Tag: Black-Scholes
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Converting the Black-Scholes Equation to the Diffusion Equation
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in MathematicsThis post discusses three transformations that convert the Black-Scholes Equation to the Diffusion Equation. Black-Scholes Equation: Diffusion Equation: Note: In the images below, tau (τ) is written as l.
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Deriving the Black-Scholes Equation
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in MathematicsConsider a portfolio X that holds stocks and cash, such that where X = portfolio valueq = quantity of stockS = stock priceC = quantity of cashM = price of cash We’ll let this portfolio be self-financing. A self-financing portfolio is one where there is no exogenous infusion or withdrawal of money. Therefore, the purchase…