Term to maturity

An increase in the initial short-rate r will have the effect of raising forward rates, as will increasing the long-run mean value b. The effect of an increase in r is most pronounced at shorter maturities, whereas an increase in b has the greatest effect the longer the term to maturity. An equal increase or decrease in both... 

A landmark development in interest-rate modelling has been the specification of the dynamics of the complete term stracture. In this case, the volatility of the term structure is given by a specified functiOTi, which may be a function of time, term to maturity or zero-coupon rates. A simple approach is described in the Ho-Lee model, in which the volatility of the term structure is a parallel shift in the yield curve, the extent of which is independent of the current time and the level of current interest rates. The Ho-Lee model is not widely used, although it was the basis for the HJM model, which is widely used. The HJM model describes a process whereby the whole yield curve evolves simultaneously, in accordance with a set of volatility term structures. The model is usually described as being one that describes the evolution of the forward rate however, it can also be expressed in terms of the spot rate or of bond prices (see, e.g., James and Webber (1997), Chapter 8). For a more detailed description of the HJM framework refer to Baxter and Rennie (1996), Hull (1997), Rebonato (1998), Bjork (1996) and James and Webber (1997). Baxter and Reimie is very accessible, while Neftci (1996) is an excellent introduction to the mathematical background. 

In Equation (4.3), the drift and volatility coefficients are functions of time t and T. For all forward rates7) in the period [0, T, the only source of uncertainty is the Brownian motion. In practice, this would mean that all forward rates would be perfectly positively correlated, irrespective of their terms to maturity. However, if we introduce the feature that there is more than one source of uncertainty in the evolution of interest rates, it would result in less than perfect correlation of interest rates, which is what is described by the HIM model. 

Setting Po as 5.0 means that the spot rate has been set to a common value of 5.0%. As an exercise, we evaluate the possible results with the same parameters used by Anderson and Sleath in their analysis with the exception of the initial spot rate, and change the values for the term to maturity to 10, 20, 30 and 1000 years and the value of a to —5, —3, — 1,0,1,3 and 5. Our results are given in Table 5.1. As the value for T increases to very high values, the convergence of spot rates to the initial value proceeds only slowly. However, our results illustrate the process. 

Term to Maturity Gilt Redemption Yield % Term to Maturity Gilt Redemption Yield %... 

The probabilities of each of these occurrences are 10%, 80% and 10%, respectively that is, the most likely scenario is a rise in the short rate from 6% to 8%. For each scenario, we assume that the short rate approaches the expected Iraig-term level in exponential fashion. The expected interest-rate scenario, therefore, is a rise from 6% to 8%. From Figure 7.2, we see that the forward rate curve behaves differently to expected future short-rate levels. The forward rates peak at around 12-14 years and then steadily decline as the term to maturity increases. The zero-coupon yield curve, which can be derived from the forward yield curve, has a different shape and starts to decline from the 20-year term period. 

A bond is a debt capital market instrument issued by a borrower, who is then required to repay to the lender/investor the amount borrowed plus interest, over a specified period of time. Bonds are also known as fixed income instruments, or fixed interest instruments in the sterling markets. Usually bonds are considered to be those debt securities with terms to maturity of over one year. Debt issued with a maturity of less than one year is considered to be money market debt. There are many different types of bonds that can be issued. The most common bond is the conventional (or plain vanilla or bullet) bond. This is a bond paying periodic interest pay-... 

The term to maturity of a bond is the number of years after which the issuer will repay the obligation. During the term the issuer will also... 

When an option-free bond is issued, the coupon rate and the term to maturity are fixed. Consequently, as yields change in the market, bond prices will move in the opposite direction, as we will see in the next two scenarios. Generally, a bond s coupon rate at the time of issuance is set at approximately the required yield demanded by the market for comparable bonds. By comparison, we mean bonds that have the same maturity and the same risk exposure. The price of an option-free coupon bond at issuance will then be approximately equal to its par value. In the example presented above, when the required yield is equal to the coupon rate, the bond s price is its par value ( 100). 

Term to Maturity in Years Premium Bond 8% Coupon Discount Bond 6% Coupon Par Bond 7% Coupon... 

Note that spread for life considers only the accretion/amortization of the discount/premium over the floater s remaining term to maturity but does not consider the level of the coupon rate or the time value of money. 

There are four characteristics of a bond that affect its price volatility (1) term to maturity, (2) coupon rate, (3) the level of yields, and (4) the presence of embedded options. In this section, we will examine each of these price volatility characteristics. 

