The term volatility denotes the pace and magnitude of swings of an asset’s price/value over a defined period. Typical measure for an asset’s volatility is the standard deviation of its price i.e. the dispersion of the price values from the mean/current at the money forward value (ATMF) over the period being analysed. When you prefix the term ‘implied’ to volatility it denotes the expected/perceived future volatility of an asset’s price as implied by the traded market prices of the options or by taking cues from the recent realized volatility of the asset and adjusting for price sensitive events ahead.
Statistically speaking, implied volatility is an annualised percentage metric that denotes the one standard deviation movement of a stock’s price from its current/at the money levels or values observed within 68.27% confidence intervalfor a specified time frame. The percentage value can be converted to absolute unit value of the price by multiplying it with the current stock price and the square root of the ratio of number of (business) days to expiry to 252 i.e. total business days in a year. For instance, a stock currently valued at $200, with a 3-month implied volatility of 20% can swing either side by 200 x 20% x √63/252 = $20 or within a range of $40 in a span of 3 months. For the sake of simplicity, I have assumed standard 21 business days per month, but for practical accuracy we must account for any public holidays for each month.
Implied volatility (IV) of an asset would generally spike ahead of a market-sensitive macro event like a central bank meeting, inflation/growth sensitive data or in case of stocks, company specific micro events like earnings report, potential merger and acquisition, changing sector laws/regulations etc. IV tends to come off once the event has passed.
In the world of option pricing, volatility of the stock/underlying being optionalised is a key input. Referring to the ‘dispersion from ATMF value’ measure as stated above a stock with a higher IV would have a wider probability distribution for where it might end up over a specific time frame. And vice versa a stock with lower IV would have a narrower distribution of the expiry outcome. Intuitively then, if you see IV for a stock going higher it would imply that out of the money strikes would now have a higher probability of ending up in the money which increases the option premium. The increase in the option’s value comes from the higher probability of gaining money-ness or extrinsic value, but intuitively the impact is like an option gaining (time) value as it’s expiry is pushed out. Conversely, options on stocks with lower implied vol would be cheaper.Implied volatility is often compared with realized/historical volatility to assess the relative cheapness and richness of an option on an underlying within a certain timeframe. Intuitively you’d expect higher realized vol to catch up with implied vol overtime but that may not always be the case if future uncertainty is expected to fade in the wake of a light events calendar.
The Black Scholes model assumed constant volatility for an asset for over a defined period i.e. the asset’s price follows a lognormal distribution. In reality however the distribution can take various forms and dealers end up trading different IVs for different strikes for the same option maturity. Plotting the implied vol values across different strikes of an underlying for the same option expiry gives us the Volatility Smile which could be symmetric or skewed depending on the relative demand for call versus puts.Proprietary volatility models of dealers (depending on their assumptions) can throw up different values of implied volatility for the same market price. Black Scholes model acts as the bridge between the quoted dealer vol and market price that counterparties eventually agree to trade. Or understood another way plugging the dealer’s vol into the BS model is a hygiene check that assure alignment of fair value of implied vols across dealer models on the street. This is also why implied vol is commonly referred to as Black Scholes vol.
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