Interest Rate Models

Interest Rate Models#

When you price an equity option, you model one thing: the stock price. Interest rates refuse to cooperate. A single yield curve contains dozens of maturities, each moving with its own dynamics, and any model you write down has to keep all of them internally consistent. That's the central problem of fixed income, and it's harder than it sounds.

Short-rate models attack this by picking one number, the instantaneous rate $r(t)$, and de...