Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines

Download
2017
Kalaycı, Betül
Stochastic Differential Equations (SDEs) rapidly become the most well-known format in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, micro-economic systems, and human behaviour. They are one of the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on several empirical phenomena regarding the behaviour of individual investors, such as how their emotions and opinions influence their decisions. Emotions can affect the way of thinking. A negative state leads to be risk-averse, while a positive state leads to be ambitious, and to act in a risky way even. All those emotions and opinions are described by the word Sentiment. In finance, stochastic changes might occur according to investors’ sentiment levels. In our study, we aim to represent the mutual effects between some financial process and investors’ sentiment with constructing a coupled system of non-autonomous SDEs, evolving in time. These equations are hard to assess and solve. Therefore, we express them in a simplified manner of an approximation by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables, based on high-dimensional and big data. Hereby, we treat time as another spatial variable. Afterwards, we will present a modern application with real-world data. The thesis finishes with a conclusion and an outlook towards future studies.

Suggestions

Refinements, extensions and modern applications of conic multivariate adaptive regression splines
Yerlikaya Özkurt, Fatma; Weber, Gerhard Wilhelm; Department of Scientific Computing (2013)
Conic Multivariate Adaptive Regression Splines (CMARS) which has been developed at the Institute of Applied Mathematics, METU, as an alternative approach to the well-known data mining tool Multivariate Adaptive Regression Splines (MARS). CMARS is based on given data and a penalized residual sum of squares for MARS, interpreted as a Tikhonov Regularization problem. CMARS treats this problem by a continuous optimization technique called Conic Quadratic Programming (CQP). This doctoral thesis adapts the CMARS ...
Two studies on backward stochastic differential equations
Tunç, Vildan; Sezer, Ali Devin; Department of Financial Mathematics (2012)
Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t); y(t)}; t is in [0; 1]} with values i...
Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS
Kalayci, Betul; Ozmen, Ayse; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01)
Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on s...
Application of stochastic volatility models with jumps to BIST options
Rahiminejat, Monireh; Sezer, Ali Devin; Department of Financial Mathematics (2017)
This thesis gives a derivation of call and put option pricing formulas under stochastic volatility models with jumps; the precise model is a combination of Merton and Heston models. The derivation is based on the computation of the characteristic function of the underlying process. We use the derived formulas to fit the model to options written on two stocks in the BIST30 index covering the first two months of 2017. The fit is done by minimizing a weighted $L_2$ distance between the observed prices and the ...
A STOCHASTIC APPROACH TO MODEL HOUSING MARKETS: THE US HOUSING MARKET CASE
YILMAZ, BİLGİ; Kestel, Sevtap Ayşe (2018-12-01)
This study aims to estimate the price changes in housing markets using a stochastic process, which is defined in the form of stochastic differential equations (SDEs). It proposes a general SDEs system on the price structure in terms of house price index and mortgage rate to establish an effective process. As an empirical analysis, it applies a calibration procedure to an SDE on monthly S&P/Case-Shiller US National Home Price Index (HPI) and 30-year fixed mortgage rate to estimate parameters of differentiabl...
Citation Formats
B. Kalaycı, “Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines,” M.S. - Master of Science, Middle East Technical University, 2017.