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Choosing Discount Rates from the Yield Curve

Article Quant Q&A · Author: kamikaze_pilot
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Summary

The document explains how to select an interest rate when converting future cash flows into present values for U.S. securities. Its main guidance is to match each payment date with the corresponding zero-coupon rate from a yield curve, rather than applying one rate uniformly across all maturities. This approach reflects that borrowing costs and investment returns can differ with time to payment.

The choice of curve depends on market convention and the product being valued. The response describes swaps-based rates as a common reference, while noting that Treasury rates may be preferred for especially liquid instruments. It also offers a simpler approximation for an individual trading futures intraday: short-dated Treasury bill rates may be adequate. The discussion does not provide a worked valuation, quantify the error from using a single rate, or prescribe one curve for every asset. It is concise practical guidance, so actual curve selection still depends on the instrument, its collateral and funding arrangements, and the conventions used by the relevant market.

Key ideas

  • Use rates that correspond to the timing of each cash flow when calculating present value.
  • A zero-coupon yield curve provides maturity-specific discount rates.
  • The appropriate curve can vary with product liquidity and market convention.
  • Short-dated Treasury rates may serve as a practical approximation for personal intraday futures trading.
  • The guidance does not establish one universally correct curve for all valuations.

Tags

Fixed incomeDerivatives pricingFuturesStatistics
Full text
# Which interest rate should I use for the discount rate in real-world pricing?


# Which interest rate should I use for the discount rate in real-world pricing?












Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation.

Which real world interest rate would best be used here, assuming that I'm concerned with US securities?

Should I use the Fed Funds rate? Should I use the T-bill/bond rates? If so, which period T-bill/bond rates should I use? Should I use the short-term interest rate or long-term interest rate?

## Answer by Tal Fishman (score 7, accepted)

https://quant.stackexchange.com/a/2664

You should use the full yield curve, discounting cash flows at specific dates using the appropriate zero-coupon interest rate. As to which yield curve, that is often a matter of convention. Generally one uses the LIBOR/swaps curve for all but the most liquid products (in which case you use the treasury curve). The curve is constructed from LIBOR/Eurodollar futures at the short end and swaps at the long end.

## Answer by LazyCat (score 3)

https://quant.stackexchange.com/a/2666

Depends on circumstances - if you just trade futures intraday for yourself, secondary market T-bills (http://www.federalreserve.gov/releases/h15/data.htm#fn3) will be good enough.

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.