The fixed rate is some spread above the benchmark yield curve with the same term to maturity as the swap. In our illustration, suppose that the 10-year benchmark yield is 8.35%. Then the offer price that the dealer would quote to the fixed-rate payer is the 10-year benchmark rate plus 50 basis points versus receiving EURIBOR flat. For the floating-rate payer, the bid price quoted would be EURIBOR flat versus the 10-year benchmark rate plus 40 basis points. The dealer would quote such a swap as 40-50, meaning that the dealer is willing to enter into a swap to receive EURIBOR and pay a fixed rate equal to the 10-year benchmark rate plus 40 basis points and it would be willing to enter into a swap to pay EURIBOR and receive a fixed rate equal to the 10-year benchmark rate plus 50 basis points. 

Another key feature of a bond is its term to maturity the number of years over which the issuer has promised to meet the conditions of the debt obligation. The practice in the bond market is to refer to the term to maturity of a bond simply as its maturity or term. Bonds are debt capital market securities and therefore have maturities longer than one year. This differentiates them from money market securities. Bonds also have more intricate cash flow patterns than money market securities, which usually have just one cash flow at maturity. As a result, bonds are more complex to price than money market instruments, and their prices are more sensitive to changes in the general level of interest rates. 

A bond s term to maturity is crucial because it indicates the period during which the bondholder can expect to receive coupon payments and the number of years before the principal is paid back. The principal of a bond—also referred to as its redemption value, maturity value, par value, or face value—is the amount that the issuer threes to repay the bondholder on the maturity, or redemption, date, when the debt ceases to exist and the issuer redeems the bond. The coupon rate, or nominal rate, is the interest rate that the issuer agrees to pay during the bond s term. The annual interest payment made to bondholders is the bond s coupon. The cash amount of the coupon is the coupon rate multiplied by the principal of the bond. For example, a bond with a coupon rate of 8 percent and a principal of 1,000 will pay an annual cash amount of 80. 

A bond s term to maturity also influences the volatility of its price. All else being equal, the longer the term to maturity of a bond, the greater its price volatility. 

At issue, if a bond is priced at par, its coupon will equal the yield that the market requires, reflecting factors such as the bond s term to maturity, the issuer s credit rating, and the yield on current bonds of comparable quality. 

Remember that in any market a number of bonds exist with different issuers, coupons, and terms to maturity. It is their yields that are compared, not their prices. 

Most bonds pay a part of their total return during their lifetimes, in the form of coupon interest. Because of this, a bonds term to maturity does not reflect the true period over which its return is earned. Term to maturity also fails to give an accurate picture of the trading characteristics of a bond or to provide a basis for comparing it with other bonds having similar maturities. Clearly, a more accurate measure is needed. 

Duration varies with maturity, coupon, and yield. Broadly, it increases with maturity. A bonds duration is generally shorter than its maturity. This is because the cash flows received in the early years of the bond s life have the greatest present values and therefore are given the greatest weight. That shortens the avetj e time in which cash flows are received. A zero-coupon bond s cash flows are all received at redemption, so there is no present-value weighting. Therefore, a zero-coupon bond s duration is equal to its term to maturity. 

A zero-coupon bond is the simplest fixed-income security. It makes no coupon payments during its lifetime. Instead, it is a discount instrument, issued at a price that is below the face, or principal, amount. The rate earned on a zero-coupon bond is also referred to as the spot interest rate. The notation P t, T) denotes the price at time r of a discount bond that matures at time T, where T >t - The bond s term to maturity, T - t, is... 

In practice, the term structure of coupon bonds is not complete, so the coefficients in (3.33) cannot be identified. To address this problem, McCulloch (1971, 1975) prescribes a spline estimation method that assumes zero-coupon bond prices vary smoothly with term to maturity. This approach defines price as a discount function of maturity, P N), which is a given by (3.34). 

Pt = the spot price of the underlying asset at the time of delivery X = the delivery price specified in the forward contract T = the term to maturity of the contract, in years, also referred to as the time to delivery... 

This risk-free rate is known as the implied repo rate, because the rate is similar to a repurchase reement carried out in the futures market. Generally, high implied repo rates indicate high futures prices, low rates imply low prices. The rates can be used to compare contracts that have different terms to maturity and even underlying assets. The implied repo rate for the contract is more stable than its basis, but as maturity approaches it becomes very sensitive to changes in the futures price, spot price, and (by definition) time to maturity. 

As explained in chapter 3, zero-coupon, or spot, rates are true interest rates for their particular terms to maturity. In zero-coupon swap pricing, a bank views every swap, even the most complex, as a series of cash flows. The zero-coupon rate for the term from the present to a cash flows payment date can be used to derive the present value of the cash flow. The sum of these present values is the value of the swap. 

INTEREST RATE SWAP Term to maturity 5 years ... 

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