Mark-to-Market a Receiver Swap After Its First Settlement

Summary

The document works through the value of a plain receiver swap immediately after its first annual settlement. It specifies a notional amount, a fixed coupon, and a term structure of expected floating rates, then shows an attempted valuation of the remaining floating and fixed cash flows. The answer points out that the first-year settlement itself creates a difference between the fixed and floating payments. At that point, the difference is discounted by the applicable floating rate to express the mark-to-market value from one leg’s perspective.

The sign changes when the value is stated for the floating-rate payer rather than the fixed-rate side. This example highlights that valuation timing and which party’s perspective is used both matter when reporting a swap’s value. The response is brief and does not provide a full derivation using discount factors or explain how the valuation would change under market discounting, uncertain future rates, or different settlement conventions; it relies on the problem’s simplifying assumptions.

Key ideas

• The swap’s mark-to-market depends on valuing it immediately after the first settlement.
• The fixed and floating payments in the settlement period create a difference that affects the position’s value.
• The payment difference is discounted using the applicable floating rate in the example.
• The value has opposite signs when described from the fixed-leg and floating-leg perspectives.
• The calculation assumes annual compounding and expected future rates as specified in the problem.

Tags

# Something is wrong with my MtM calculation


# Something is wrong with my MtM calculation












I'm trying to value a super simple receiver swap immediately after the first swap settlement (1 year in).

The given answer is -1.91 million to the floating rate payer, but I am not coming up with that. I can't figure what I'm doing wrong.

Problem given

Notional $100 million

Fixed rate 3.95%

Floating rate term structure: Year 1: 2% Year 2: 3% Year 3: 4%

Assume the forward rates represent expected future spot rates. All rates are expressed with annual compounding to match the annual settlement cash flows.

My attempt:

Floating leg:

$\frac{100*.03}{(1+.03)} + \frac{104}{(1+.04)^2} \approx 99.06$

Fixed leg:

$\frac{100*.0395}{(1.03)} + \frac{103.95}{(1+ .04)^2} \approx 100$

Making the value to the floating rate payer $\approx$ \$1.06 million

## Answer by arodrisa (score 1)

https://quant.stackexchange.com/a/20973

If I understood the problem, you are valuying the swap in the 1st year. The MtM, as you know, is the difference of both legs.

The value of your swap will be: `100*(1+3.95%)-100*(1+2%)=1.95` in year 1.

If you want to calculate the MtM value, just divide by the floating rate: `1.95/(1+2%)=1.911`. This is from the fix leg side. If you just change it to the floating rate side, you obtain `-1.91`

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.