Assess implied volatility as a forecasting tool for future volatility, together with its weaknesses.
The idea
Implied volatility is the volatility that, put into an option pricing model such as Black-Scholes-Merton, reproduces the observed market price of the option. It is forward-looking, because it reflects what traders expect over the option's remaining life, and it adjusts immediately to news, which historical estimators cannot. Its weaknesses are real. It depends on the model, and the pattern of implied volatilities across strikes and maturities, the smile or skew, shows the model's constant volatility assumption fails. It exists only for assets with liquid options and for certain maturities. It usually exceeds subsequently realised volatility on average, partly because it embeds a premium for bearing volatility risk, so it is a biased forecast. Illiquidity, bid-ask spreads and demand for protection also move it. Treat it as a useful, informative but imperfect input, and quote it annualised, converting with 252 trading days.
A practice question
What is the implied volatility of an option?
- The standard deviation of the underlying's returns measured after the option expires.Why not: Describes realised volatility, which is backward-looking and observed only after the fact.
- The historical volatility of the option's own price over the past 30 days.Why not: Confuses the volatility of the option price with the volatility of the underlying that the model needs.
- The volatility input to the pricing model that makes the model price equal the observed market price. - correct
- The EWMA volatility estimate that is inserted into the pricing model to produce a theoretical price.Why not: Describes a model price from a historical estimate; implied volatility works backward from the market price.
The option price is an increasing function of volatility, so the market price can be inverted numerically to find the volatility the market is implicitly using. It reflects expectations over the option's life.
A harder one
An option priced at 4.10 corresponds to an implied volatility of 18%. Its vega is 0.20 price units per one percentage point of volatility. If its market price rises to 4.80 with everything else unchanged, what is the new implied volatility, using a linear approximation?
- 18.7%Why not: Adds the price change (0.70) directly to the volatility instead of dividing by vega.
- 21.1%Why not: Scales volatility in proportion to price, though price is not proportional to volatility in this way.
- 14.5%Why not: Gets the size right but subtracts the move; a price rise means implied volatility rises.
- 21.5% - correct
Change in volatility = price change / vega = 0.70 / 0.20 = 3.5 points, so implied volatility rises from 18% to 21.5%.
The hardest tier
On a 30-day equity index option, implied volatilities are 17% at the money, 21% for puts struck at 90% of spot and 14% for calls struck at 110% of spot. What does this smile or skew imply for a risk manager who wants one volatility to forecast downside risk?
- The at-the-money 17% is the best single forecast, because the other strikes are rarely traded and add noise.Why not: Overlooks that differing implied volatilities by strike violate the model's constant-volatility assumption and carry tail information.
- The higher put volatility shows the market expects the index to rise, since puts are bought by bulls.Why not: Misreads the skew: high put volatility reflects demand for downside protection and a priced left tail, not a bullish view.
- The differences are model noise, so averaging 21%, 17% and 14% gives the unbiased forecast.Why not: A simple average ignores the information in the skew and has no theoretical link to realised volatility.
- The market prices a fatter left tail than constant volatility allows, so the at-the-money figure alone probably understates downside risk and no single implied volatility fits all strikes. - correct
Under Black-Scholes-Merton all strikes would share one implied volatility. The skew, with higher volatility for low strikes, shows the market assigns more probability to large falls than the model, so the at-the-money number can understate tail risk.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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