Valuing Multi-Currency Swaps with a Collateral Choice Option
Summary
The document explains how a swap’s discounting can change when the collateral poster may choose between eligible currencies. This choice resembles a cheapest-to-deliver option: the poster prefers the collateral class with the most favorable return, and the preferred currency may change over the trade’s life. A single overnight curve therefore may not capture the collateral economics.
A simple approximation assumes current forward rates are realized and builds a blended curve by selecting the highest forward rate among eligible collateral classes at each date. The answer cautions that this ignores rate dynamics and tends to understate the expected benefit of the option. More complete valuation requires modeling the optimal posting strategy over time. The cited approach uses historical observations because observable volatility and correlation measures for the relevant indices are unavailable, leaving uncertainty around calibration and hedging. The document does not specify the FX and cross-currency basis transformations needed to construct a USD-based discount curve.
Key ideas
- A choice among eligible collateral currencies gives the poster an option to select the most favorable collateral return.
- The optimal collateral class can vary over the life of a swap.
- A blended curve based on the highest forward rate at each date is a simple approximation.
- Ignoring rate dynamics can understate the expected value of the collateral choice.
- Historical calibration can support modeling when market volatility and correlation indicators are unavailable, but hedging remains difficult.
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Full text
# Which discount curve to use when valuing multi currency swaps # Which discount curve to use when valuing multi currency swaps I've been looking around the internet but cannot find the exact answer to my question. Normally when valuing an IRS one uses eonia (for eur swaps) to discount the cashflows. Let's imagine I have a 30 year IRS for which both USD and EUR collateral can be posted (in bonds). Now the counterparty which is posting collateral has the option to post collateral in EUR bonds or in USD govt bonds (collateral funding option). I have read that one cannot use the eonia curve anymore to discount the cashflows but has to use some sort of blended curve (or maybe just a curve with the highest interest rates for simplicity). My question is: Is it correct to use the USD ois curve to discount the swaps cashflows (when you have an IRS for which both EUR and USD govt bonds can be posted)? If yes how does this curve needs to be transformed (FX and x-ccy basis)? I assume one cannot just take the USD ois curve and use that for discounting. ## Answer by atkins (score 1) https://quant.stackexchange.com/a/30061 This is a "cheapest-to-deliver" option - in the absence of any restrictions, the rational investor would post whichever collateral class offers the best rate of return at each moment in time (of course, this could vary over the life of the trade). Thus, to price in the presence of this option, you need to model the optimal posting strategy. You mentioned one very simple approach which is to assume that current forward rates will be realised, and thence build a blended curve by taking the maximum forward rate amongst the deliverable set on each date over the life of the trade. However, by ignoring the rate dynamics, this systematically underestimates the expected return on collateral. Better modelling of this option has been receiving quite a bit of research attention. For example, this recent paper offers a fairly practical approach to modelling it: http://www.risk.net/risk-magazine/technical-paper/2428223/collateral-option-valuation-made-easy The main difficulty is the absence of observable volatility and correlation indicators for the deliverable indices. The authors in this case use historical observation in lieu, which allows the model to be calibrated and the impact on pricing to be assessed. However, there still remains the problem of hedging those historically calibrated parameters.
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