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.
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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".
$\begingroup$
$\endgroup$
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.
