The Sentiment Augmented GARCH‑LSTM Hybrid Model for Value‑at‑Risk Forecasting

Does sentiment predict volatility?

Before building a model, the paper asks whether the signal exists. For every stock in the S&P 500 it takes five years of daily data from Bloomberg: the price, and four sentiment indices, each the share of that day's tweets or news items about the company that Bloomberg's sentiment tool marks as negative or positive. A Granger test then asks whether yesterday's sentiment helps predict today's variance beyond what the variance's own past already explains.

The linear version of the test finds a modest signal: the negative Twitter index predicts next-day variance for 27 percent of the stocks at the 5 percent level, and the other three indices for fewer than one in ten. The nonlinear version, which fits a small neural network instead of a linear equation, finds the same signal in 83 percent of the stocks for negative Twitter and 81 percent for positive Twitter, and in well over a third for the two news indices. The relationship is there, it is mostly nonlinear, and in the nonlinear test the ranking holds at every significance level: negative Twitter, positive Twitter, negative news, positive news. The paper reads this as predictive power, not strict causality.

Switch between the two tests and the three significance levels. The faint lines show the other test.

What Value-at-Risk is, and how a forecast fails

The 2.5 percent Value-at-Risk for tomorrow is the loss that should be exceeded on only one day in forty. The Basel rules make banks backtest their desks' daily VaR at that level, which is why every result in the paper is at 2.5 percent. Under the paper's delta-normal assumption the VaR is simply a multiple of the volatility forecast, so forecasting VaR well means forecasting volatility well.

A day on which the loss is worse than the VaR is a violation. Two tests judge a forecast by its violations. The Kupiec test checks that the share of violations is close to 2.5 percent, and rejects a model that has too many or too few. The Christoffersen duration test checks that violations do not cluster. A joint test combines the two. Separately, loss functions score how large the violations were, and the firm loss also charges for the capital set aside on the other days.

The two views can disagree. A forecast that sits far below the returns is rarely violated, so its loss looks small, but it fails the coverage test and ties up capital. That is the situation the results below turn on.

Simulated returns for illustration; no paper data. Pick a scenario.

The model

The literature's fix for GARCH's shortcomings is a hybrid: fit a GARCH model, then feed its volatility forecasts into an LSTM network that learns the corrections. The paper's model keeps that hybrid and adds the four lagged sentiment indices to the network's inputs, so it can react to news that has not yet shown up in returns. The network is trained to predict realized volatility measured over a 10-day window, and the VaR follows from the formula above.

Four models are compared, all trained the same way for every stock. Plain GARCH(1,1). GARCH with the four sentiment indices added to its variance equation, with lag counts chosen by the Schwarz criterion. The GARCH-LSTM hybrid fed only GARCH forecasts. And the GARCH-LSTM hybrid fed GARCH forecasts and sentiment, which is the proposed model. The paper calls them GARCH, GARCH_X, NN and NN_Sentiment_Index; the two networks differ only in their inputs.

Which model wins depends on what you ask

Every model was fitted to every stock and backtested on the last 357 trading days. The paper compares them pairwise, counting the share of stocks on which one model beats another, under three kinds of criterion: how close the volatility forecast came to the realized volatility, how small the expected loss of the VaR was, and how often the VaR passed the statistical tests.

On volatility accuracy the sentiment model beats every other model on every error metric: the plain hybrid in roughly three quarters of the stocks and the two GARCH models in roughly three fifths. On the backtests it passes the duration and joint tests far more often than any other model. On expected loss the picture reverses and plain GARCH wins every pairing.

Choose a criterion. Read across: the row model against the column model.

The paper's explanation, offered for the three stocks it prints in detail, is that GARCH generally overestimates the VaR over the whole period. A forecast that sits too low is rarely violated, so the loss functions score it well, while the coverage test punishes exactly that: on those three stocks, GARCH fails every test. The claim the paper makes is therefore conditional. Among the models that pass the statistical tests, the sentiment model is the one with the smallest expected loss for most stocks, and it is the most accurate volatility forecaster outright. Adding sentiment buys accuracy and test compliance at the cost of a higher expected loss on some stocks.

A quieter result sits in the same tables. The hybrid without sentiment never beats another model on more than half of the stocks on any error metric and loses every expected-loss pairing to the other three. The paper offers overfitting as a possible explanation: the network only pays off once it is given something the GARCH forecasts do not contain.

Three stocks up close

For three randomly selected stocks with high volatility, Alphabet, IBM and Tesla, the paper prints the forecasts themselves. The line to watch is the sentiment model's: when returns turn turbulent it drops further and sooner than the others, then comes back up in calm periods. GARCH barely moves, a smooth line that neither drops in the turbulent stretches nor lifts in the calm ones; the paper puts its low losses down to a general tendency to overestimate the VaR over the whole period.

Pick a stock. The table under the figure gives the numbers for it.

Read down the table. On the error metrics the sentiment model has the lowest value in seven of the nine cells, ties one with GARCH with sentiment on Alphabet, and loses one to it on Tesla. On the tests, GARCH fails all nine, the other benchmarks pass nothing beyond the coverage test, and GARCH with sentiment fails even that on IBM; the sentiment model is the only one to pass the joint test on all three stocks. On the losses, GARCH is lowest in eight of nine cells; the one exception is the smooth loss on IBM, where the sentiment model is lower.

What to take away

Twitter sentiment about a company carries information about its next-day volatility for most S&P 500 stocks, news sentiment for well over a third, and the relationship is nonlinear, which is why a linear test barely sees it and a neural network does. A GARCH-LSTM hybrid that is given that sentiment is the most accurate volatility forecaster of the four models and the one whose Value-at-Risk passes the duration and joint backtests most often. Plain GARCH has the lowest expected loss because, the paper argues, it generally overestimates the VaR, so the question worth asking is which model has the lowest loss while passing the tests, and there the sentiment model comes first.

Limits the paper states: one set of hyperparameters for every stock, five years of data that do not reach back to a stressed market, a one-day horizon only, and a sentiment feed whose algorithm Bloomberg does not publish.

Cite

@article{leber2026sentiment,
  title   = {The Sentiment Augmented {GARCH-LSTM} Hybrid Model for Value-at-Risk Forecasting},
  author  = {L{\'e}ber, D{\'a}niel and Egyed, Bal{\'a}zs},
  journal = {Computational Economics},
  volume  = {67},
  pages   = {313--353},
  year    = {2026},
  doi     = {10.1007/s10614-025-11042-8}
}