Why Interest Rate Swaps Need Models for Potential Future Exposure
Summary
An interest rate swap’s current value can be calculated from the yield curve, without specifying a stochastic model for future rate movements. That valuation answers what the swap is worth now under the curve and arbitrage-free pricing conventions; it does not describe how the value may change over time.
Potential future exposure (PFE) estimates how large the swap’s mark-to-market could become at a future date. Because future exposure depends on possible rate movements, its calculation requires assumptions about rate volatility and a method for projecting or simulating future values. The discussion compares this distinction to pricing a stock portfolio versus estimating its value-at-risk. It gives no particular model calibration or PFE procedure, and Hull–White is mentioned in the question rather than established as the only suitable model. The result therefore depends on modeling and simulation choices.
Key ideas
- A swap’s current value can be derived from the present yield curve without modeling future curve movements.
- PFE estimates possible future changes in a swap’s mark-to-market value.
- Rate volatility affects the potential size of future exposure.
- PFE requires assumptions and a projection or simulation method, so its estimate depends on model choices.
Tags
Full text
# Is it true that pricing an IR swap doesn't require any stochastic model but calculation of the PFE of an IR swap would? # Is it true that pricing an IR swap doesn't require any stochastic model but calculation of the PFE of an IR swap would? > Pricing an IR swap doesn't require any stochastic model but calculation of the PFE for an IR swap would require the Hull White Model or any other stochastic short rate or forward rate model. Is this statement correct and if so, why? ## Answer by joelhoro (score 7) https://quant.stackexchange.com/a/3772 A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future. The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile rates are, the higher the PFE. It's a bit like saying that the price of a portfolio of stocks does not require models, but the VaR does. ## Answer by GWD (score 1) https://quant.stackexchange.com/a/3803 Fully support the prior comment. Swaps can basically be priced off the current Yield curve in an arbitrage free manner. The PFE as the name "potential" future exposure suggests refers to a value something (i.e. the swap) could potentially realize. Hence one needs to decide upon a simulation method to derive this potential value. The PFE as a measure of future (mark-to-market) credit exposure is often also referred to as the "Upside VaR", which is another hint in that direction, since VaR methods are usually also parametric (in the sense that price/value changes are assumed to follow certain distributions) or simulation based. Cheers.
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