The Meaning of Implied Volatility

The meaning of Implied volatility

·  Under the BSM model, (besides market observables like prices and rates and contract terms like strike and expiry), the value of an option contract is determined by one subjective input, the volatility of the underlying return.

o  Option value increases monotonically with the volatility input. (There is a unique one-to-one mapping between option value and volatility).

o  One can always choose a positive volatility number to match the observed price for a particular option contract, as long as this option price does not allow arbitrage. ---This volatility number is called BSM implied volatility.

·  Nowadays, both academics and practitioners have been using the BSM model to transform option prices into implied volatilities, even though they are fully aware of the deficiencies of the BSM model

o  The implied volatility of each option is just regarded as a different, transformed representation of the option value

o  This transformation has many benefits

§  More stable than price (as it does not vary as much with stock price)

§  More visually informative

§  Excludes some arbitrage

·  If you plot the implied volatility of options against the strike or some standardized moneyness measure at a fixed maturity, it tells you whether/how the underlying return distribution deviates from normal.

o  If all implied vols are at the same level across different strikes à the underlying return is normally distributed with the annualized vol=implied vol.

o  If low strike implied vol is higher than high strike implied vol à The return is negatively skewed (Left tail is fatter than right tail)

o  If both low strike and high strike implied volatilities are higher than at-the-money implied volà Both tails are fatter than normal tail (kurtosis).

o  Over-the-counter currency options are quoted in terms of risk reversals and butterflies. They reflect the skewness and kurtosis of the currency return distribution, respectively.

·  When you use a standardized measure of moneyness (such as d1, d2, or delta), you can compare the implied vol plot at different maturities and learn how the return distribution shape varies at different horizons.

·  If you plot implied volatility over time, you gain insights on how volatility varies over time.