The Vasicek interest rate model is given by dRt= (α − βRt)dt + σdWt where α, β, and σ are positive constants. This exercise shows how to derive this solution. (i) Use the Ito formula to derive d(eβtRt); (ii) Integrate the equation you obtained in (i) and solve for Rt

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The Vasicek interest rate model is given by

dRt= (α − βRt)dt + σdWt

where α, β, and σ are positive constants. This exercise shows how to derive this solution.

(i) Use the Ito formula to derive d(eβtRt);

(ii) Integrate the equation you obtained in (i) and solve for Rt

Text Book: Stochastic Calculus for Finance, Shreve vol. II

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