Consider the HullWhite model where the short rate is defined by Suppose we define a new variable x(t) where Also, show that the bond price B(t,T ) can be expressed as (Kijima and Nagayama, 1994) dr(t) (t) ar (t) dto dz(t) ...

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Consider the HullWhite model where the short rate is defined by Suppose we define a new variable

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Consider the Hull–White model where the short rate is defined by

Suppose we define a new variable x(t) where

dx (t) = -ax(t) dt + o dZ(t), and let (t) = r(t) = x(t). Show that (t) and (t) are related by - '(t) + ay(t)

Also, show that the bond price B(t,T ) can be expressed as (Kijima and Nagayama, 1994)

B(0, T) B(0, t) 0 + 43 {1-[2-e-a(T-1)]+ (2 - e- - (2 eat)}. In B(t, T) In + - - - [e-a (T-1) e-(Tt) 1][r(t)

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 04, 2023 05:22 AM

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Consider the HullWhite model where the short rate is defined by Suppose we define a new variable

Question:

dr(t) = [(t) - ar (t)] dto dz(t).

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Mathematical Models Of Financial Derivative

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