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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?

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  • $\begingroup$ I would question why you are currently using Libor for this purpose. If the options you are pricing are exchange traded, you should be using a risk free rate. SOFR for example. $\endgroup$
    – dm63
    Nov 28 '20 at 0:27
  • $\begingroup$ It is not up to me to use LIBOR for existing evaluation. Existing database, such as the IvyDB option database, already uses LIBOR for evaluation for the past decay. People will have to deal with the above question when comparing SOFR based calculation with the historical LIBOR based one. I am wondering if there is a way already figured out to deal with this? $\endgroup$
    – user40979
    Nov 28 '20 at 0:56
  • $\begingroup$ Noted. My answer is that since Libor is inappropriate , the new method will probably be better. Maybe you should ask the database provider what they will do $\endgroup$
    – dm63
    Nov 28 '20 at 4:10
  • $\begingroup$ @dm63 If LIBOR is inappropriate SOFR would be as well. If your borrow costs are in LIBOR it's appropriate. $\endgroup$
    – pyCthon
    Nov 28 '20 at 4:47
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    $\begingroup$ I’d like to offer the middle ground: the correct rate is stipulated by collateral/funding. It could thus be: approximated byLIBOR (uncollatetalized); a PAI rate (ESTR, SOFR...); a CSA Rate (Same, probably with spreads); or a repo rate, no? For short term options, though, the effect shouldn’t be too material, no? $\endgroup$ Nov 28 '20 at 7:45
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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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