### IR long time horizon simulation model - Rebonato++ ?

Posted:

**October 6th, 2021, 2:31 pm**Is anybody aware of any IR modelling papers, for long time horizons (~20 years) that builds on the work of Rebonato et al (2005), "Evolving Yield Curves in the Real-World Measures: A Semi-Parametric Approach."? I.e. similar model with some enhancements?

Specifically, the Rebonato model ensures (1) mean reversion of shortest and longest tenors via a standard Ornstein Uhlenbeck process, and (2) smooth curves, via a penalisation function of the 2nd derivative.

But it doesn't enforce other things we see empirically:

- low slope at the long end, i.e.. the 20/30 year yield is rarely much different in level from the 50 year yield

- similar variances and mean of yield level across different simulations, across all the long end tenors. The model tends to produce variances on intermediate tenors that are significantly higher than the final tenor.

The paper uses only 8 or 9 tenors. Modern systems tend to have 20+ tenors for their yield curves. This might be another area where the model needs a 'refresh'.

Specifically, the Rebonato model ensures (1) mean reversion of shortest and longest tenors via a standard Ornstein Uhlenbeck process, and (2) smooth curves, via a penalisation function of the 2nd derivative.

But it doesn't enforce other things we see empirically:

- low slope at the long end, i.e.. the 20/30 year yield is rarely much different in level from the 50 year yield

- similar variances and mean of yield level across different simulations, across all the long end tenors. The model tends to produce variances on intermediate tenors that are significantly higher than the final tenor.

The paper uses only 8 or 9 tenors. Modern systems tend to have 20+ tenors for their yield curves. This might be another area where the model needs a 'refresh'.