Студент Александар Милинковић је у четвртак, 28. септембра 2023. године одбранио свој мастер рад на тему Financial derivatives pricing using artificial neural networks пред ментором др Бранком Урошевићем и члановима комисије др Миланом Недељковићем и др Андрејом Стојићем.
У уводу свог рада Александар је истакао:
Assets of all sorts are traded in financial markets: stocks and stock indices, foreign currencies, loan contracts with various interest rates, energy in many forms, agricultural products, precious metals, etc. The prices of these assets fluctuate, sometimes wildly.
If one could anticipate the price fluctuations to any significant extent, then he/she could clearly make a great amount of money very quickly. The fact that many people are trying to do exactly that makes the fluctuations essentially unpredictable for practical purposes. A fundamental principle of finance, the efficient market hypothesis, asserts that all information available to anyone anywhere is instantly expressed in the current price, as market participants race to be the first to profit from new information. Thus successive price changes may be considered to be uncorrelated random variables, since they depend on as-yet unrevealed information. This principle is the subject of intensive analytical testing and some controversy, but is an excellent approximation for our purposes.
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Nowadays, machine learning method such as neural networks in financial market has been a hot issue. Among them, derivatives pricing plays an important role in both academia and actual transactions. Deep learning algorithms that keep pace with the times also have good model generalization capabilities as their prediction accuracy has surpassed the traditional financial models. For example, compared with the more traditional Monte Carlo method, LSTM achieves higher accuracy within smaller time. What’s more, to the non-linear, high-dimension data, machine learning methods would do better than traditional methods. In addition, we can select different features and enter different variables to improve the accuracy of prediction, while for traditional methods, we might need to construct another PDE or SDE to descibe the underlying dynamics.
Neural network can be used to solve the Black Scholes partial differential equation with finite difference method using radial basis function. It is shown that even if the speed of convergence of Monte Carlo method was closer to the radial basis function network, the value obtained from neural network was closer to the semi-analytic solution. Also, the problem of dimensionality always exists when using Monte Carlo method. For this reason, several studies appear to reduce this problem (variance reduction, quasi-Monte Carlo, discrepancy sequences, etc.). However, using neural networks leads to solving, somehow inherently, this curse of dimensionality. – закључио је Александар.
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