In bond markets, bids/offers are often quoted in bps of yield. Example – Seller and buyer each convert 200bps yield into price and always get the same dollar price. It’s like converting between meter and inch, or between Celsius and Fahrenheit.

The conversion between hazard rate and market quotes is less clear.

Similarly, in many option markets, prices are quoted in implied volatility. Seller and buyer each convert 20%/year[1] to price, using Black-Scholes and always get the same dollar price.

Price/vol conversion is similar to price/yield conversion because …… in each case price is a poor parameter for __relative value__ analysis, and investors found a superior apparatus to compare 2 securities — yield for bonds and i-volatility for options. Wikipedia says “Often, the implied volatility of an option is a more useful measure of the option’s relative value than its price.”

Price/vol conversion is similar to price/yield conversion because ….. from (mid-point of quoted) bid/ask prices, you get an implied-vol or implied-yield[3], over the remaining lifetime of the instrument. The vol and yield are both forecasts, verifiable at end of that “lifetime”. I-vol vs Historical-Vol. Implied Yield vs real inflation rate.

Price/vol conversion is similar to price/yield conversion because ….. everything else is held constant in the equation. Specifically,

** underlying price is held constant — Tricky. Even though underlying price changes every minute, investors each try to estimate the volatility of the underlying price over the _next_ month. If UBS assume stability, then UBS may use a 19%/year vol. As underlying price moves, UBS option pricing will move accordingly, but always lower than a hypothetical Citi trader (who assume instability).

When a buyer compares 2 competing quotes for the same option, she sees 2 i-vol estimates[2]. 19% by UBS, and 22% by Citi. As underlying price wiggles by the minute, both quotes move, but Citi quote always higher.

Next day, UBS uses a higher vol of 21.9%. As before, both quotes move along with underlying price, but now the spread between UBS and Citi quotes narrow.

At any underlier spot price, say underlying S = $388, one can convert the UBS quote to a lower implied vol and convert the Citi quote to a higher implied vol. During this conversion, underlying price is held constant.

** time to expiration is held constant — Tricky. This situation exists in price/yield conversion too.

[1] same dimension as yield? P276 [[complete guide]]

[3] Implied-Yield is not a common term but quite accurate.