Exercise 12.7: Let 0 < c < 1, and γ(t) a bounded deterministic function be given. Show that ther

Question

Exercise 12.7: Let $0 < c < 1$, and $\gamma(t)$ a bounded deterministic function be given. Show that there is a process $\beta(s)$ such that $c + (1 - c)\mathcal{E}(\int_0^t \gamma(s)dB(s)) = \mathcal{E}(\int_0^t \beta(s)dB(s))$. Hence deduce the existence of forward rates volatilities $\sigma(t, T)$ in HJM from specification of the forward LIBOR volatilities $\gamma(t, T)$ in BGM.

          Exercise 12.7: Let $0 < c < 1$, and $\gamma(t)$ a bounded deterministic function be given. Show that there is a process $\beta(s)$ such that
$c + (1 - c)\mathcal{E}(\int_0^t \gamma(s)dB(s)) = \mathcal{E}(\int_0^t \beta(s)dB(s))$.
Hence deduce the existence of forward rates volatilities $\sigma(t, T)$ in HJM from specification of the forward LIBOR volatilities $\gamma(t, T)$ in BGM.

Exercise 12.7: Let 0 < c < 1, and γ(t) a bounded deterministic function be given. Show that there is a process β(s) such that
c + (1 - c)ℰ(∫0^t γ(s)dB(s)) = ℰ(∫0^t β(s)dB(s)).
Hence deduce the existence of forward rates volatilities σ(t, T) in HJM from specification of the forward LIBOR volatilities γ(t, T) in BGM.

Added by Jon C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/08/2023

Step 1

Step 1: Start by defining the process s as a function of the forward LIBOR volatilities t and T in the BGM model. Show more…

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Exercise 12.7: Let 0 be given. Show that there is a process s such that c+1-cdB = ef(SaB()) specification of the forward LIBOR volatilities t, T in BGM