The time- t price of a stock is S(t). You are given:
(i) The stock’s price follows geometric Brownian motion with expected rate of price appreciation of 0 and σ = 0.2
(ii) S(0) = 40
Calculate Pr(S(5) > 50).
In the solution, ln(S(0)) is not added to the mean. Why is this? I thought ln(S(5)│S(0)) ~ N(lnS(0) + (ξ-.5σ^2 )t, σ^2 t).
In chp. 26, there is an example:
Interest rates follow a Rendleman-Bartter model with a = 0.001 and σ = 0.01. Current rates are 0.04. Calculate the probability that rates will be higher than 0.04 three months from now.
The solution adds ln(r(0)) to the mean.
(i) The stock’s price follows geometric Brownian motion with expected rate of price appreciation of 0 and σ = 0.2
(ii) S(0) = 40
Calculate Pr(S(5) > 50).
In the solution, ln(S(0)) is not added to the mean. Why is this? I thought ln(S(5)│S(0)) ~ N(lnS(0) + (ξ-.5σ^2 )t, σ^2 t).
In chp. 26, there is an example:
Interest rates follow a Rendleman-Bartter model with a = 0.001 and σ = 0.01. Current rates are 0.04. Calculate the probability that rates will be higher than 0.04 three months from now.
The solution adds ln(r(0)) to the mean.
Brownian Motion
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