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Choosing Historical Risk-Free Rates for Option Valuation

Article Quant Q&A · Author: QMath
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Summary

The document raises the problem of selecting a risk-free rate when valuing historical option data. It notes that rates such as Treasury or constant-maturity yields, OIS, SOFR, LIBOR, and policy rates have all been suggested, and asks which benchmark fits different historical periods.

The central concern is consistency with the conventions and information available at the time. Using a benchmark adopted later may introduce look-ahead bias, while a rate that does not match market practice or the valuation framework may distort discounting. The author asks when transitions around the financial crisis and LIBOR’s decline should be dated, including when to switch to alternatives such as SOFR or OIS. No answer, timeline, rate series, or empirical comparison is supplied, so the document identifies a research question rather than prescribing a benchmark-selection method.

Key ideas

  • Historical option valuation requires choosing a rate benchmark for discounting.
  • Candidate benchmarks mentioned include Treasury yields, OIS, SOFR, LIBOR, and policy rates.
  • Using a later-adopted benchmark for earlier data may create look-ahead bias.
  • The document asks for transition dates but does not provide a timeline or recommendation.

Tags

OptionsDerivatives pricingFixed incomeBacktesting
Full text
# What to use as the risk-free rate when working with historical data?


# What to use as the risk-free rate when working with historical data?












When analyzing option data, the concept of a risk-free rate is at the basis of risk-neutral valuation/discounting and when working with historical option data, I assume this is not much different. However, I am struggling with coming to a consensus on what to use as the risk-free rate for various periods in history when we are trying to analyze options data from these periods.

On this site, I have seen recommendations to use Treasury yields/CMT yields, to not use Treasury yields/CMT yields, to use OIS, to use SOFR, to use LIBOR (at least before the LIBOR transition), etc. so I am a somewhat divided on which to use currently and, even more so, which to use for specific date ranges in the past e.g. when to start/stop using LIBOR, SOFR, OIS, etc. so as to be accurate and avoid look-ahead bias.

As an example, say I am looking at financial data such as option prices from before the LIBOR scandal. If while valuing these options, I used a measure such as fed rates or OIS as the risk-free rate to avoid this while LIBOR was the standard, would I not be including a form of look-ahead bias? Also, when exactly would I want to start/stop using LIBOR and use a different measure as the risk-free rate?

I have been made aware of this question that is quite similar to mine. I definitely see how this addresses not using treasury rates/why this isn't a good idea and what we should use instead, but I believe that mine is different as I am asking what risk-free rates are used over what ranges of history/what those ranges would be (what rate do we use before/after the global financial crisis, the LIBOR scandal, etc.? and on what specific dates do we define those changes as taking place (when do we stop using LIBOR and start using SOFR/OIS/fed rates?).

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.