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Marking a Forward-Starting Swap to Market After Entry

Article Quant Q&A · Author: Tempor
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Summary

The document explains how to mark a forward-starting interest rate swap after the trade date. Its central point is that a 2Y1Y swap entered on day T is a contract with specified future effective and termination dates and an agreed fixed rate. On a later date, value that same contract using the updated curve and its original dates and terms.

The question proposes instead tracking a rolling 2Y1Y rate by shortening both forward dates each day, then estimating P&L from the rate difference and a stated DV01 position. The answer says that this rolling rate is a chart measure, not the instrument already traded. It does not provide a full valuation or confirm the proposed dollar P&L calculation; accurate P&L requires repricing the actual swap under the relevant market conventions, using the new curve and original contract terms.

Key ideas

  • A forward swap entered on a given date has fixed effective and termination dates.
  • To measure later P&L, reprice the existing contract using the later date’s curve.
  • Do not substitute a newly rolled forward swap for the instrument already held.
  • A plotted rolling forward rate is not itself the value of the original swap.
  • The document does not validate the proposed DV01-based dollar P&L calculation.

Tags

Fixed incomeDerivatives pricingRisk managementBacktesting
Full text
# Backtesting an Interest Rate Swap Strategy


# Backtesting an Interest Rate Swap Strategy












I'm trying to value a forward starting interest rate swap and calculate the PnL of my trade. Say these are the zero rates:

On day T

| Year | Rate |
| 1 | 1.1 |
| 2 | 1.3 |
| 3 | 1.5 |

On day T+1

| Year | Rate |
| 1 | 1.08 |
| 2 | 1.29 |
| 3 | 1.48 |

Say that on day T, I receive a 2Y1Y (2 year forward 1 year rate) swap.

Using the zero rates above, on day T, this would be traded at:

((1 + .015)^3 / (1 + .013)^2) - 1 = 1.9%.

In order to calculate my PnL from this receiver after one day, would it be correct to now calculate the (1 year 364 day forward 1 year rate) swap and compare the rate? So, specifically, I need to track the IRS which now has a forward that is 1 day less, or the 1 year 364 day forward year rate.

Therefore, the rate of my IRS on day T+1 would be:

forward_years = 2 - (1/365) = 1.997

end_years = 3 - (1/365) = 2.997

((1 + .0148)^(2.997) / (1 + .0129) ^ (1.997)) = 1.8%

Therefore, my PnL for having a $1000 DV01 position would be 1000 * (1.9 - 1.8) * 100 = 10,000 dollars.

Is this correct?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/81193

There is no such thing as a rolling 2Y1Y IRS (sure you can plot a rate on a chart but you cant trade it).

If on day T, lets call it Monday 18th Nov 2024, you execute a 2Y1Y swap then that swap will have effective date 18th Nov 2026 and termination 18th Nov 2027 (at least in GBP).

On any other day, be it T+1, or whenever, if you want to know the PnL of the instrument you have traded, then you price the instrument that you have traded which is a swap with effective date 18th Nov 2026 and termination 18th Nov 2027 with the fixed rate as specified when you traded the contract, with the curve you have constructed on date T+1 or whenever.

I cannot ascertain any more information that is needed to answer this question.

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.