Choosing Discount Curves for Non-LIBOR Swaps
Summary
The document considers how to value a fixed-for-floating swap whose floating leg references a rate other than LIBOR, with a CNY example. It explains that the appropriate discount curve depends on the transaction’s collateral terms: for fully collateralized trades, discount using a curve tied to the collateral remuneration rate. Partially collateralized or uncollateralized trades require more complex treatment.
For a swap with both legs in CNY, the answer recommends building curves from liquid CNY market instruments, such as deposits and swaps, rather than discounting with LIBOR curves. Bootstrapping from those instruments is described as a way to obtain discount factors consistent with local market pricing, so the swap can be set to zero value at inception. The discussion is conceptual and gives no detailed curve-building procedure; instrument choice and collateral terms depend on the market and contract.
Key ideas
- Discounting for collateralized swaps should reflect the rate earned on posted collateral.
- Uncollateralized and partially collateralized swaps require more involved valuation assumptions.
- For a CNY swap, construct curves from liquid CNY instruments instead of using LIBOR curves.
- Bootstrapped discount factors can align the initial swap value with local market pricing.
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Full text
# How to value non-libor swaps (not basis swaps)? # How to value non-libor swaps (not basis swaps)? What discount curve should be used for a swap with a fixed leg and variable leg, where the variable leg is based on rate other than Libor (in my case 1-year deposit rate). Hull (5th edition, page 595) say we always use Libor for discounting (his example however is a basis swap). That seems inconsistent to me, 1) the value of the swap won't be zero at inception 2) value of swap will change due to Libor/Swap rates. My case is somewhat more complicated by the fact that cash-flows are in RMB currency, while that's not the core of my question, any additional thoughts on that would be welcome. ## Answer by mepuzza (score 4) https://quant.stackexchange.com/a/3332 Discounting in "post-crunch finance" depends on collateral agreements, e.g. CSA. For fully collateralized transactions you discount off the curve corresponding to the rate you receive on collateral. For non-collateralized or partially collateralized transactions it's more tricky and it's not something I can explain in a short answer, have a look on the internet, try for example "discounting csa". Forget about Hull, that's "pre-crunch finance". ## Answer by Wei Ran (score 4) https://quant.stackexchange.com/a/20816 If both legs are in CNY, you definitely cannot discount using Libor curves. Instead, you need to construct CNY curves with "primary" instruments (deposits, swaps, FRA, futures) which have the best liquidity in the CNY market. As far as I know, some banks use deposit rate up to 1M, fixed-float swap with quarterly payments up to 15Y to bootstrap the discount curve. In this way, your swap will be valued zero at inception (that's how you solve for the discounting factors) and value of swap won't be changed by Libor rates.
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