A Neural Stochastic Volatility Model
In this paper, we show that the recent integration of statistical models with recurrent neural networks provides a new way of formulating volatility models that have been popular in time series analysis and prediction. The model comprises a pair of complementary stochastic recurrent neural networks: the generative network models the joint distribution of the stochastic volatility process; the inference network approximates the conditional distribution of the latent variables given the observable ones. Our focus in this paper is on the formulation of temporal dynamics of volatility over time under a stochastic recurrent neural network framework. Our derivations show that some popular volatility models are a special case of our proposed neural stochastic volatility model. Experiments demonstrate that the proposed model generates a smoother volatility estimation, and largely outperforms a widely used GARCH model on several metrics about the fitness of the volatility modelling and the accuracy of the prediction.
The authors propose a recurrent variational neural network approach to modelling volatility in financial time series. This model consists of an application of Chung et al.’s (2015) VRNN model to volatility forecasting, wherein a Variational Autoencoder (VAE) structure is repeated at each time step of the series. The paper is well written and easy to follow (although this reviewer suggests applying a spelling checking, since the paper contains a number of harmless typos). The paper’s main technical contribution is to stack two levels of recurrence, one for the latent process and one for the observables. This appears to be a novel, if minor contribution. The larger contribution is methodological, in areas of time series modelling that are both of great practical importance and have hitherto been dominated by rigid functional forms. The demonstration of the applicability and usefulness of general-purpose non-linear models for volatility forecasting would be extremely impactful. I have a few comments and reservations with the paper: 1) Although not mentioned explicitly, the authors’ framework are couched in terms of carrying out one-timestep-ahead forecasts of volatility. However, many applications of volatility models, for instance for derivative pricing, require longer-horizon forecasts. It would be interesting to discuss how this model could be extended to forecast at longer horizons. 2) In Section 4.4, there’s a mention that a GARCH(1,1) is conditionally deterministic. This is true only when forecasting 1 time-step in the future. At longer horizons, the GARCH(1,1) volatility forecast is not deterministic. 3) I was initially unhappy with the limitations of the experimental validation, limited to comparison with a baseline GARCH model. However, the authors provided more comparisons in the revision, which adds to the quality of the results, although the models compared against cannot be considered state of the art. It would be well advised to look into R packages such as `stochvol’ and ‘fGarch’ to get implementations of a variety of models that can serve as useful baselines, and provide convincing evidence that the modelled volatility is indeed substantially better than approaches currently entertained by the finance literature. 4) In Section 5.2, more details should be given on the network, e.g. number of hidden units, as well as the embedding dimension D_E (section 5.4) 5) In Section 5.3, more details should be given on the data generating process for the synthetic data experiments. 6) Some results in the appendix are very puzzling: around jumps in the price series, which are places where the volatility should spike, the model reacts instead by huge drops in the volatility (Figure 4(b) and (c), respectively around time steps 1300 and 1600). This should be explained and discussed. All in all, I think that the paper provides a nice contribution to the art of volatility modelling. In spite of some flaws, it provides a starting point for the broader impact of neural time series processing in the financial community.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A Neural Stochastic Volatility Model
In this paper, we show that the recent integration of statistical models with recurrent neural networks provides a new way of formulating volatility models that have been popular in time series analysis and prediction. The model comprises a pair of complementary stochastic recurrent neural networks: the generative network models the joint distribution of the stochastic volatility process; the inference network approximates the conditional distribution of the latent variables given the observable ones. Our focus in this paper is on the formulation of temporal dynamics of volatility over time under a stochastic recurrent neural network framework. Our derivations show that some popular volatility models are a special case of our proposed neural stochastic volatility model. Experiments demonstrate that the proposed model generates a smoother volatility estimation, and largely outperforms a widely used GARCH model on several metrics about the fitness of the volatility modelling and the accuracy of the prediction.