Practical Calibration Questions for Multicurve HJM Models

Summary

The document asks how to put a Heath–Jarrow–Morton model into practice after bootstrapping separate risk-free and risky curves. It describes a two-factor Brownian setup with distinct forward-rate processes and asks whether both drift conditions can be applied, and how FRA or other derivative prices might be used to calibrate the model for a fixed six-month tenor.

It does not provide a calibration procedure, instruments, parameterization, or empirical results. Its contribution is to identify practical design questions: how market prices connect to model parameters, and how the multicurve structure affects calibration. The discussion is therefore a starting point for research rather than a worked method. It leaves unspecified the volatility form, calibration objective, data conventions, and treatment of market quotes, so it cannot by itself guide implementation or establish model performance.

Key ideas

• The question concerns calibrating a two-factor HJM model with separate risk-free and risky forward curves.
• It assumes that zero and swap curves have already been bootstrapped.
• It asks whether FRA and other derivative prices can provide calibration targets for a fixed tenor.
• No calibration algorithm, volatility specification, or empirical result is supplied.

Tags

# Calibrate an HJM model in a multicurve setup


# Calibrate an HJM model in a multicurve setup












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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