Quantitative Analyses on Non-Linearities in Financial Markets
Creators: name: CAFFERATA, ALESSIA
Publisher: name: Universit� degli studi di Genova
Year: 2019

description: "The brief market plunge was just a small indicator of how
complex and chaotic, in the formal sense, these systems
have become. Our nancial system is so complicated and so
interactive [...]. What happened in the stock market is just
a little example of how things can cascade or how technology
can interact with market panic" (Ben Bernanke, IHT, May
17, 2010)
One of the most important issues in economics is modeling and fore-
casting the 
uctuations that characterize both nancial and real mar-
kets, such as interest rates, commodities and stock prices, output
growth, unemployment, or exchange rate. There are mainly two op-
posite views concerning these economic 
uctuations. According to
the rst one, which was the predominant thought in the 1930s, the
economic system is mainly linear and stable, only randomly hit by
exogenous shocks. Ragnar Frisch, Eugen Slutsky and Jan Tinbergen,
to cite a few, are important exponents of this view, and they demon-
strated that the 
uctuations observed in the real business cycle may
be produced in a stable linear system subject to an external sequence
of random shocks. This view has been criticized starting from the
1940s and the 1950s, since it was not able to provide a strong eco-
nomic explanation of observed 
uctuations. Richard Goodwin,John
Hicks and Nicholas Kaldor introduced a nonlinear view of the econ-
omy, showing that even in absence of external shocks, 
uctuations
might arise. The economists then suggested an alternative within
the exogenous approach, at rst by using the stochastic real busi-
ness cycle models (Finn E. Kidland and Edward C. Prescott, 1982)
and, more recently, by the adoption of the New Keynesian Dynamic
Stochastic General Equilibrium (DSGE) models, very adopted from
the most important institutions and central banks. These models,
however, have also been criticized for the assumption of the rational-
ity of agents' behaviour, since rational expectations have been found
to be systematically wrong in the business cycle. Expectations are of
fundamental importance in economics and nance, since the agents'
decisions about the future depends upon their expectations and their
beliefs. It is in fact very unlikely that agents are perfect foresighters
with rational expectations in a complex world, characterized by an
irregular pattern of prices and quantities dealt in nancial markets,
in which sophisticated nancial instruments are widespread.
In the rst chapter of this dissertation, I will face the machine learn-
ing technique, which is a nonlinear tool used for a better tting, fore-
casting and clustering of dierent nancial time series and existing
information in nancial markets. In particular, I will present a collec-
tion of three dierent applications of these techniques, adapted from
three dierent joint works:
 "Yield curve estimation under extreme conditions: do RBF net-
works perform better?, joint with Pier Giuseppe Giribone, Marco
Neelli, Marina Resta, published Anna Esposito, Marcos Faundez-
Zanuy, Carlo Francesco Morabito, Eros Pasero Edrs, Multidisci-
plinary Approaches to Neural Computing/Vol. 69/ WIRN 2017
and Chapter 22 in book "Neural Advances in Processing Non-
linear Dynamic Signals", Springer;
 Interest rates term structure models and their impact on actuarial
forecasting, joint with Pier Giuseppe Giribone and Marina Resta,
presented at XVIII Quantitative Finance Workshop, University
of Roma 3, January 2018;
 Applications of Kohonen Maps in financial markets: design of
an automatic system for the detection of pricing anomalies, joint
with Pier Giuseppe Giribone and published on Risk Management
Magazine, 3-2017.
In the second chapter, I will present the study A nancial market
model with conrmation bias, in which nonlinearity is present as a
result of the formation of heterogeneous expectations. This work is
joint with Fabio Tramontana and it has been presented during the
X MDEF (Dynamic Models in Economics and Finance) Workshop at
University of Urbino Carlo Bo.
Finally, the third chapter is a rielaboration of another joint paper,
"The eects of negative nominal risk rates on the pricing of American
Calls: some theoretical and numerical insights", with Pier Giuseppe
Giribone and Marina Resta, published on Modern Economy 8(7), July
2017, pp 878-887. The problem of quantifying the value of early ex-
ercise in an option written on equity is a complex mathematical issue
that deals with continuous optimal control. In order to solve the con-
tinuous dynamic optimization problem that involves high non linearity
in the state variables, we have adopted a discretization scheme based
on a stochastic trinomial tree. This methodology reveals a higher
reliability and 
exibility than the traditional approaches based on approximated quasi-closed formulas in a context where financial markets
are characterized by strong anomalies such as negative interest rates.