Calculating the Maturity Payoff of a Zero-Coupon Inflation Swap
Summary
The discussion shows how to calculate the terminal cash flows of a zero-coupon inflation swap that receives CPI performance and pays a fixed rate. The inflation leg is notional multiplied by the percentage change from the base index to the maturity index. The fixed leg is notional multiplied by the accumulated zero-coupon fixed return over the swap tenor. The net payoff depends on which side of the swap is held and is the received amount less the paid amount.
An example uses a base CPI level of 236, a hypothetical terminal level of 300, and a notional of 100,000 to illustrate the inflation leg. A separate illustrative fixed rate is used to show netting the two legs. The example is only illustrative: the fixed rate must come from the trade terms, and actual contracts may specify index dates, lags, interpolation, day-count rules, or settlement details that affect the payoff.
Key ideas
- The floating leg pays notional times the percentage change in the CPI reference index.
- The zero-coupon fixed leg compounds the agreed rate over the swap tenor.
- The terminal net amount is the cash flow received minus the cash flow paid.
- A numerical payoff requires the contractual fixed rate and the specified index observations.
- Contract conventions such as index lag and settlement rules can affect the realized amount.
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Full text
# Calculate single cashflow at maturity for a Total Return Inflation swap (zero coupon)
# Calculate single cashflow at maturity for a Total Return Inflation swap (zero coupon)
I'm a newbie to the world of swaps.
If I have a Total Return Inflation Swap (Receive CPI, Pay Fixed Zero Coupon)
Based on CPI Index starting level = 236 Notional = 100,000 Term = 5 Years
How can I calculate the final payoff at maturity using a hypothetical future CPI level e.g. 300 ? Are there any excel and/or R examples?
## Answer by Helin (score 3, accepted)
https://quant.stackexchange.com/a/18283
For ZC inflation swaps, the fixed side cash flow is $$ N \big((1 + r)^T - 1\big), $$ where $N$ is the national amount, $r$ is the agreed upon ZC swap rate, and $T$ is the tenor of the swap.
The floating side cash flow is $$ N\left( \frac{I(T)}{I_\text{base}} - 1 \right), $$ where $I_\text{base}$ is the base index level (reference index as of the effective date) and $I(T)$ is the reference index as of the termination date.
## Answer by vega (score 0)
https://quant.stackexchange.com/a/18280
The trick to swap calculations is understanding what your profit is. Profit is (what you receive - what you pay). You can use this to calculate swaps on interest rates, equity swaps, and so on.
What will you receive? You are receiving: CPI appreciation x Notional. (300/236 - 1) * 100,000 = 27,118.
What are you paying? You are paying the zero coupon rate. Let's say it is 10%, which is 10,000.
Final payoff to swap long at maturity = 27,118 - 10,000 = 17,118. You said "you have" the swap, so I assume you are the fixed rate payer.
In Excel, you could do something like this: http://www.fincad.com/resources/resource-library/article/how-build-workbook-value-total-return-swap-floating-rate-loan
Modify for you specific 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.