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I read a book where it was written :

1/ "implied volatility is the market's consensus on the volatility of the asset between now and the maturity of the option". -> Could someone explain me this sentence ? How can we arrive at this conclusion ?

2/ "if an asset drops in price, this is generally accompanied by an increase in it's volatility" -> Is this a fact of the market, an observed property ?

3/ and further : "this is reflected in the IV of the OTM puts being higher than the OTM calls because puts pay on the downside" enter image description here This sentence is for me weird. If someone could explain me ?

Tx a lot !

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    $\begingroup$ I think you need to quote a little bit more of "Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading". The fragments you've quoted are insufficient out of context. The book actually goes on to explain the statements you are asking about. $\endgroup$
    – user59
    Commented May 5, 2016 at 14:40
  • $\begingroup$ I've just read the entire paragraph the book you're referring. I understand the sentences that I didn't copy-past here. Besides your remark doesn't answer my precise questions. Cheers $\endgroup$
    – glork
    Commented May 5, 2016 at 15:09
  • $\begingroup$ Yes, that's why it was a comment, not an answer. I'm saying that other people who answer should have the opportunity to see what the book says and how the book explains these phenomena. $\endgroup$
    – user59
    Commented May 5, 2016 at 15:10
  • $\begingroup$ The sentences I didn't copy past are not explanations of the ones above. Would you want that I copy past the whole book ? Please if you don't have the answer, don't comment. Many thanks :) $\endgroup$
    – glork
    Commented May 5, 2016 at 15:13
  • $\begingroup$ #2 is an observed property of the stock market, which became quite apparent after the Stock Market Crash of 1987, although it was already recognizable in the Mid 1970s recession. Since then it has been pretty consistently true (ex. 2007-2008): Stoc market down, volatility up. $\endgroup$
    – nbbo2
    Commented May 5, 2016 at 15:57

3 Answers 3

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  1. You can show that "the implied variance of an ATM short maturity option is equal to the expectation under the risk neutral measure of the integrated variance over the life of the option." As you move away from the assumptions: ie not ATM, longer maturity, risk neutral measure far from true, then the forecasting power diminishes. (Google 'stochastic volatility ghysels harvey renault')

  2. It holds for stock indices as an empirical observation. Not any asset. There are models that capture it through dynamics, eg negative correlation between spot shocks and vol shocks (leverage effect).

  3. Put option are an insurance against bad states of the world (ie stock market crashes). Therefore market participants are willing to pay a bit more for them (buyers) or are more reluctant to write them (sellers). The outcome is a higher option price, which is reflected by a higher IV.

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  • $\begingroup$ +1. I would add that implied volatility could be interpreted as a "market expectation of future realised volatility" in the following sense. (1) there is a 1 to 1 relationship between price and volatility under BS assumptions (2) the market price is an equilibrium price (supply/demand) i.e. a consensus between the prices at which parties are willing to buy/sell the instrument. Hence the implied volatility corresponding to an equilibrium price could be interpreted as an average of different market participants' views on future realised volatility under BS assumptions. $\endgroup$
    – Quantuple
    Commented May 10, 2016 at 7:47
  • $\begingroup$ This should not be misinterpreted though (as it would give one view of future volatility per option, which shows why BS assumptions are wrong), the true market expectation of future realised variance (under less restrictive, pure diffusion, assumptions) is given by the price of a variance swap (strike weighted OTM options) $\endgroup$
    – Quantuple
    Commented May 10, 2016 at 7:50
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    $\begingroup$ Many thanks for your explanations too @Quantuple it was very clear ! $\endgroup$
    – glork
    Commented May 10, 2016 at 8:38
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1 is wrong. The implied vol is a convenient way to look at the option price, nothing more.

2 is an observed fact for equities in general but not the case for some other assets eg commodity futures.

3 is also an observed fact for equities generally (but not for single stocks with short time to expiry).

If 1 and 2 were true, then 3 would naturally follow. If we use a local volatility model (where instantaneous vol is a function of the stock price) then the shape of the local vol (from statement 2) would determine the shape of the implied vol (statement 3).

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Implied Volatility means the option is overpriced versus the model price. It means I'm paying more to buy an option than normally. For example, when a gap happens on the stock, the option price is high. It has no bearing on what will happen, but more on what did. The Bid and Ask price are set by people with expectations. And those prices are out of line with "normal" due to some recent move and expectation. I teach Day Trading and have built software for this. It's not a prediction. It's a mistake (distraction) to treat it as a prediction. This is what traders want (Ask). As a writer of contracts, it would be risk and possible reward. Still gets back to using something else as confirmation of a trend. The night before Earnings announcements there are often big price increases for the 2 weeks leading up to that day. These are expectations again and reflect risk to the writer. However, in my research, 9 out of 10 options are NOT worth while to buy the high imp vol options. The 1 that works doesn't pay for the 9 that failed. Being a seller is statistically better, but if one that goes off is like recent GOOG or AMZN, selling a naked option is very expensive.

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