I've noticed that for a given strike price, the shorter expiration dates of options have more pronounced volatilities
why is that?
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.
Sign up to join this communityI've noticed that for a given strike price, the shorter expiration dates of options have more pronounced volatilities
why is that?
You have to remember that implied volatility comes from a "wrong" model to give the right answer. Option prices are determined by supply and demand (subject to a few arbitrage bounds). A higher implied volatility for OTM/ITM options relative to ATM options simply means that the prices of these options are higher than the Black-Scholes model would imply (using constant ATM implied volatility as the volatility of the underlying price diffusion).
The Black-Scholes model makes several strong assumptions, none of which are true. The implied volatility smile is simply an expression of "how wrong" the model is relative to market prices. For short maturities, Black-Scholes option for OTM options are basically zero. The reason is that the stock price is modeled as a (continuous) diffusion and therefore there is only a very small chance that the money will finish in the money. Market participants, on the other hand, may think that the probability is actually much higher because prices do jump and change rapidly within small time frames. Hence, the pronounced shape of the implied volatility smile at short maturities.
To expand on pbr142,
If the implied volatility (vis. Black & Scholes) is persistently higher for short-expiry contracts away from the money, the problem is the model, not the thing that's modeled. The price of a contract at a given point in time is the "correct" price at that point in time (or we should move this to philosophy.stackexchange.com). So how come these contracts aren't described as well by a simple, closed-form (at least in Europe) model? Some possibilities:
Black & Scholes or similar implied volatility can still be a helpful descriptive parameter, particularly on a comparative basis. It is usefully wrong.
What you suggest is mainly true in times of stress. The shorter maturity deals are priced with larger implied volatility to incorporate the short term volatility in the market.