[Verse 1] Market prices hold a secret deep inside Black-Scholes gives us numbers we can't hide But flip the formula, work it in reverse Find the volatility the market does rehearse When traders buy and sell their option plays They show us what they think the future pays [Chorus] Implied vol, implied vol What the market thinks will be Not the past but crystal ball Forward-looking, can't you see Smile and skew, smile and skew Patterns dancing left and right Higher strikes and lower too Tell us where the fear takes flight [Verse 2] Start with option price that's trading on the floor Plug in strike and spot and time and nothing more Interest rates and dividends complete the set Black-Scholes backwards gives the vol we get This implied volatility we found Shows market sentiment that's underground [Chorus] Implied vol, implied vol What the market thinks will be Not the past but crystal ball Forward-looking, can't you see Smile and skew, smile and skew Patterns dancing left and right Higher strikes and lower too Tell us where the fear takes flight [Bridge] Volatility smile curves up on both ends Out-of-money options where the pattern bends At-the-money lower, that's the smile we see Crash fears and jump risks drive asymmetry Skew means puts cost more than calls today Downside protection traders want to pay [Verse 3] Time to expiration adds another layer Near-term options show what short-term players Think will happen in the weeks ahead While longer terms show different fears instead Term structure maps the vol across the time Each expiry has its own design [Chorus] Implied vol, implied vol What the market thinks will be Not the past but crystal ball Forward-looking, can't you see Smile and skew, smile and skew Patterns dancing left and right Higher strikes and lower too Tell us where the fear takes flight [Outro] From market prices to implied we go Reading trader minds in patterns that they show Volatility surface tells the complete tale Of market expectations without fail
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