Forecasting Volatility of Stock Index: Deep Learning Model with Likelihood-Based Loss Function

Fang Jia,Boli Yang,Benjamin Miranda Tabak

doi:10.1155/2021/5511802

Fang Jia, Boli Yang + Show 1 more

Open Access

https://doi.org/10.1155/2021/5511802

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Abstract

Volatility is widely used in different financial areas, and forecasting the volatility of financial assets can be valuable. In this paper, we use deep neural network (DNN) and long short-term memory (LSTM) model to forecast the volatility of stock index. Most related research studies use distance loss function to train the machine learning models, and they gain two disadvantages. The first one is that they introduce errors when using estimated volatility to be the forecasting target, and the second one is that their models cannot be compared to econometric models fairly. To solve these two problems, we further introduce a likelihood-based loss function to train the deep learning models and test all the models by the likelihood of the test sample. The results show that our deep learning models with likelihood-based loss function can forecast volatility more precisely than the econometric model and the deep learning models with distance loss function, and the LSTM model is the better one in the two deep learning models with likelihood-based loss function.

Highlights

In finance, volatility refers to the variation degree of asset price, and it measures the uncertainty of the price
We use deep learning models, an econometric model, and a simple statistical method to forecast the volatility of three US stock indices
Different from related research studies, we further introduce a likelihood-based loss function to train the deep learning models and test all the methods by the likelihood of the test sample

Summary

Introduction

Volatility refers to the variation degree of asset price, and it measures the uncertainty of the price. It plays an important role in both academic research and financial industry. In risk management and performance measurement, volatility is a risk indicator itself and can be a part of some other indicators, like the Sharpe ratio. Markowitz [1] used volatility to measure the risks of assets and the overall risk of the portfolio. Volatility is both the input and the optimization target of the portfolio construction model. Prices of derivatives can be determined by the volatility of the underlying assets [2]

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Conclusion