Finance fiction: LIBOR fallback and FIReD
More than 10 years ago, I proposed a (slightly) exotic product that I called Floored Instrument on Rolled Deposit, abbreviated with the eye catching name of FIReD.
If the ISDA Fallback procedure is decided as announced recently with the adjusted RFR based on compounded overnight setting in arrears, my fictional FIReD will become a very common product. All IBOR cap-floors will be on FIReD.
To explain this statement, I need to step back a little bit.
A first version of the working paper describing the details of the product was published in 2005 ( SSRN: https://ssrn.com/abstract=888484). A related article was published in Journal of Risk (Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options, The Journal of Risk, 9 (4), Summer 2007).
The idea of the product is the following: Money is invested at a given benchmark rate, let say overnight, for a long period with capital plus interest reinvested (compounded) at the end of each benchmark period. Up to now this is similar to a standard cash-account with money left for a long period. But a minimum rate is guaranteed, the return is floored. The floor is not on each of the fixing but on the composition at the end of the product. The original reason to propose such a product was for investments linked to a short rate benchmark (Fed Fund, repo, T-bill, etc.) but for which the investor required a minimal return to pay its expenses.
The current proposal by ISDA for the fallback procedure after the preliminary analysis of the consultation is to use overnight compounding setting in arrears. As I have documented in details in my Quant perspective on fallback and in many blogs (here, here, here, here and here), I believe that this approach is not achievable.
But for the sake of interest in my financial fiction, suppose we ignore the non-good business day issue and look at a single caplet. What is the very important difference between an IBOR caplet and a new RFR based caplet after fallback, beyond the change from one benchmark to another? The striking difference (pun intended) is not the strike (spread adjusted) but the exercise date. The actual rate is know only at the end of the period (in arrears), to the dynamic of the rates need to be measured not to the original exercise date but to the maturity date. The rate is averaged (in a special way, called compounding) over the accrual period. The dynamic of the rates between the start date and the end date is important and this importance changes each day. The change of dynamic of the final rate will depend of the number of day left in the period. The vanilla IBOR cap/floor are becoming path-dependent Asian option using compounding as averaging method on rates.
The vanilla IBOR cap/floor are becoming path-dependent Asian options. They become in some sense similar to the futures on overnight as traded on CME, ICE and CurveGlobal, the the optionality changing through the accrual period. For the futures the resulting convexity adjustment is small because the futures expiries are relatively short term. But for cap/floors, we can have maturities up to 30 years and the optionality is a major feature of the product.
Here is an extract from my 2007 paper in Journal of Risk that describe the pricing of the product in a generic HJM model. For the caplets, the n would be the number of (business) days in the IBOR period, i.e. around 60 for a three-month IBOR.
Obviously the formula can be made more explicit in a Gaussian HJM. It becomes:
It is up to the reader to decide if he wants to qualify this product as an exotic derivative or not.
This could be the new episode of my series on Finance Fiction. The previous episodes are listed below.
Note that in the first episode, I indicated "For obvious marketing reasons, I do not highlight the proposals that failed to materialize, like options on composition or OIS swaption." Which means that my real mocking of my own fiction is becoming obsolete as more fiction is becoming reality.
Previous Finance Fiction episodes
If the ISDA Fallback procedure is decided as announced recently with the adjusted RFR based on compounded overnight setting in arrears, my fictional FIReD will become a very common product. All IBOR cap-floors will be on FIReD.
To explain this statement, I need to step back a little bit.
FIReD
A first version of the working paper describing the details of the product was published in 2005 ( SSRN: https://ssrn.com/abstract=888484). A related article was published in Journal of Risk (Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options, The Journal of Risk, 9 (4), Summer 2007).
The idea of the product is the following: Money is invested at a given benchmark rate, let say overnight, for a long period with capital plus interest reinvested (compounded) at the end of each benchmark period. Up to now this is similar to a standard cash-account with money left for a long period. But a minimum rate is guaranteed, the return is floored. The floor is not on each of the fixing but on the composition at the end of the product. The original reason to propose such a product was for investments linked to a short rate benchmark (Fed Fund, repo, T-bill, etc.) but for which the investor required a minimal return to pay its expenses.
Cap-floor becoming Asian options
The current proposal by ISDA for the fallback procedure after the preliminary analysis of the consultation is to use overnight compounding setting in arrears. As I have documented in details in my Quant perspective on fallback and in many blogs (here, here, here, here and here), I believe that this approach is not achievable.
But for the sake of interest in my financial fiction, suppose we ignore the non-good business day issue and look at a single caplet. What is the very important difference between an IBOR caplet and a new RFR based caplet after fallback, beyond the change from one benchmark to another? The striking difference (pun intended) is not the strike (spread adjusted) but the exercise date. The actual rate is know only at the end of the period (in arrears), to the dynamic of the rates need to be measured not to the original exercise date but to the maturity date. The rate is averaged (in a special way, called compounding) over the accrual period. The dynamic of the rates between the start date and the end date is important and this importance changes each day. The change of dynamic of the final rate will depend of the number of day left in the period. The vanilla IBOR cap/floor are becoming path-dependent Asian option using compounding as averaging method on rates.
Exotics?
The vanilla IBOR cap/floor are becoming path-dependent Asian options. They become in some sense similar to the futures on overnight as traded on CME, ICE and CurveGlobal, the the optionality changing through the accrual period. For the futures the resulting convexity adjustment is small because the futures expiries are relatively short term. But for cap/floors, we can have maturities up to 30 years and the optionality is a major feature of the product.
Here is an extract from my 2007 paper in Journal of Risk that describe the pricing of the product in a generic HJM model. For the caplets, the n would be the number of (business) days in the IBOR period, i.e. around 60 for a three-month IBOR.
Obviously the formula can be made more explicit in a Gaussian HJM. It becomes:
Finance Fiction
This could be the new episode of my series on Finance Fiction. The previous episodes are listed below.
Note that in the first episode, I indicated "For obvious marketing reasons, I do not highlight the proposals that failed to materialize, like options on composition or OIS swaption." Which means that my real mocking of my own fiction is becoming obsolete as more fiction is becoming reality.
Previous Finance Fiction episodes
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