Maintaining Comparable Equity Option Volatility Through the LIBOR Transition
Summary
The document addresses how to compare equity option implied volatilities across the transition from LIBOR to SOFR discount curves. Its answer points to contractual benchmark fallback conventions: a replacement risk-free rate can be paired with a spread adjustment to create a fallback rate for legacy LIBOR exposures. This gives practitioners a way to preserve a LIBOR-linked reference when the benchmark itself is no longer available, subject to the relevant fallback terms and data.
The response notes that the appropriate discounting convention may already differ from the curve historically used, so a switch in curves does not by itself establish that volatility estimates are comparable or incomparable. Reconstructing historical fallback-based values may require specialized data, and legacy LIBOR-based quotes could persist. The discussion is brief and does not provide a full option-pricing procedure or quantify how curve choice changes implied volatility; consistent comparisons still depend on matched conventions and inputs.
Key ideas
- Benchmark fallback conventions can combine a replacement risk-free rate with a spread adjustment.
- Legacy LIBOR-linked exposures may therefore have a defined reference after LIBOR is discontinued.
- Comparisons across discount curves require consistent valuation conventions and inputs.
- Historical fallback data may be complex or costly to obtain, and some legacy quotes may remain available.
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# Compare equity option volatility under SOFR vs LIBOR # Compare equity option volatility under SOFR vs LIBOR We know that after the big bang from LIBOR to SOFR, LIBOR will eventually disappear. This brings up one question that I do not have a clue to answer: How to evaluate derivative in a consistent manner that is comparable before/after the transition? For example, we are currently using LIBOR zero curve to evaluate equity option's implied volatility. If we switch to SOFR curve with a spread/gap comparing to the LIBOR curve, we would know for sure that our evaluated implied volatility is not comparable to the old LIBOR one. The zero curve spread between LIBOR and SOFR can be evaluated when both of them exist. But when LIBOR is eventually retired, we cannot know the gap anymore. How do we deal with this dilemma? ## Answer by AKdemy (score 1) https://quant.stackexchange.com/a/63628 I do not think there is any problem. Firstly, you also did not use OIS but LIBOR now, although the "appropriate" risk free rate would be OIS. You also did not compare the two. To address the risk that one or more IBORs are discontinued while market participants continue to have exposure to that rate, counterparties are encouraged to agree to contractual fallback provisions that would provide for adjusted versions of the RFRs as replacement rates. These consultations yielded industry consensus, and more information about them can be found in following link. Bloomberg Index Services Limited (BISL) has been selected to calculate and publish adjustments related to fallbacks that ISDA intends to implement for certain interest rate benchmarks in its 2006 ISDA Definitions. These interest rate benchmarks include the LIBORs. In a nutshell, Fallback Rate = Adjusted Reference Rate + Spread Adjustment. So you can replace LIBOR with RFR+ISDA fallback (spread). Just like you still find German Mark, Italian Lira quotes and the like for swaps and bonds from back in the days. You may potentially have to buy this data, as its more complex than fixing the DEM exchange rate to EUR and carry forward. However, as I mentioned before, you also did not compute a OIS vs Libor option vol at the moment. Also, maybe some contributors may publish some "zombie" libor based prices.
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