Deriving the Black-Scholes Pricing Equation

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This video is part of my series on the Black-Scholes model.
Disclaimer: I do not know, why we use the normal pdf - shouldn't we use the lognormal pdf as the random variable is lognormal? If anybody knows, please leave me a comment.
  1. FinanceAndEconomics
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Автор

Hi Could you make video about Monte Carlo option pricing?

michanieznanski
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When you're calculation the Expected value by an integral that is f(x) * x where f(x) is your PDF of Normal Distribution and x is your payoff.
How come that if x = f(Ste^(mu-1/2sigma^2)(T-t) + sigma^2(SQRT(T-t)Y)) with f(x) i.e. the PDF you only look at the Y variable. You completely ignore mu, sigma, T-t, St.

You're basically saying when calculating f(x) i.e. the PDF that x is effectively just Y the normally distributed variable, completely ignore all other variables that come into the ST calculation

Nenormalnika
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we know that the term inside f is lognormally distributed but you haven't specified any assumption on what f is, so I guess something is not right there! I mean how would we know pdf of f without knowing what function f is?

Appreciate your content overall though, it is very helpful. Just here I am not clear!

harbirkaur