# 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?

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.

• thanks for the answer. Is there a source / link to these formulas for all types of swaps? Jun 10, 2015 at 21:42
• This open gamma one is the first thing that popped into my head... developers.opengamma.com/quantitative-research/… I think they have a bunch of references for other instruments too. Specifically for inflation swaps, there are a lot of really good sell-side research papers. Search for Lehman Brothers, Inflation Derivatives Explained, as an example. Jun 10, 2015 at 21:48
• In terms of valuation, how do I go about estimating the expectation of $I(T)$ for some date $t<T$ before I can observe the index fixing? Apr 19, 2021 at 16:11
• @KevinT These are inferred from quoted ZC inflation swaps, from which you'd construct an inflation swap curve. Apr 19, 2021 at 17:32
• Hi @Helin, many thanks for following up on this older thread. Setting up the curve now, and I was wondering about interpolation. Is it better practice to interpolate the CPI values, or to interpolate the zero-coupon rates (i.e., basically given quoted zero rates, is interpolation done before or after finding the corresponding index values)? Apr 26, 2021 at 7:45

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.