# RFR discounting - swaption compensation

Later this month the discount rate for EUR interest rate instruments changes from Eonia to EuroSTR. In October SOFR replaces EFFR. These changes will affect the value of uncleared swaptions and there has been a lot of discussion of the desirability of compensation arrangements that reverse these gains and losses as will happen for cleared instruments. Both ARRC and the Euro working group have recommended compensation. It seems to me there is a difference between valuation effects that reverse themselves over time and permanent gains and losses. If I for instance suffer a discounting loss on a swap as a result of the change, this amortises back over time since the cash flows are unaffected and the swap has to be zero at expiry. The loss might be unwelcome in accounting terms but I have not suffered a permanent economic loss. As far as I can see, the same applies to a swaption that settles physically. At the expiry of the swaption I will ether exercise or not and, if I exercise, the cash flows on the swap are unaffected by the change in discount rate. But if I cash-settle the cash amount is altered by the change in the discount rate, which is a real economic gain/loss. Do others agree?

• The payoff at option expiry does not depend on any discounting (annuity implied by a curve). By design it only depends on the swap rate itself, which should be observable to allow the cash settlement mechanism. Does this help? – ir7 Jul 9 '20 at 16:54
• Thank you for the observation. I'm not sure I agree, though. Physical settlement does not depend on discounting - the option holder exercises his/her right to pay or receive at the strike or allows the option to lapse. But a cash settlement requires a valuation and therefore depends on the discounting convention. – Patrick Carey Jul 15 '20 at 8:31
• I put up some formulas to explain what I meant. – ir7 Jul 17 '20 at 0:54

Payoff at option expiry $$T$$ for physically-settled swaption is

$$\left(\sum_i \tau_i P(T,T_{i+1})(L(T,T_i,T_{i+1})-K)\right)^+$$

with $$P$$ discount factors and $$L$$ Libor (forward) rate. So, to figure out the exercise value one needs a discount curve which can be estimated differently by different parties (bid/ask, different curve models).

Payoff at option expiry $$T$$ for cash-settled swaption is

$$\alpha(S(T))(S(T)-K)^+$$

with

$$\alpha(x) = \sum_i \frac{\tau_i}{ \prod_j (1+\tau_jx)}$$

so a well-defined payoff (we discount with the swap rate itself), assuming the swap rate is observable.

• Thank you for your reply - you're correct. – Patrick Carey Jul 20 '20 at 12:48
• There is also a convention (at least in the EUR market + the younger past, see ISDA here: isda.org/2018/11/26/…) to cash-settle swaptions with a "true/correct" discounting approach using the prevailing spot curve instead of the flat curve / swap rate method described in this answer. NB: such a cash settlement style would make it equal to the physical settlement, in which case I would say that it does (not) depend on the discounting just in the same fashion as the phyiscally settled option. – KevinT Jan 28 at 14:58

I disagree with you. When a cleared swap changes its discount rate , actual cash flows are affected. This is because the exchange pays interest on the variation margin, which will change from Fed Funds to SOFR in the US. The actual interest paid on the valuation of the position changes. Same thing when a swaption is exercised into a clearable swap.

• You're absolutely right about PAI flows and there is a real gain / loss arising from this effect. But the major part of the valuation change comes from applying a different discount rate to the contractual fixed and projected floating flows. Any gain or loss amortises / accretes back over time, which prompted my original question - does it matter? – Patrick Carey Jul 20 '20 at 12:53
• I would tend to agree wit dm63 here; or could you (OP) specify how exactly you think the gains/losses amortize back over the lifetime of the swap? Via the PAI mechanism? If there is no economic impact, why would there be the need for compensation payments in the first place? – KevinT Jan 28 at 15:02