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Lecture

Estimating the Term Structure: Smoothing Methods

Description

This lecture covers smoothing methods used to estimate a smooth forward curve from market rates, focusing on Nelson-Siegel and Svensson curves. It discusses key criteria for smoothing methods, estimation methods by central banks, and the Hilbert space approach for smoothing splines. The presentation concludes with Lorimier's theorem and the choice of parameter a in smoothing splines.

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Related concepts (32)

Yield curve

In finance, the yield curve is a graph which depicts how the yields on debt instruments – such as bonds – vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value.

Interest rate swap

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs). In its December 2014 statistics release, the Bank for International Settlements reported that interest rate swaps were the largest component of the global OTC derivative market, representing 60%, with the notional amount outstanding in OTC interest rate swaps of

381 trillion, and the gross market value of

14 trillion.

Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Interest rate

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized.

Interest rate derivative

In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.

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Explores exact methods for estimating the term structure in interest rate models, emphasizing the importance of choosing the right discount curve.

Interest Rates and Bonds

Explores interest rates, bonds, yield curves, and factors influencing interest rates in reality.

Interest Rates and Contracts: Duration and Convexity

Explores duration and convexity in interest rate models for bond portfolio hedging.

Estimating the Term Structure: Bootstrapping Example

Explores bootstrapping to build the term structure from short to long maturities using market data on LIBOR, futures, and swaps.

Interest Rate Derivatives: Calibration Example

Covers the calibration of interest rate models using a two-factor Gaussian HJM model and the computation of Black and Bachelier cap vegas.