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Black-Scholes Formula Derivation
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You can cut equal time intervals and each interval B changes by a normal random variable with 0 mean and time length variance; each B change in a time interval has nothing to do with another B change in a different interval.
As Δt gets small, mathematicians argue the square of ΔB has a quite steady mean Δt with a negligible (higher order) variance 2*Δt2. Hence here comes
Thus, to approach a difference of a function which involves a brownian motion B in it directly or indirectly, you have to use Taylor expansion with order 2 to capture the innegligible dB2.
thus here come the dc
o(dt) is higher order term of dt, negligible the same way we do our normal calculus. And the final formual for dc is:
Last edited by George,Y (2008-04-20 03:09:29)