Discount-Rate Changes and Swaption Compensation
Summary
The document considers the impact of replacing established overnight discount rates with new risk-free rates on uncleared swaptions. It asks whether valuation changes should be compensated, distinguishing temporary changes in a swap’s discounted value from lasting economic effects. The discussion compares physically settled swaptions, which lead to a swap with underlying cash flows, with cash-settled swaptions, whose settlement amount depends on valuation at expiry.
One response describes the physical swaption’s exercise value as dependent on discount factors and forward rates, while the cash-settled payoff uses a defined annuity based on the observed swap rate. Another response argues that discount-rate changes can affect actual cash flows through interest paid on variation margin, including after exercise into a cleared swap. The exchange highlights that settlement mechanics and margin remuneration matter; it does not provide a general quantitative estimate of compensation or resolve every market-specific convention.
Key ideas
- A discount-curve change can alter the measured value of swap and swaption positions.
- Physical settlement leads to a swap whose exercise value depends on discount factors and forward rates.
- Cash settlement uses an amount determined by the swap rate and a corresponding annuity convention.
- Variation-margin interest can transmit discount-rate changes into actual cash flows for cleared positions.
- The economic effect depends on settlement and margin arrangements, so the discussion does not establish one universal compensation rule.
Tags
Full text
# RFR discounting - swaption compensation
# 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?
## Answer by ir7 (score 1)
https://quant.stackexchange.com/a/55733
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.
## Answer by dm63 (score 1)
https://quant.stackexchange.com/a/55734
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.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.