Editing Yield curve (section)

===Historical development of yield curve theory===
On August 15, 1971, U.S. President [[Richard Nixon]] announced that the U.S. dollar would no longer be based on the [[gold standard]], thereby ending the [[Bretton Woods system]] and initiating the era of [[floating exchange rate]]s.

Floating exchange rates made life more complicated for bond traders, including those at [[Salomon Brothers]] in [[New York City]]. Encouraged by [[Martin L. Leibowitz|Marty Liebowitz]], traders began thinking about bond yields in new ways by the middle of the 1970s. Rather than think of each maturity (a ten-year bond, a five-year, etc.) as a separate marketplace, they began drawing a curve through all their yields. The bit nearest the present time became known as the ''short end''—yields of bonds further out became, naturally, the ''long end''.

Academics had to play catch up with practitioners in this matter. One important theoretic development came from a Czech mathematician, [[Oldrich Vasicek]], who argued in a 1977 paper that bond prices all along the curve are driven by the short end (under risk-neutral equivalent martingale measure) and accordingly by short-term interest rates. The mathematical model for Vasicek's work was given by an [[Ornstein–Uhlenbeck process]], but has since been discredited because the model predicts a positive probability that the short rate becomes negative and is inflexible in creating yield curves of different shapes. Vasicek's model has been superseded by many different models including the [[Hull–White model]] (which allows for time varying parameters in the Ornstein–Uhlenbeck process), the [[Cox–Ingersoll–Ross model]], which is a modified [[Bessel process]], and the [[Heath–Jarrow–Morton framework]]. There are also many modifications to each of these models, but see the article on [[short-rate model]]. Another modern approach is the [[LIBOR market model]], introduced by Brace, Gatarek and Musiela in 1997 and advanced by others later. In 1996, a group of derivatives traders led by Olivier Doria (then head of swaps at Deutsche Bank) and Michele Faissola, contributed to an extension of the swap yield curves in all the major European currencies. Until then the market would give prices until 15 years maturities. The team extended the maturity of European yield curves up to 50 years (for the lira, French franc, Deutsche mark, Danish krone and many other currencies including the ecu). This innovation was a major contribution towards the issuance of long dated [[zero-coupon bond]]s and the creation of long dated mortgages.