[Verse 1] There's a model that changed how we price options Black Scholes Merton made the complex clear Five key inputs that drive every calculation Let me break it down for you to hear Stock price today is our starting point Strike price set when the contract's made Risk-free rate from treasury bonds Time to expiry can't be delayed [Chorus] S for Stock price, X for Strike R is the Risk-free rate we like T for Time until it ends Sigma's volatility, our five best friends European options, exercise at expiration No dividends paid, constant variation BSM assumptions keep it clean and tight Pricing options with mathematical sight [Verse 2] Volatility sigma shows how much stocks swing Measured as standard deviation per year Higher the sigma, higher the premium More uncertainty brings more fear Constant risk-free rate we must assume No transaction costs or taxes too Markets are liquid, trading's smooth Perfect world that helps us get through [Chorus] S for Stock price, X for Strike R is the Risk-free rate we like T for Time until it ends Sigma's volatility, our five best friends European options, exercise at expiration No dividends paid, constant variation BSM assumptions keep it clean and tight Pricing options with mathematical sight [Bridge] Call option values rise when stock price climbs Put option values fall in bullish times Delta measures sensitivity to stock moves Gamma shows how delta's curve improves Time decay theta works against you Vega captures volatility's view [Verse 3] Normal distribution drives the stock returns Continuous compounding year round Current stock price times N of d-one Minus present value strike when expiry's found For puts we flip the normal probabilities Same five inputs, different dance European style means wait until the end No early exercise, no second chance [Chorus] S for Stock price, X for Strike R is the Risk-free rate we like T for Time until it ends Sigma's volatility, our five best friends European options, exercise at expiration No dividends paid, constant variation BSM assumptions keep it clean and tight Pricing options with mathematical sight [Outro] Black Scholes Merton, Nobel Prize winning Foundation for derivatives trading Five simple inputs, complex solution Financial markets' greatest equation
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