Course Details for A.Y. 2013/2014
Name:
Modelli e Algoritmi per la Finanza Aziendale mod II / Modelli e Algoritmi per la Finanza Aziendale mod II
Basic information
Credits:
: Laurea Magistrale in Matematica 6 CFU (c)
Degree(s):
Laurea Magistrale in Matematica 2° anno curriculum Generale Opzionale
Language:
Italian
Course Objectives
Martingale pricing models for industrial investments, i.e. real options, for fixed income securities, e.g. mortgages, bonds. Financial Structure and Dividend policy will be studies from both a normative and a positive economics points of view.
Course Content
 Introduction to derivative securities: options
(a) payoff diagrams
(b) position diagrams
(c) put call parity
(d) composite positions:
i. spread;
ii. combination;
iii. hedge.
 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;
ii. multivariate GBM with correlated Wiener Processes:
A. construction and simulation of a multivariate GBM with correlated Wienere processes;
B. bivariate case: analytic (Cholesky) transformation of two uncorrelated shocks into two correlated ones;
C. general case: Choleski decomposition of a correlogram;
D. parametric Monte Carlo study of the estimates of correlation between two time series generated by correlated GBMs.
E. Boyle, Evnine, Gibbs 1989, multivariate binomial model: bivariate case programmed in Aptech Gauss;
(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. Binomiale approximation Sick 1995
(f) volatility estimate for univariate processes:
i. inverting Black e Scholes 1973 and deriving a volatility surface
ii. equally weighted estimates;
iii. ARCH(m);
iv. EWMA: exponentially weighted moving average;
v. GARCH(1,1):
A. volatility clustering detection;
B. leverage effect detection;
C. plain vanilla GARCH(1,1)
D. GARCH(1,1) as a discrete time counterpart of an Orn
stein Uhlenbeck process;
E. IGARCH
vi. review of some models that accomodate volatility leverage:
A. AGARCH;
B. EGARCH;
C. GRJGARCH;
D. NLGARCH;
E. Smooth Transition GARCH;
F. Markov Switching GARCH;
vii. GARCH(1,1) estimation:
A. MLE methods in general;
B. MLE methods for GARCH(1,1) numerical examples on
Excel:
3 parameters estimation;
2 parameters estimation variance targeting;
MLE estimate of EWMA;
tness tests: Box Pierce, Ljung Box, autocorrelogram
viii. Use of GARCH() models to forecast volatility:
A. GARCH volatility term structure;
B. GARCH average volatility.
ix. GARCH models and Options Pricing:
A. local risk neutrality, Duan 1995;
B. numerical example: Monte Carlo simulation of a GBM
with stochastic volatilty generated by a GARCH(1,1)
(g) Variance covariance matrix estimation for multivariate processes:
i. equally weighted estimates of covariances;
ii. EWMA with no cross terms.
iii. modelling of variance covariance matrix, review, with speci
cation of the respective LL function:
iv. direct:
VEC GARCH,
BEKK GARCH,
v. indirect:
CCC GARCH,
DCC GARCH.
 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
iii. Boyle, Evnine, Gibbs 1989
(b) european options valuation, in addiction to the preceding sub (a):
i. derivation of Black e Scholes 1973 as a limit case for Cox, Ross, Rubinstein 1979;
ii. Stultz 1982, Johnson 1987 rainbow options valuation, bivariate case programming in Aptech Gauss
iii. Monte Carlo simulations for both univariate and multivariate cases;
 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 KulatilakaTrigeorgis:
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

Student must have a thorough and deep knowledge of some modelling approaches in finance. Moreover, she/he must be knowledgeable with the general themes of finance.

The student is enabled to use her/his programming skills to models and algorithms in finance not only with respect to those dealt with in the course but also to other problems.

Informed judgements and choices student's skills in the field of finance are built up thanks to a wide variety of models dealt with in the course and to an hands on approach which privileges practice over theory.

Students are under constant pressure to provide feedback to instructor. This is true both with respect to class participation and written exams and homeworks.

Since teaching is based mostly on methods and less on models by themselves, students are enabled to extend their knowledge of models and algorithms of finance well beyond those dealt with in the course.
Prerequisites and Learning Activities
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
Two written exams during the 14 weeks course, mid term and final. The same exercises will be given during ordinary exams sessions during the year. Written test account for 90% of final valuation. A short oral exam is due to get the final grade by those students who got at least an average pass grade for the written tests.
Textbooks
 Thomas E. Copeland, J. Fred Weston, and Kuldeep Shastri, Financial Theory and Corporate Policy (4th Edition) , AddisonWesley. 2005.
 Luenberger, D., Investment Science , Oxford University Press. 1988.
 John C. Hull, Options, Futures and Other Derivatives (6th edition) , Prentice Hall. 2005.
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 21 marzo 2014, 14:26