The dynamics of the instantaneous forward rate F(t,T ) under the risk neutral measure Q is governed

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The dynamics of the instantaneous forward rate F(t,T ) under the risk neutral measure Q is governed by

m dF(t,T) = - i=1 goB aT m (t,T)g(t,T) dt + i=1 ark B {(t, T) dZ;(t), aT

where (Z₁(t)···Z_m(t))^T is an m-dimensional Brownian process under Q. Let (W₁(t)··· W_m(t))^T be an m-dimensional Brownian process under the T′- forward measure Q_T′ and write

B(t, T) = = B (t, T). aT

Show that the dynamics of F(t,T ) under Q_Tc is given by

m m dF(t, T) = o(t, T) dW; (t) + o(t, T) [of(t, T') o'(t, T)] dt. i=1 i=1

In particular, when T′ = T , we obtain

dF(t,T) = g(t,T) dW;(t). = i=1

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Nov 30, 2023 07:31 AM

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The dynamics of the instantaneous forward rate F(t,T ) under the risk neutral measure Q is governed

Question:

m dF(t,T) = Σ - i=1 goB aT m (t,T)σg(t,T) dt + Σ i=1 ark B {(t, T) dZ;(t), aT

Step by Step Answer:

To derive the dynamics of the instantaneous forward rate FtT under the T forward measure QT well sta...View the full answer

Mathematical Models Of Financial Derivative

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