What does implied volatility mean?

accord to BS formula,given a volatility δ,there will be a corresponding option price, so in same way,given a price,there will be an implied volatility,more details is included it John Hull'book,maybe,it's better to learn this notion from book, just my suggestion

The value of options (such as calls and puts) will be higher when the volatility of the underlying security has more volatility. For example, the value of a call on a stock with a strike price of $50, when the stock price never fluctuates much from $40, will be close to $0. Similarly, the higher the value of an option, the higher the "implied volatility" of the underlying security.

While all answers previously entered are correct , I find them a little too roundabout. The Black-Scholes formula calculates the "fair" price of an option given some information as input. Most of the input is known facts - the prIce of the stock, the risk-free rate of return, etc. ONE of the inputs to the formula is a prediction - the volatility (how much the price of the stock WILL change until option expiration). Since it is a prediction, it is really a guess. If you have a different guess, you will get a different result from the formula.   Now it is an observable fact that the actual price of options in the market is not the same as the "fair" price the formula calculates, if you use "historical volatility" as input ( which means you are assuming that the volatility in the future will be the same as it was in the past). So, if you assume the BS formula is correct, and still the market price is different than the result, you can ask : Which value of input to the BS formula would have caused it to produce the market price as the result?  The only input that CAN be changed is the Volatility, so you can work the formula "backward" and figure  out which value of Volatility used as an input will result in the price actually seen in the market --> this is the Implied volatility. To add to the "intuition behind the dependence of volatility and option price" - Assume a call option for 3 months into the future, and assume it is out of the money - the strike price is above the current price. What is the chance this this option will be worth anything at expiration? Case 1: If the stock is very stable, and it price usually does not change,             then there is a low chance the price will rise above the strike price             of the option, and thus, there is a low chance the options will be             worth anything at expiration, and a high chance it will expire             worthless. Case 2: The stock is given to wild jumps in price (up and down). What is             the chance now that at expiration, the price will be higher than            the options's strike price? Higher. Therefore, with a more volatile stock, the chance of options that are now out-of-the-money becoming in-the-money is higher, and this makes them more valuable ==> their price is higher.

Implied volatility is one of the most mis-understood terms in finance. Here's how to understand it for the layperson.One way to view options is to treat them as insurance. People buy life insurance for a payout when they die. You are protecting against an adverse event: death. Similarly, you buy options when you think the market will move drastically up or down. You are protecting against an adverse event: big market moves (volatility).Both insurance contracts and options require payment of premium. Premium is high if the chance of the event is high, and low if the chance is low.For life insurance, premiums are higher for a 60 year old than a 20 year old. For options, premiums are higher for a highly volatile stock (like Tesla) versus a slow moving stock (like Johnson & Johnson) So as you can see, you can communicate the premium of an insurance contract by reasoning about the risk/probability of the adverse event. And similarly, you can communicate the price of an options contract by talking about the stock's (implied) volatility. So basically, when someone tells you an option has implied volatility of 32%, it means that the option seller believes that the stock will move at 32% volatility. To understand what 32% volatility means, simply divide the figure by 16 to get a daily volatility. 32% volatility means that the option seller believes the stock will move 2% (32/16) per day.Btw, you would like to learn how to trade options properly & rigorously, I want to invite you to https://doggy.typeform.com/to/m9gtC4 community. Trading can suck and really costly, especially without a good education. It’s in beta now, but it is designed to teach options trading in a proper, structured manner.

