# How do you forecast implied volatility

## implied volatility

1. *Concept and background: *Volatility that results when the option premium traded on the market is entered into an option valuation model (e.g. Black-Scholes model) and the corresponding valuation equation is solved according to the volatility parameter; Since this is mostly not possible with the usual option valuation models, certain numerical search algorithms are used for the calculation. In contrast to historical volatility, implied volatility is based on the market expectations of the participants in options trading. The first basic prerequisite for such an implicit valuation concept is the enormous practical relevance of the option valuation models used as the prevailing "industry standard", since it allows the information processing method that characterizes the market to be understood and thus to infer the information input from the market prices. The fact that a single, unknown, critical variable, volatility, can be inferred is ensured by the second basic requirement: that all other influencing variables relevant to the valuation (option, pricing) can be assumed to be known; that is the case according to H.M.

2. *Systematic history of the implied volatility*: The common option valuation models in the spirit of Black / Scholes (Cox / Ross / Rubinstein insofar as analogous) assume constant local volatility (volatility surface), i.e. that the implied volatility is the same for all strike prices and remaining terms. However, this prerequisite is usually not met on the markets, i.e. the measured implied volatilities regularly differ systematically between the various option series; characteristic patterns emerge, so that stylized facts i.S. empirical economic research can be spoken of. The best-known pattern is the so-called volatility smile, according to which the implied volatility of at-the-money options is lower than that of in-the-money options and out-of-the-money options with the same remaining term. If the implied volatilities for a given remaining term continuously decrease or increase with an increasing strike price, we are talking about a volatility skew, more precisely: vertical volatility skew - in contrast to the horizontal volatility skew, which is the continuously decreasing or increasing implied volatility at a given strike price with increasing Term to maturity. The latter connection is embedded in the so-called volatility cone, which describes the conical structure of the historical minima and maxima of the implied volatilities as a function of the remaining term. These phenomena have not only been discussed intensively in science for a long time, but also shape the professional, practical options business.

3. *Model risk and the implied volatility as a market price*: Ultimately do this *systematically* (and not only sporadically / randomly) observable progression patterns of the implied volatility for model errors, more precisely: a model risk due to influencing variables not taken into account in the respective option valuation model, which only accumulate in the implied volatilities because the prices in most markets today are in line with the usual the volatility dimension, i.e. expressed in implicit vola points (volatility unit); These phenomena rarely have anything to do with actual volatility. It can be seen that every implied volatility is primarily a market price, which is based on supply and demand, and only secondarily a debatable method for volatility forecasting. It is precisely these market prices that make it possible to manage the model risk in that the "error in the model" is compensated for by pragmatically adapted model inputs, in this case volatility inputs; In advanced practice, proper smile / skew libraries are kept for this purpose, in which the smile or skew structures are typified according to different markets and market situations. See also skew risk, skew trading.

4. *Implied volatility as an instrument for volatility forecasting*:

a) Basic relationships: If these different implied volatilities are weighted ((theoretically justifiable) regularly only via the different strike prices, not via the different remaining terms (different methods), one obtains the condensed assessment of the future market participants derived from the option prices observable on the market Volatility of the underlying; it is important to make use of this "wisdom of the marketplace". The prognosis quality of the implied versus the historical volatility has been examined in countless articles for decades; However, these often suffer from the fact that the preferred concept is, on the one hand, a crude historical comparative estimate or, on the other hand, a stand-alone estimate - which is only rightly popular in pre-crash times - with the implied volatility of only the vega maximum and so that particularly volatility-sensitive near-the-money or at-the-money options (ATMF; cf. moneyness) are compared. Unbiased empirical studies, on the other hand, show a clear parallel between the implicit and the GARCH volatilities (historical volatility, No. 3).

b) The information content of the implied volatility over time: Overall, there is some evidence that the relative information content of the implied volatility initially increased over time and has recently declined again: the former is likely to be related to the fact that the one described in section 1 is Only had to establish the traffic validity of the models in the spirit of Black / Scholes in the markets. On the one hand, the latter can be achieved in conjunction with the fact that, in the course of time, contrary to the fruitful idea of error compensation according to section 3, a fragmentation of the model applications has taken hold, which increasingly undermines the core idea of implied volatities; on the other hand, there is the risk of a so-called *Informational freeloading* Grown: The more market participants orientate themselves on the implied volatilities and thus rely as free riders on the volatility estimates of the other market participants, the less independent volatility opinions have an impact on the market and the less informative the implied volatility is. More recent empirical studies, even one, point in this direction *trailing* the implied versus the actual volatility: Accordingly, the actual volatility can be used to predict the implied volatility better than the other way round.

c) Recommendation: In principle, historical volatility estimates can be corrected more easily than implicit ones: So you know what you are doing, while in the absence of a convincing one you know*positive* Conversely, the theory of volatility estimation does not know which information has already flowed into the implied volatilities in order to be able to further process it in a targeted manner. In this respect, there is some evidence that the market rarely foresees major changes in volatility, but these have occurred, its assessment is corrected very quickly and slow historical volatility estimates have proven to be superior to the fact that the volatility within the meaning of p. of volatility clustering (historical volatility, section 3) tends to initially remain at the new level. Conversely, in order to avoid overreactions, it is better to reconstruct this yourself using faster historical estimation methods and only in such cases one *Mixed estimate* are used in which there is information about anticipated price-relevant events in the market (cf. historical volatility, section 4). In fact, a simple addition of the implied volatility depending on the (essentially information-driven) trading volume has already been tested positively for predictability; it seems even more consistent to give more weight to implied volatility whenever historical and implied volatility diverge. The statistical problem of overfitness of mixed estimates from highly correlated variables for out-of-the-sample questions must be admitted here; this is one of the reasons why the alternative volatility forecast by using volatility indices is discussed there, section 5.

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