Browsing by Author "Klingberg Malmer, Oliver"

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Deep Learning and the Heston Model:Calibration & Hedging
(2020-07-03) Klingberg Malmer, Oliver; Tisell, Victor; University of Gothenburg/Department of Economics; Göteborgs universitet/Institutionen för nationalekonomi med statistik
The computational speedup of computers has been one of the de ning characteristics of the 21st century. This has enabled very complex numerical methods for solving existing problems. As a result, one area that has seen an extraordinary rise in popularity over the last decade is what is called deep learning. Conceptually, deep learning is a numerical method that can be "taught" to perform certain numerical tasks, without explicit instructions, and learns in a similar way to us humans, i.e. by trial and error. This is made possible by what is called arti cial neural networks, which is the digital analogue to biological neural networks, like our brain. It uses interconnected layers of neurons that activates in a certain way when given some input data, and the objective of training a arti cial neural network is then to let the neural network learn how to activate its neurons when given vast amounts of training examples in order to make as accurate conclusions or predictions as possible. In this thesis we focus on deep learning in the context of nancial modelling. One very central concept in the nancial industry is pricing and risk management of nancial securi- ties. We will analyse one speci c type of security, namely the option. Options are nancial contracts struck on an underlying asset, such as a stock or a bond, which endows the buyer with the optionality to buy or sell the asset at some pre-speci ed price and time. Thereby, options are what is called a nancial derivative, since it derives its value from the under- lying asset. As it turns out, the concept of nding a fair price of this type of derivative is closely linked to the process of eliminating or reducing its risk, which is called hedging. Traditionally, pricing and hedging is achieved by methods from probability theory, where one imposes a certain model in order to describe how the underlying asset price evolves, and by extension price and hedge the option. This type of model needs to be calibrated to real data. Calibration is the task of nding parameters for the stochastic model, such that the resulting model prices coincide with their corresponding market prices. However, traditional calibration methods are often too slow for real time usage, which poses a practical problem since these models needs to be re-calibrated very often. The hedging problem on the other hand has been very di cult to automate in a realistic market setting and su ers from the simplistic nature of the classical stochastic models. The objective of this thesis is thus twofold. Firstly, we seek to calibrate a speci c prob- abilistic model, called the Heston model, introduced by Heston (1993) by applying neural networks as described by the deep calibration algorithm from Horvath et al. (2019) to a major U.S. equity index, the S&P-500. Deep calibration, amongst other things, addresses the calibration problem by being signi cantly faster, and also more universal, such that it applies to most option pricing models, than traditional methods. Secondly, we implement arti cial neural networks to address the hedging problem by a completely data driven approach, dubbed deep hedging and introduced by Buehler et al. (2019), that allows hedging under more realistic conditions, such as the inclusion of costs associated to trading. Furthermore, the deep hedging method has the potential to provide a broader framework in which hedging can be achieved, without the need for the classical probabilistic models. Our results show that the deep calibration algorithm is very accurate, and the deep hedging method, applied to simulations from the calibrated Heston model, nds hedging strategies that are very similar to the traditional hedging methods from classical pricing models, but deviates more when we introduce transaction costs. Our results also indicate that di erent ways of specifying the deep hedging algorithm returns hedging strategies that are di erent in distribution but on a pathwise basis, look similar.
Tidying up the factor zoo: Using machine learning to find sparse factor models that predict asset returns.
(2020-07-01) Klingberg Malmer, Oliver; Pettersson, Gustav; University of Gothenburg/Department of Economics; Göteborgs universitet/Institutionen för nationalekonomi med statistik
There exist over 300 firm characteristics that provide significant information about average asset return. John Cochrane refers to this as a “factor zoo” and challenges researchers to find the independent characteristics which can explain average return. That is, to find the unsubsumed and non-nested firm characteristics that are highly predictive of asset return. In this thesis we act on the posed challenge by using a data driven approach. We apply two machine learning methods to create sparse factor models composed by a small set of these characteristics. The two methods are one unsupervised learning method, the Principal Component Analysis, and one supervised learning method, the LASSO regression. The study is done using the S&P 500 index constituents and 54 firm characteristics over the time period 2009-07-01 to 2019-07-01. The performance of the factor models is in this study measured using out-of-sample measurements. Using established methods of post-LASSO regression and new developed techniques for variable selection based on PCA, we generate four new factor models. The latter mentioned variable selection method based on PCA is, to our knowledge, an original contribution of this thesis. The generated factor models are compared against the Fama French factors in the out-of-sample test and are shown to all outperform. The best performer is a LASSO generated factor model containing 6 factors. By analysing the results we find that momentum factors, such as price relative to 52-week-high-price, are highly predictive of return and are commonly selected factors, which confirms the results of previous responses to the same challenge.