Consider the HullWhite model where the short rate process follows where Z t is a Brownian process under the risk neutral measure Q Using the relation show that Accordingly, the mean and variance of t T r(u) du are found to be Compute the bond price B(r, t T) dr (t) art dt o dZt, ...

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Consider the HullWhite model where the short rate process follows where Z t is a Brownian process

Question:

Consider the Hull–White model where the short rate process follows

dr = [(t) art] dt + o dZt, -

where Z_t is a Brownian process under the risk neutral measure Q. Using the relation

d[r(t)eat] = $(t)eat dt + oeat dz(t), show that

S.T 1- e-(T-t) r(u) du = r(t). n J_J+ 1 = r(t). JJ - e-(T-1) + oe-a(u-s) dz(s) du (u)e-a(u-s) ds du T [ (u).

Accordingly, the mean and variance of ∫_t^T r(u) du are found to be

1 (1) - e-a(T-1) T T var (f

Compute the bond price B(r, t; T).

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Related Book For answer-question

Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 05, 2023 12:56 AM

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Consider the HullWhite model where the short rate process follows where Z t is a Brownian process

Question:

dr = [(t) art] dt + o dZt, -

Step by Step Answer:

Mathematical Models Of Financial Derivative

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