Exercise 17.1 in the ASM manual asks:
The time-t price of a stock is S(t). You are given that S(0)=40 and
dS(t)/S(t) = .10dt + .40dZ(t)
Calculate Cov(S(2),S(4)).
In the solution, they use the formula:
Cov(X(t),X(u)) = E(X(t)X(u)) - E(X(t))*E(X(u)) where u>t
So first they solve for E(S(2)) and E(S(4)).
They say
E(S(2)) = 40*e^(2*.1))
What formula are they using? Is it E(S(t)) = S(0) *e^(mt) ?
Where S(0) = 40, m = .1, t=2?
Why do they not use
(E(X(t)) = X(0)* e^ (mt+.5tσ^2)) ?
The time-t price of a stock is S(t). You are given that S(0)=40 and
dS(t)/S(t) = .10dt + .40dZ(t)
Calculate Cov(S(2),S(4)).
In the solution, they use the formula:
Cov(X(t),X(u)) = E(X(t)X(u)) - E(X(t))*E(X(u)) where u>t
So first they solve for E(S(2)) and E(S(4)).
They say
E(S(2)) = 40*e^(2*.1))
What formula are they using? Is it E(S(t)) = S(0) *e^(mt) ?
Where S(0) = 40, m = .1, t=2?
Why do they not use
(E(X(t)) = X(0)* e^ (mt+.5tσ^2)) ?
Ito's Process - Differentials
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