Applications of neural networks in market risk

Abstract

Market risk refers to the potential loss that can be incurred as a result of movements inmarket factors. Capturing and measuring these factors are crucial in understanding andevaluating the risk exposure associated with an investment portfolio. This process iscomplicated by the fact that not all factors are directly measurable in the market; also, theasset returns exhibit stylised facts which complicate the modelling process. Risk models arerequired to capture this dynamic behaviour of the asset price to enable forecasting, pricingand evaluation of the current and future portfolio position. Statistical models applied in thisdomain have limitations in representing and capturing the dynamic behaviours in themarket. This limitation is caused by the necessary assumptions of the model in theunderlying process to allow for the mathematical derivation of the model such as thenormality in the asset return series. Such assumption drastically impacts upon the accuracy and the stability of the model.For this reason, neural networks are proposed as an alternative solution to statistical models as they are data-driven which does not require any assumptions in the underlying data. Although neural networks have been applied successfully in many disciplines, they have shown limited success in market risk. In this thesis, we study the application of neural networks in market risk; in particular, we study the application of neural networks in volatility forecasting, option pricing and hedging.Neural networks have been applied heavily to time forecasting with superior performances over standard time series models. Typically in risk management models, forecasting accuracy is dependent on how well the model is able to capture the volatility process. In the literature, volatility forecasting results are indecisive and in some instances misleading. For this reason, the majority of volatility forecasting research relies on hybrid methods that combine time series models and neural networks to further increase the accuracy of forecasting. This limitation is due to the neural networks' (MLP) inability to cater for key stylised facts in the data. For this reason, we turn our attention to mixture density networks (MDNs) as they are most suitable for modelling key stylised facts, such as heteroskedasticity.There are several MDN volatility forecasting papers where the forecasting results are aligned with other research conducted in this domain. The mixed results reported in the literature are analysed and the key variables impacting on the results are studied. Our research identified key oversights in the model design and optimisation process that has led to the conflicting results in the research. To demonstrate the impacts of these oversights and the capabilities of the MDNs, we conduct an extensive experiment by varying multiple factors in the MDN models. The results demonstrate the out-of-sample forecasting capabilities of the MDN and show how the time series models are directly affected by these variables. Also, MDN models displayed superiority over GARCH models when the correct model is selected.Neural networks have been utilised for option pricing with the aim of overcoming the inefficiencies and assumptions of the BSOPM. The research results demonstrate the superiority of the neural networks’ pricing accuracy over the BSOPM. However, the majority of neural network research in option pricing thus far has focused mainly on improving the pricing capabilities of the BSOPM; next to no work has been done with respect to other advanced models such as GOPM. In this thesis, we explain how the weak performance of neural networks is due to the method and data used in optimising the neural network. We devise a new method for pricing option by training the neural network on the implied volatility rather than the option price.This method overcomes the data issues and allows the neural network to capture key behaviours in the options data. The results show significant improvements of neural networks which demonstrate the superiority of the neural network over the GOPM and the BSOPM. To further test the neural network capabilities, a delta hedging scenario was devised for all models. The results indicated that the performance of the neural networks was similar to that of the BSOPM, whereas the GOPM's performance was inferior to other models.The results in this thesis demonstrate the power of neural networks in learning complex behaviour from the underlying data. These features allow them to be applied to market risk problems to overcome classical issues associated with statistical models. As an extension to this research, we design a neural network based on the outcomes of this thesis to address VaR modelling issues. This experiment will be left for future research.