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. (i) Use the ordinary differential equations (6.5.8) and (6.5.9) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Hull-White model to show that this model satisfies the HJM no-arbitrage condition (10.3.27). (ii) Use the ordinary differential equations (6.5.14) and (6.5.15) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Cox-Ingersoll-Ross model to show that this model satisfies the HJM no-arbitrage condition $(10.3 .27)$.

    . (i) Use the ordinary differential equations (6.5.8) and (6.5.9) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Hull-White model to show that this model satisfies the HJM no-arbitrage condition (10.3.27).
(ii) Use the ordinary differential equations (6.5.14) and (6.5.15) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Cox-Ingersoll-Ross model to show that this model satisfies the HJM no-arbitrage condition $(10.3 .27)$.

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Stochastic Calculus for Finance II : Continuous-Time Models

Stochastic Calculus for Finance II : Continuous-Time Models

Steven E. Shreve 1st Edition

Chapter 10, Problem 10

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### Part (i): One-factor Hull-White Model ** Show more…

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. (i) Use the ordinary differential equations (6.5.8) and (6.5.9) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Hull-White model to show that this model satisfies the HJM no-arbitrage condition (10.3.27). (ii) Use the ordinary differential equations (6.5.14) and (6.5.15) satisfied by the functions $A(t, T)$ and $C(t, T)$ in the one-factor Cox-Ingersoll-Ross model to show that this model satisfies the HJM no-arbitrage condition $(10.3 .27)$.

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