Estimating the Term Structure: Exact Methods

This lecture covers exact methods for estimating the term structure in interest rate models. It starts with the general formulation of discount curves and market prices, then delves into bond markets and cash flow dates. Sparse cash flow matrices are discussed, leading to formalizations in money, FRA, and swap markets. The lecture presents solutions to under-determined linear systems using bootstrap and pseudoinverse methods, emphasizing the importance of choosing the right discount curve. Examples from the US market illustrate the application of these methods, resulting in smooth discount curves and implied forward rates.

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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.

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.

Bond market

The bond market (also debt market or credit market) is a financial market where participants can issue new debt, known as the primary market, or buy and sell debt securities, known as the secondary market. This is usually in the form of bonds, but it may include notes, bills, and so on for public and private expenditures. The bond market has largely been dominated by the United States, which accounts for about 39% of the market.

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.

Interest rate parity

Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors interest rates available on bank deposits in two countries. The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from covered interest arbitrage. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic and foreign assets.

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