SOFR Curve Fitting with Meeting-Date Rate Jumps

Summary

The document outlines a proposed approach to constructing the front end of a SOFR forward curve from one-month and three-month SOFR futures. It represents Federal Open Market Committee meeting effects as discrete rate jumps, places curve nodes at meeting dates and futures-period boundaries, and proposes fitting forward rates and jumps to observed futures prices. It also mentions a second-difference penalty on neighboring meeting-date jumps as a regularization choice.

The author asks how convexity adjustments should enter the optimization, how to interpolate between nodes, and whether a cubic spline with IMM-date knots is appropriate. They also question whether smoothing adjacent jumps imposes an undesirable pattern when policy shifts between cuts and hikes. No answers, equations for futures pricing, data, or comparison of interpolation and regularization choices are supplied. The text is useful as a statement of the modeling setup and unresolved design decisions, but it does not validate a particular curve-construction method.

Key ideas

• The proposed front-end curve uses one-month and three-month SOFR futures as market inputs.
• FOMC meeting effects are represented as discrete jumps in rates at meeting dates.
• The fitting setup includes forward-rate nodes at meeting dates and futures-period boundaries.
• A second-difference penalty is considered to regularize the sequence of meeting-date jumps.
• Convexity treatment, interpolation choice, and the penalty’s behavior across policy reversals remain unresolved.

Tags

# Curve construction and convexity adjustment


# Curve construction and convexity adjustment












I am trying to understand better how to build the front end of the curve.

For SOFR to construct the front end of the curve we can use all the 1 Month SOFR Futures and the 3 Month SOFR futures. Also $\theta_i$ are rate jumps at the FOMC meetings.

Then the idea is to write the 1 &3 month sofr futures as a function of forward rates and $\theta_i$. Hence we have different nodes to solve for which are the FOMC dates and the beginning and end of the futures. So for example for the December $1$ month future we'll have a node on the $1$s of December and on the $31$ of December.

Then we solve an optimization problem using the futures as market-prices which will find the jumps on the FOMC dates and the forward curve. Now I have seen people adding regularization on the FOMC jumps, for example adding some penalty term like: $\sum (2\theta_j - \theta_{j-1} - \theta_{j+1})^2$. Now I have a few questions:

- How is the convexity adjustment taken into account in the optimization problem? I didn't find any literature on this

- What's the best way to interpolate between the nodes? Should cubic spline be used? and why? I've seen people using cubic spline with knots equal to the IMM dates.

- Why does something like: $\sum (2\theta_j - \theta_{j-1} - \theta_{j+1})^2$ make any sense? Because this forces rates cut to be increasing or decreasing, but when there is a change of policy (going from cutting rates to hiking rates) this might create a wrong curve.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.