[Verse 1] Market prices whisper secrets hidden deep inside Black-Scholes equation needs one puzzle piece to find We know the strike, the underlying, time until expiration But volatility stays masked, requiring calculation [Pre-Chorus] Flip the formula backwards now Extract what markets truly vow [Chorus] Implied vol tells the story, what the traders really think Smile curves and skew patterns, volatility's missing link ATM is cheapest, wings get expensive fast Implied vol's the crystal ball that makes predictions last [Verse 2] Out-of-money puts trade rich when fear grips every floor Crash protection costs a premium, volatility soars Call side shows a gentler slope, the smile's asymmetric dance Skew reveals the market's mood, not left purely up to chance [Pre-Chorus] Time decay shifts the surface Calendar spreads serve their purpose [Chorus] Implied vol tells the story, what the traders really think Smile curves and skew patterns, volatility's missing link ATM is cheapest, wings get expensive fast Implied vol's the crystal ball that makes predictions last [Bridge] Term structure slopes and twists through months ahead Short dates spike explosive, long dates smooth instead Sticky strike or sticky delta, models try to capture How the smile evolves and morphs as markets shift and fracture [Verse 3] Vega risk lurks in portfolios when volatility swings Hedging gamma costs you dearly, that's what trading brings Convert those option prices, see what vol's implied within Surface interpolation helps fill gaps where data's thin [Chorus] Implied vol tells the story, what the traders really think Smile curves and skew patterns, volatility's missing link ATM is cheapest, wings get expensive fast Implied vol's the crystal ball that makes predictions last [Outro] From market price to vol surface Every strike serves its purpose Smile and skew reveal the fear Implied volatility makes it clear
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