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You are not logged in. #1 20080418 09:14:09
BlackScholes Formula DerivationOn this page 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. And hence As Δt gets small, mathematicians argue the square of ΔB has a quite steady mean Δt with a negligible (higher order) variance 2*Δt^{2}. Hence here comes Ito's lemma dB*dB=dt; dt*dt=o(dt); dB*dt=o(dt) 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 dB^{2}. thus here come the dc where 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 (20080420 03:09:29) X'(yXβ)=0 