Updated: corrected quote attibution of the second quote.
I am posting for comments an introductory note on two curve models. This note which I wrote largely to improve my own understanding of this subject, represents my interpretation of the results presented in various papers listed in the bibliography and does not claim to contain any original content.
The following two quotations give a sense of what two curve models are all about:
LCH.Clearnet Ltd (LCH.Clearnet), which operates the world’s leading interest rate swap (IRS) clearing service, SwapClear, is to begin using the overnight index swap (OIS) rate curves to discount its $218 trillion IRS portfolio. Previously, in line with market practice, the portfolio was discounted using LIBOR. ... After extensive consultation with market participants, LCH.Clearnet has decided to move to OIS to ensure the most accurate valuation of its portfolio for risk management purposes. (LCH.Clearnet, June 17, 2010)
Ten years ago if you had suggested that a sophisticated investment bank did not know how to value a plain vanilla interest rate swap, people would have laughed at you. But that isn’t too far from the case today. (Deus Ex Machiatto, June 23, 2010)
The topic is quite complex even by the standards of this blog and it takes me twelve pages of occasionaly dense mathematics to explain what I have understood of its basic ideas. To fully understand two curve models you would need to read a lot more of even denser mathematics. If you do not have the patience for that, you should just ignore this post.
What I would really love is for some of my readers to provide comments and suggestions to improve this note and correct any errors that might be there.