[Verse 1] Stock price dancing at S today Strike price X waits in the wings Risk-free rate r shows the way Time to expiry T, what it brings Volatility sigma swirls around These five inputs make the magic sound [Chorus] S and X, r and T, sigma too Black-Scholes formula breaking through European options can't exercise early Perfect markets, no dividends clearly Constant rates and volatility BSM shows probability [Verse 2] Geometric Brownian motion flows Stock prices follow random walks Continuous trading never slows While logarithmic returns talk No transaction costs or taxes here Assumptions crystal pure and clear [Chorus] S and X, r and T, sigma too Black-Scholes formula breaking through European options can't exercise early Perfect markets, no dividends clearly Constant rates and volatility BSM shows probability [Bridge] Call option rises when stock climbs high Put option profits when prices die Delta measures price sensitivity Theta tracks time's hostility Higher vol means higher premium Lower strikes boost call momentum [Verse 3] Normal distribution curves the way N of d-one and d-two appear Present value calculations weigh What future payoffs might be near Risk-neutral world we simulate Option values we calculate [Chorus] S and X, r and T, sigma too Black-Scholes formula breaking through European options can't exercise early Perfect markets, no dividends clearly Constant rates and volatility BSM shows probability [Outro] When markets match these conditions tight BSM predictions shine so bright Five inputs tell the pricing story Black-Scholes-Merton's lasting glory
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