SOFR, so Good

SOFR is the Secured Overnight Financing Rate. Quants should be overjoyed that there is a highly liquid market instrument that is a proxy for the continously compounded risk-free forward rate, f_t. The reality is that SOFR can spike, as it did in September 2019.

D_t = \exp(-\int_0^t f_s\,ds).

D_t(u) = E_t[D_u]/D_t = \exp(-\int_t^u f_t(s)\,ds).

Term SOFR is an average of backward looking rates, similar to Fed Fund Futures settelment quotes.

S_t(t - h, t) = (1/h)\int_{t - h}^t f_s\,ds

Forward rate at t over [t, t + h].

F_t(t, t + h) = (1/h)(1/D_t(t + h) - 1) \approx (1/h)\int_t^{t + h} f_t(s)\,ds