An easy way to understand this may be by using an example of actually pricing options. Here is an example from http://zoonova.com.  This screen image shows the calculation of an AAPL Call and Put option, strike price is 100, expiry is March 18, 2016,  the underlying stock price is 99.94, the risk free rate is 1%, 60 day historical volatility is 28.43%, premium for the call option is 4.90, and premium for the put options is 5.35. Using these premiums as input, the calculated IV for the call options is 32.3649%, and the calculated IV for the put option is 35.9136%. The Fair Value is calculated by using 60 day volatility as input, which is 28.43%. So this example shows how you can calculate IV from option premium, or calculate the premium from IV. By doing What-If analysis on option IV premiums, historical volatility and implied volatility, by simply plugging different values in the option calculator, one can see how premium, and volatility are related. The Option Greeks are also very important to understand if you are creating different option strategies. Here is some explanation on that.The option sensitivites (a.k.a. "Greek") are as follow:Delta (Δ)Δ = ∂V / ∂SDelta is a measure of an option's sensitivity to changes in the price of the underlying asset.Gamma (Γ)Γ = ∂Δ / ∂SGamma is a measure of Delta's (see above) sensitivity to changes in the price of the underlying asset.Vega (ν)ν = ∂V / ∂σVega (a.k.a. "kappa" or "tau") is a measure of an option's sensitivity to changes in the volatility of the underlying asset.Theta (Θ)Θ = ∂V / ∂tTheta is a measure of an option's sensitivity to time decay.Rho (Ρ)Ρ = ∂V / ∂rRho is a measure of an option's sensitivity to changes in the "interest rate". The primary Rho is for "Risk-Free Rate" (a.k.a. "Domestic Rate" – representing the rate at which money is borrowed/loaned); the secondary Rho is for "Convenience Yield" (a.k.a. "Foreign Rate" or "Dividend Yield" – representing the rate of return on investment).Implied Volatility ( IV )Implied Volatility is the estimated volatility of a security's price. In general, implied volatility increases when the market is bearish and decreases when the market is bullish. This is due to the common belief that bearish markets are more risky than bullish markets. NOTE: By default, http://zoonova.com, calculates the "fair value" of options with corresponding sensitivities. However, clicking the checkbox next to the the "Premium" field allows the user to define a custom option value which will, consequently, "imply" a new volatility and corresponding sensitivities.Cheers.

Note that IV has nothing to do with the actual volatility of the underlyer. If it did, then the IV of puts and calls for a given expiration will be the same for every strike. And this is certainly not the case.IV is a way of "normalizing" a quote on an option. Many traders look at IV across a broad range of options, and have their own models of vol, and find out which options are cheap and which are expensive.Many people first looking at black scholes, assume there is some way to measure underlyer volatility, and use that as input. Actually, the input is the realized vol as measured at expiration. Which is in the future. So IV is in a way a statement from market prices what vol will be-- but market price also reflect liquidity,spread, and other things not in the formula.

I would describe Implied Volatility in simple terms - IV is the estimate of a stocks price range over a given period of time stated as a percentage. For example, Tesla is currently trading around $200 (we'll keep it simple for the math) with an Implied Volatility of approx 60%. This means the expected move for the next year is $200 +/- 60%, or $80 - $320.Where it can get tricky is with options, where each contract period will have it's own IV. This obviously makes sense given the example above since Options contracts can range from a few days to a few years so these variances in duration must be accounted for.Also, to think of Options as Insurance is also misleading since IV plays a crucial role in their pricing (along with a few other things, but currently IV is the predominant player) - this means that as IV increases so does the price of options. In other words, if you wanted to buy "insurance" for your positions you would be doing so at a huge premium this week. On the other hand, if you are a seller of Options (or a seller of Premium) now is a great time!Here's some math to add to the conversationExpected Move = stock price x IV/100 x SQ. Root of (DTE/365)DTE = Days to expiration

Implied volatility - The measure of the expected range of stock prices in the future, which are stated in percentage terms.Implied volatility typically is oscillating meaning it will increase or decrease. This increase or decrease will cause the same affect to option pricing because either the market is pricing in a possible big more or not.Overall, it’s the most important aspect to understanding and creating success with trading options.

Implied volatility is probably one of the most important aspects of options trading. Many traders overlook this parameter. As an example, IV is very elevated before major event like earnings. It will crash once earnings are announced. That means that even if the stock price remains stable, the prices of the options will collapse. Many traders buy options before earnings and are surprised why they lose money even while being right on direction. https://steadyoptions.com/articles/post/steadyoptions/understanding-implied-volatility-r132