Wedge Trades: Rate Correlation and Residual Forward Volatility
Summary
The document explains a rate-options structure called a wedge: a long at-the-money cap or floor straddle paired with a short at-the-money swaption straddle. It describes the trade as having exposure to both correlation among short-term forward rates and volatility remaining after the swaption expires. The name is linked to the triangular shape of its exposure when forward volatility is plotted against calendar time.
The discussion distinguishes the instruments’ sensitivities. A cap or floor is a basket of caplets or floorlets and is presented as insensitive to correlation, while a swaption’s payoff depends on a basket of forward rates and therefore responds to their correlation. In an HJM framework, the correlation exposure is attributed to the swaption, while the net volatility exposure reflects the difference between the cap or floor’s and swaption’s vegas. The description is qualitative: it gives no pricing formula, market data, or risk measures for a particular trade, and the named structure is described as trading terminology rather than a standard literature term.
Key ideas
- A wedge pairs a long at-the-money cap or floor straddle with a short at-the-money swaption straddle.
- The swaption is sensitive to correlation among the forward rates in its underlying basket.
- Caps and floors are described as insensitive to correlation because they comprise individual options on short-term rates.
- The structure can be short short-rate correlation and long residual forward volatility.
- Its net volatility exposure depends on the relative vegas of the two legs.
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Full text
# How to understand wedge?
# How to understand wedge?
It is heard that trading wedges (cap/floor straddle - swaption) is actually trading the correlation btw forward rates. How to understand this? Either swaption or cap/floor seem to be insensitive to the correlation and that's one reason it is often suggested to calibrate correlation structure of LMM/HJM to CMS spread options. Pls let me know if I missed sth.
## Answer by dm63 (score 5, accepted)
https://quant.stackexchange.com/a/73907
A ‘wedge’ as understood by interest rate options traders is a structure of the form : long a cap/floor straddle struck ATM for a period of 1 yr starting in N years / short a N year into 1 year swaption straddle also struck ATM. Usually the cap/floor underlying is 3mo Libor but nowadays it can be daily SOFR.
This transaction has two principal exposures (a) it is short the correlation between the short term rates (either quarterly Libor or daily SOFR ) and (b) it is long volatility , specifically the forward vols of the short term rates that remain after swaption has expired.
‘Wedge’ is indeed a term recognized by the trading community. If you draw a diagram of forward vol vs calendar vol , the region of exposure of this trade is represented by a triangle that looks like a ‘wedge’.
To answer the comment of @JUW: yes this is well expressed in HJM framework. In that model, correlations are defined as between pairs of short term rates. Therefore as you say , (a) comes only from the swaption. However (b) is the net exposure (eg cap/floor is long 120 units of Vega/ swaption is short 100 units).
## Answer by siou0107 (score 3)
https://quant.stackexchange.com/a/73904
I have never seen the wedge term in the literature, where do you get it from?
Caps and floors are indeed insensitive to correlation, since they are baskets of options (caplets/floorlets), but this is not the case of swaptions. Indeed, their single payoff at $T_\text{expiry}$ is $$ \left[\sum\limits_{i = 1}{P \left(T_\text{expiry}, T_i\right) \left[F \left(T_\text{expiry}, T_{i - 1}, T_i\right) - K\right]}\right]^+ $$ Because they are options on a basket, they are sensitive to the correlation between the components of the underlying basket, which are the forward rates $F \left(\cdot, T_{i - 1}, T_i\right)$.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.