Topic 1: Bond Mathematics

Compounding, spot & forward rates, yield curves, FRNs, swaps, caplets

EAR vs APR vs Continuous Compounding

Compounding conventions and the continuous limit

Spot vs Forward: Average Speed vs Current Speed

Spot rates as running averages of forward rates

Forward Rate Blender

Long spot rate as a time-weighted average of the short spot and the forward(s) — toggle 2 or 3 periods

Nelson-Siegel Shape Explorer

Term-structure shapes from Nelson-Siegel and Svensson

FRN Single-Coupon Replication

Two zeros plus a one-period reinvestment replicate the floating coupon

Swap = Fixed-rate Bond − Floater

Decomposing an interest rate swap; snap to par

Black vs Bachelier Caplet Pricing

Lognormal vs normal caplet pricing, including negative forwards