Forecasting S&P 500 Volatility with R GARCH Models

Summary

The document describes a plan to forecast daily realized volatility from S&P 500 returns and then evaluate a straddle strategy using historical options data. The author has calculated log returns and rolling volatility and asks how to retain fitted values and forecasts when working with four R packages: Stochvol, rugarch, fGarch, and tseries. The example specifications include stochastic volatility and several GARCH variants, with differing model and return distribution choices.

The material is a request for implementation guidance rather than a completed forecasting study. It gives no fitted results, forecast comparison, strategy backtest, or evidence that any package specification is suitable. It also does not explain how to define realized volatility, align option observations with forecasts, or account for transaction costs and risk. Those steps would be needed before drawing conclusions about predictive performance or straddle profitability.

Key ideas

• The proposed task forecasts volatility from S&P 500 log returns.
• The author wants to collect fitted values and forecasts from four R modeling packages.
• The candidate approaches include stochastic volatility and multiple GARCH specifications.
• A straddle strategy is proposed for evaluation using historical option chains.
• No forecast results or strategy evidence are provided.

Tags

# Fitting a forecasting S&P500 roll volatilities


# Fitting a forecasting S&P500 roll volatilities












I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I have the full option chain time series on the same future underlying).

For the purpose, I am pondering 4 different R libraries. Being new to R, for all of them I would like to have the whole series of fitted values in a list, same for forecast ones.

These are the specs:

- Stochvol::

```
    res <- svsample(op$ret, priormu = c(-10, 1), priorphi = c(20, 1.1), priorsigma = 0.1) 
    pred <- predict(res, 2)
```

- rugarch::

```
spec <- ugarchspec(mean.model = list(armaOrder = c(1, 1)), variance.model = list(model = 'eGARCH', garchOrder = c(2, 1)), distribution = 'nig')
forecast <- ugarchforecast(spec, data = op$ret)
```

- fGarch::

```
fit2=garchFit(~ garch(1,1), data = op$ret, include.mean=FALSE, trace=F)
```

- tseries::

```
fit1=garch(op$ret, order = c(1, 1), control = garch.control(trace = F))
predict(fit1, n.ahead=1, doplot=F)
```

Do you guys can help? Many thanks

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