Replicating an Amortising Swap with Constant-Notional Swaps

Summary

An amortising swap’s declining payment notionals can be decomposed into a stack of constant-notional swaps with different maturities. Each component starts with part of the total notional and remains active through its own maturity; adding their notionals period by period reconstructs the amortisation schedule. The example illustrates this decomposition for a schedule of 1000, 600, 300, and zero.

That replication applies to the underlying swap cashflows, but it does not make an option on the amortising swap equivalent to a collection of options on the component swaps. A single European swaption gives one exercise decision over the combined position, whereas separate swaptions can be exercised independently. The split may provide an upper or lower bound, but the document does not specify which bound applies under what conditions or provide a valuation method.

Key ideas

• An amortising swap can be represented as constant-notional swaps of different maturities.
• The component notionals add up to the target amortisation schedule in each period.
• Replicating the underlying swap does not exactly replicate a single swaption.
• Separate options on component swaps allow independent exercise and can only provide bounds in the stated discussion.

Tags

# Turning an amortising swaption into a normal swaption


# Turning an amortising swaption into a normal swaption












Is there a way to enter a trading strategy in which the notional of the cashflows of an amortising swaption become all the same?

For example, imagine the notional for the first four cashflows of an amortising swaption would be 1000, 1000, 500, 300. What can I trade to convert them all into 1000 notional cashflows? I am reading that you can do that by going long and short swaps of different maturities but I am not sure how that would work.

Thanks in advance.

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/40309

Say you had an amortising notional reflecting a receiver swap:

```
1000, 600, 300, 0.
```

This is reflective of 3 constant notional swaps (of different maturities), which can be executed simultaenously and therefore their notionals sum up:

```
1) 400, 0, 0, 0
2) 300 300, 0, 0
3) 300, 300, 300, 0
```

## Answer by James65 (score 1)

https://quant.stackexchange.com/a/40319

For a swap you can replicate amortising swap with a series of constant notional swaps of different maturity as answered. If it is a European swaption into an amortising swap then cannot exactly replicate by splitting up as having one option to exercise on one amortising swap is different from several options that can be exercised independently. It can create and upper or lower bound.

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.