Bermudan Swaption Exercise Conditions and the Absence of Put–Call Parity
Summary
The document asks whether Bermudan swaptions have a put–call parity relationship, how to think about optimal exercise, and whether one side’s decision to exercise determines the other side’s choice. It also considers a callable payer swap with opposing Bermudan options. The response says there is no put–call parity for Bermudan swaptions, because the exercise decisions occur over multiple dates and depend on the rate state.
It gives a necessary, but not sufficient, exercise condition for a receiver swaption: for exercise into a swap with ten years remaining, the relevant spot swap rates across the remaining maturities must all be below the contract fixed rate. This condition is attributed to a quantitative finance textbook. It does not provide a full optimal exercise rule, a proof, or a complete analysis of the callable swap example, so the condition should not be treated as a standalone pricing or exercise algorithm.
Key ideas
- Bermudan swaptions do not have a general put–call parity relationship.
- Exercise decisions depend on the rates and remaining swap cash flows at each exercise date.
- For a receiver Bermudan, a necessary exercise condition is that relevant spot swap rates remain below the fixed rate.
- The stated rate condition is necessary but not sufficient to establish optimal exercise.
Tags
Full text
# Bermudan Swaption # Bermudan Swaption Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I would say it is when the swaption worths less than the underlying swap. When such condition arises ? Can we assume that if it is not optimal to exercise the payer swaption then the receiver swaption exercise is optimal. (Intuitively if such preposition is true than the call put parity exists) ‐-----‐--- ### EDIT An other question, let say I have a callable payer swap by both counterpaties. Hence I am long a payer swap + receiver bermuda and short a payer bermuda to my cpty. Is the fact that if one cpty exercises the call, the option of the other will definitly expire worthless, allows me to say that there is call-put parity in this case and I am in a position of a payer swap and forward receiver ? In a nutshul I have all in all a short maturity swap with maturity equals the first exercise date ? Or there is still a world state where it is not optimal to exercise for both cpties ? ## Answer by dm63 (score 3) https://quant.stackexchange.com/a/45049 There is no put call parity for Bermudan swaptions. There are some necessary (but not sufficient ) conditions for exercise of a Bermudan swaption. For example , consider a Bermudan receiver option exerciseable every year into a swap with remaining maturity of 10 years. Then for optimal exercise it is necessary that the spot starting swap rate with maturity i, for all i = 1,2,3,...10 is less than the fixed rate on the swap. For a proof and further details , consult Blyth “An Introduction to Quantitative Finance” , chapter on Bermudan swaptions.
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.