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The authors propose a recurrent variational neural network approach to modelling volatility in financial time series. This model consists of an application of Chung et al.’s (2015) VRNN model to volatility forecasting, wherein a Variational Autoencoder (VAE) structure is repeated at each time step of the series. The paper is well written and easy to follow (although this reviewer suggests applying a spelling checking, since the paper contains a number of harmless typos). The paper’s main technical contribution is to stack two levels of recurrence, one for the latent process and one for the observables. This appears to be a novel, if minor contribution. The larger contribution is methodological, in areas of time series modelling that are both of great practical importance and have hitherto been dominated by rigid functional forms. The demonstration of the applicability and usefulness of general-purpose non-linear models for volatility forecasting would be extremely impactful. I have a few comments and reservations with the paper: 1) Although not mentioned explicitly, the authors’ framework are couched in terms of carrying out one-timestep-ahead forecasts of volatility. However, many applications of volatility models, for instance for derivative pricing, require longer-horizon forecasts. It would be interesting to discuss how this model could be extended to forecast at longer horizons. 2) In Section 4.4, there’s a mention that a GARCH(1,1) is conditionally deterministic. This is true only when forecasting 1 time-step in the future. At longer horizons, the GARCH(1,1) volatility forecast is not deterministic. 3) I was initially unhappy with the limitations of the experimental validation, limited to comparison with a baseline GARCH model. However, the authors provided more comparisons in the revision, which adds to the quality of the results, although the models compared against cannot be considered state of the art. It would be well advised to look into R packages such as `stochvol’ and ‘fGarch’ to get implementations of a variety of models that can serve as useful baselines, and provide convincing evidence that the modelled volatility is indeed substantially better than approaches currently entertained by the finance literature. 4) In Section 5.2, more details should be given on the network, e.g. number of hidden units, as well as the embedding dimension D_E (section 5.4) 5) In Section 5.3, more details should be given on the data generating process for the synthetic data experiments. 6) Some results in the appendix are very puzzling: around jumps in the price series, which are places where the volatility should spike, the model reacts instead by huge drops in the volatility (Figure 4(b) and (c), respectively around time steps 1300 and 1600). This should be explained and discussed. All in all, I think that the paper provides a nice contribution to the art of volatility modelling. In spite of some flaws, it provides a starting point for the broader impact of neural time series processing in the financial community.
assistant
The authors propose a recurrent variational neural network approach to modelling volatility in financial time series. This model consists of an application of Chung et al.’s (2015) VRNN model to volatility forecasting, wherein a Variational Autoencoder (VAE) structure is repeated at each time step of the series. The paper is well written and easy to follow (although this reviewer suggests applying a spelling checking, since the paper contains a number of harmless typos). The paper’s main technical contribution is to stack two levels of recurrence, one for the latent process and one for the observables. This appears to be a novel, if minor contribution. The larger contribution is methodological, in areas of time series modelling that are both of great practical importance and have hitherto been dominated by rigid functional forms. The demonstration of the applicability and usefulness of general-purpose non-linear models for volatility forecasting would be extremely impactful. I have a few comments and reservations with the paper: 1) Although not mentioned explicitly, the authors’ framework are couched in terms of carrying out one-timestep-ahead forecasts of volatility. However, many applications of volatility models, for instance for derivative pricing, require longer-horizon forecasts. It would be interesting to discuss how this model could be extended to forecast at longer horizons. 2) In Section 4.4, there’s a mention that a GARCH(1,1) is conditionally deterministic. This is true only when forecasting 1 time-step in the future. At longer horizons, the GARCH(1,1) volatility forecast is not deterministic. 3) I was initially unhappy with the limitations of the experimental validation, limited to comparison with a baseline GARCH model. However, the authors provided more comparisons in the revision, which adds to the quality of the results, although the models compared against cannot be considered state of the art. It would be well advised to look into R packages such as `stochvol’ and ‘fGarch’ to get implementations of a variety of models that can serve as useful baselines, and provide convincing evidence that the modelled volatility is indeed substantially better than approaches currently entertained by the finance literature. 4) In Section 5.2, more details should be given on the network, e.g. number of hidden units, as well as the embedding dimension D_E (section 5.4) 5) In Section 5.3, more details should be given on the data generating process for the synthetic data experiments. 6) Some results in the appendix are very puzzling: around jumps in the price series, which are places where the volatility should spike, the model reacts instead by huge drops in the volatility (Figure 4(b) and (c), respectively around time steps 1300 and 1600). This should be explained and discussed. All in all, I think that the paper provides a nice contribution to the art of volatility modelling. In spite of some flaws, it provides a starting point for the broader impact of neural time series processing in the financial community.