, actually introducing extant session;
C) short seminars: students are required to apply their skills in Calculus, Stochastic Calculus, Numerical Analysis and Mathematical Statistics to specific problems in finance, proposing their own solutions previously prepared as homeworks.

Summative Assessment

The summative assessment of this course is performed through

A) Written tests:
- i) during the semester module a mid term and a final test at the end of the semester are given for students attending lessons;
- ii) a comprehensive test is given in ordinary exam sessions for students not attending lessons and for attending students that do not pass mid term and final semester tests;
B) Homeworks and take home projects: some compulsory homeworks are given on specific topics to let students delve into the subject at her/his own pace; some optional take home projects are suggested to students particularly interested in applying quantitative methods of their choice to finance problems.
C) Oral exams: after achieving at least an average pass grade in written tests during the semester or, as an alternative, an equivalent valuation on a comprehensive written test in an ordinary exam session, students are required to take an oral exam made up of:
- 1) questions about mistakes in written tests;
- 2) one's choice topic question.

aims and formative purposes

students are evaluated with respect to three different dimensions of learning:

A) Baseline theoretical knowledge provided through lessons and suggested reading list: tested through open questions to be answered through short essays;
B) Problem solving involving symbolic calculus and stochastic calculus capabilities: tested through questions about model building and algorithms tuning for specific formal problems;
C) Programming capabilities: tested through small (large) problems in class (at home) assignments to be programmed in a high level language, e.g. MatLab, Gauss, Ox, Scilab.

Evaluation criteria

final numerical results achievement;
style:
- 2.1) in modelling – possibly new – solutions in a symbolic layout;
- 2.2) in writing codes for extant models;
- 2.3) in prose for short essays questions.

Assessment breakdown

Formative and Summative Assessment towards the definition of a final grade weights on the final grade:

In class participation 5%;
Summary of previous week lessons 10%;
Short seminars (if given, else the weight is given to class participation) 5%;
In Class written tests 50%;
Home assignments (homeworks and take home projects) 25%;
Oral Exam 5%.

Textbooks

Thomas E. Copeland, J. Fred Weston, and Kuldeep Shastri, Financial Theory and Corporate Policy , Addison-Wesley 2005. (4th Edition).
Luenberger, D, Investment Science , Oxford University Press. 1998.
Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern Portfolio Theory and Investment Analysis , Wiley. 2006.

Contatti

galesii@univaq.it
+39 0862433156

Indirizzo

Edificio Coppito 1, Room 101
Via Vetoio - 67100 L'Aquila, Italy

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Professore Associato

Giuseppe Alesii

Models and Algorithms for Financial Management

Course Objectives

Course Content

Learning Outcomes (Dublin Descriptors)

Prerequisites and Learning Activities

Assessment Methods and Criteria

Textbooks

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