CALCULUS: EARLY TRANSCENDENTALS (LCPO)
CALCULUS: EARLY TRANSCENDENTALS (LCPO)
3rd Edition
ISBN: 9780134856971
Author: Briggs
Publisher: PEARSON
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Chapter C, Problem 8E

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Complex operations Let z = − 2 + 5i and w = 3 − 4i. Compute the following quantities.

8. | w | 2

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The OU process studied in the previous problem is a common model for interest rates. Another common model is the CIR model, which solves the SDE: dX₁ = (a = X₁) dt + σ √X+dWt, - under the condition Xoxo. We cannot solve this SDE explicitly. = (a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler scheme to simulate a trajectory of the CIR process. On a graph, represent both the trajectory of the OU process and the trajectory of the CIR process for the same Brownian path. (b) Repeat the simulation of the CIR process above M times (M large), for a large value of T, and use the result to estimate the long-term expectation and variance of the CIR process. How do they compare to the ones of the OU process? Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000. 1 (c) If you use larger values than above for the parameters, such as the ones in Problem 1, you may encounter errors when implementing the Euler scheme for CIR. Explain why.

Chapter C Solutions

CALCULUS: EARLY TRANSCENDENTALS (LCPO)

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