Prévoir la volatilité des actions avec la volatilité implicite et GARCH
Résumé
Le document compare les approches prospectives et rétrospectives de l’estimation de la volatilité des actions. Pour un horizon de prévision correspondant à l’échéance d’une option, la volatilité implicite à la monnaie à terme peut servir d’estimation fondée sur le marché. Comme la volatilité implicite peut inclure une prime par rapport à la volatilité réalisée ultérieurement, la réponse suggère d’estimer cette prime à partir de données historiques ou d’appliquer un ajustement approximatif. Le VIX est présenté comme une mesure implicite de la volatilité attendue du S&P 500, tandis que les contrats à terme VIX reflètent ce que le marché pourrait anticiper pour la volatilité à une date future.
Pour les prévisions fondées sur les rendements passés, le document évoque les modèles GARCH, notamment GJR-GARCH et EGARCH, qui peuvent représenter la tendance des chocs négatifs sur les actions à influer davantage sur la volatilité que les chocs positifs. Il cite une étude comparant les méthodes fondées sur la volatilité implicite à d’autres modèles, sans fournir de résultats détaillés sur leurs performances. Le texte souligne qu’il est difficile de prévoir la volatilité et que les estimations peuvent être largement erronées, ce qui risque de créer une confiance injustifiée dans la gestion du risque. Ces approches sont des points de départ, et non des garanties fiables.
Idées clés
- Lorsque vous utilisez la volatilité implicite, faites correspondre l’échéance de l’option à l’horizon de prévision de la volatilité.
- La volatilité implicite peut dépasser la volatilité réalisée en raison d’une prime, qui peut être estimée à partir de données historiques.
- Les contrats à terme VIX reflètent les anticipations concernant la volatilité implicite future, tandis que le VIX mesure la volatilité implicite du S&P 500.
- GJR-GARCH et EGARCH peuvent tenir compte de réactions asymétriques de la volatilité des actions aux chocs positifs et négatifs.
- Considérez les prévisions de volatilité comme des indications incertaines, car les erreurs peuvent compromettre l’évaluation du risque.
Étiquettes
Texte intégral
# How would you forecast volatility without using any programming languages or machine learning or anything of that sort? # How would you forecast volatility without using any programming languages or machine learning or anything of that sort? I am trying to forecast volatility. I am on the tactical asset allocation team. No one on our team knows machine learning or any programming languages. We are fundamental equity research analysts trying to find a way to forecast volatility. We were thinking of maybe using the VIX futures? ## Answer by RWP - Down by the Bay (score 3, accepted) https://quant.stackexchange.com/a/53149 For asset allocation purposes I would use implied volatility on atmf options on the underlying with a maturity close to the term in which you are interested. There will be some premium in there so you can run a regression and find out how much premium on average is in there historically, or you can just divide by 1.1, which is a good approximation for the premium. Example: Say 1mo S&P atmf options trade with implied volatility of 50, then your estimate for 1mo vol is 50/1.1 = 45.5 ## Answer by Alba (score 6) https://quant.stackexchange.com/a/53134 Basically, you have to choose whether to use a forward-looking or a backward-looking method of forecasting volatility. Let's start with the VIX. The VIX is an implied volatility index. Option pricing models require the volatility of the underlying asset as an input. Volatility is not an observed quantity, so the people who are pricing the options have to estimate it. This means that you can plug the market price of the option back into the pricing formula, and solve it backwards for the volatility, which will then roughly correspond to the market's estimate of what the volatility will be during the maturity period of the option. The VIX is an index that tracks this implied volatility, the underlying being the S&P 500 index. It used to be calculated on the S&P 100 index using index options, but nowadays the CBOE has switched the methodology to using the broader S&P 500 and a "variance swap"-based calculation. The interpretation is however basically the same, it measures how large the volatility is expected to be over the next 12 months. This is a forward-looking volatility measure: It incorporates information of what the market believes that the volatility will be in the future. See this whitepaper for more details. VIX futures are futures on implied volatility. This means that their payoff is based on what the market, at some time in the future, will believe that the volatility will be during some maturity period. I am not sure why you would use futures on the VIX rather than just using the VIX itself. The alternative is a backward-looking measure, i.e. forecasting volatility tomorrow based on what it has been during some period in the (recent) past. Then, a good place to start would be GARCH models (Generalized Autoregressive Conditional Heteroskedasticity). This is a (very) broad class of models, but I'd say that for equity, you might want to look into the GJR-GARCH model of Glosten, Jagannathan and Runkle (1993) or the E-GARCH model of Nelson (1991). The volatility of equity tends to be asymmetric, i.e. negative shocks might affect volatility more harshly as compared to positive shocks. The GJR- and EGARCH models take this into account. Becker et. al (2007) compare implied volatility-based models to the performance of other types of volatility models. Many of these are very involved. I want to emphasize that forecasting volatility is a difficult endeavour, and from a risk-management perspective, there are arguments in favour of the view that one should not even attempt it. It can give you a false sense of security. Any volatility forecast should not be interpreted as certain, but rather as an indication that is prone to being terribly wrong.
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