Under the risk neutral measure Q, assume that the bond price B(t,T) is related to the short rate r t by Define the following probability measures Q T and Q T , where Consider a European call option on the T maturity discount bond B(t,T ) maturing at time T,T Let X be the strike price of the bond op...

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Under the risk neutral measure Q, assume that the bond price B(t,T) is related to the short

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Under the risk neutral measure Q, assume that the bond price B(t,T) is related to the short rate r_t by

B(t, T) = ea(t)-b(t)rt t = T-t.

Define the following probability measures Q_T and Q_T∗ , where

dQT dQ dQT* dQ T - ru du e B(t, T) T ru du B(T, T*) B(t, T*) e-Si

Consider a European call option on the T^∗-maturity discount bond B(t,T^∗) maturing at time T,T ∗. Let X be the strike price of the bond option and define

In T = Xa(T* - T) b(T* - T) Conditional on r_t = r, show that the price of the bond option is given by

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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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Under the risk neutral measure Q, assume that the bond price B(t,T) is related to the short

Question:

B(t, T) = e¯a(t)-b(t)rt¸ t = T-t.

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Mathematical Models Of Financial Derivative

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