Money Markets and Repo: Short-Term Funding Instruments and Overnight Rates

The risk-free rate appears everywhere in derivatives pricing — it is the discount rate in the no-arbitrage formula $F_0 = S_0 e^{rT}$, the return on the riskless hedge portfolio, and the lower bound on option values. But "the risk-free rate" is not a single observable quantity; it is a benchmark derived from a specific segment of the money market. This note maps the money-market landscape — the short-term instruments where cash is borrowed and lent overnight to several months — and traces the regulatory and market shift that moved the risk-free benchmark from LIBOR to OIS/SOFR.

Understanding this shift matters not just for trivia: the choice of discount rate directly affects every derivative valuation. The move from LIBOR to SOFR changed hundreds of basis points in the valuation of long-dated interest-rate derivatives and triggered a multi-year transition programme across global financial markets.

• identify the main money-market instruments: T-bills, commercial paper, certificates of deposit, and repo;
• explain how a repo works mechanically (the two legs, the collateral, the repo rate);
• define the Federal funds rate, LIBOR, the OIS rate, and the LIBOR-OIS spread;
• explain why LIBOR was replaced as the risk-free benchmark and what replaced it;
• state why the risk-free rate is the appropriate discount rate for derivative pricing.

1. Money-market instruments
2. Repo: the plumbing of financial markets
3. Interest rates: Treasury, Fed funds, LIBOR, OIS
4. The OIS rate and SOFR
5. The risk-free rate in derivatives pricing