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I am a mathematician and I'm working on my thesis on Financial Mathematics.

I studied this model HJM in a multicurve setup:

$$ \begin{cases} df(t,T)=a(t,T)dt+\sigma(t,T)dW_t & (\mbox{rik-free})\\ d\bar{f}(t,T)=\bar{a}(t,T)dt+\bar{\sigma}(t,T)dW_t &(\mbox{risk}) \end{cases}$$ where $W_t$ is $d-$dimensional and $\sigma dW_t$ and $\bar{\sigma}dW_T$ are scalar products.

After studied this model theoretically, I want do to somenthing pratical. After bootstrapped the zero curve and the swap curve how i can calibrate it? I can apply both drift conditions. I can suppose that the dimension is $2$. What I can do with FRA prices or any derivative prices that i can take from Bloomberg to calibrate the model? Suppose that the tenor $\Delta$ is fixed. Example 6 months.

Sorry for my bad English,

Thanks

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  • $\begingroup$ HJM is a theoretical framework, hence not used directly in interest rate models, but there are many practical models in the spirit of HJM: LIBOR market model, Swap market model etc, so please google the calibration of these models. Hope this helps! $\endgroup$ – Magic is in the chain Nov 8 '19 at 17:35

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