The Vasicek model for the spot rate r is given by dr₂ = (a - br) dt + cdW₁, ro = z. a,b,c are constants. a. If F(t,rt) = et r, obtain the stochastic differential dF. b. Using the initial condition and suitable integration write a solution for re- c. Using the following information B[*9(s., W.)daw.] ³ [([^'ƒ‚dw.) ª] = ³ [["fª]. E = 0 calculate the variance of r₂. Hint: the variance of a random variable X is V[X] = E[X²] - E² [X].
The Vasicek model for the spot rate r is given by dr₂ = (a - br) dt + cdW₁, ro = z. a,b,c are constants. a. If F(t,rt) = et r, obtain the stochastic differential dF. b. Using the initial condition and suitable integration write a solution for re- c. Using the following information B[*9(s., W.)daw.] ³ [([^'ƒ‚dw.) ª] = ³ [["fª]. E = 0 calculate the variance of r₂. Hint: the variance of a random variable X is V[X] = E[X²] - E² [X].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The Vasicek model for the spot rate rt is given by
dr = (a - br) dt + cdW₁, ro = 2.
a, b, c are constants.
a. If F(t, rt) = etre obtain the stochastic differential dF.
b. Using the initial condition and suitable integration write a solution for re-
c. Using the following information
E
3 [[*9(8,W₂) aw.]
B[(*.dw.)]
E
0
B[ds].
E
calculate the variance of rt. Hint: the variance of a random variable X is
V[X] = E [X²] - E² [X].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F057bee6a-1f2b-4b6f-a49c-30fa16594819%2F9dab64f1-af1b-497e-9c52-f34d786e8a20%2Fly7uz6n_processed.png&w=3840&q=75)
Transcribed Image Text:The Vasicek model for the spot rate rt is given by
dr = (a - br) dt + cdW₁, ro = 2.
a, b, c are constants.
a. If F(t, rt) = etre obtain the stochastic differential dF.
b. Using the initial condition and suitable integration write a solution for re-
c. Using the following information
E
3 [[*9(8,W₂) aw.]
B[(*.dw.)]
E
0
B[ds].
E
calculate the variance of rt. Hint: the variance of a random variable X is
V[X] = E [X²] - E² [X].
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