Time to maturity

Several plant parameters are important to the design of ET landfill covers. Among the most important are parameters describing rooting depth, leaf-area-index (LAI), temperature requirements, time to maturity, and water requirements. Models that are suitable for use in design of ET covers will utilize these parameters. The quality of the plant model controls the quality of AET estimates. 

A hedge (see pp.142-145) is without doubt the most environmentally beneficial garden barrier. But hedges take time to mature, require trimming, and occupy space. Solid walls and fences provide a practical alternative where space is limited and a secure definition of boundaries is an immediate priority. 

The development of enamine catalysis parallels that of iminium catalysis (Scheme 3) [24], Like iminium catalysis, the concept took a long time to mature, and also required a key discovery - the discovery of intermolecular proline-catalyzed aldol reactions by List and coworkers in 2000 [23] - to set the field in motion. The timeline of historical developments of enamine catalysis is outlined in Scheme 4. 

Fetal and postnatal maturation of the nervous system need special mention, because the nervous system is the organ system that requires the longest time to mature. Outgrowth of neuronal processes, formation and deletion of synaptic contacts and myelination take place over an extended period of time in humans and laboratory animals. This extended maturation makes the brain susceptible to environmental insult for a long period. For example, adverse neurobehavioural... 

Development rate (e.g. time for larval development, time to maturity) ... 

Ammonia technology will not change fundamentally, at least not in the next 10 to 15 years. Even if there are radical, unforeseeable developments, they will need some time to mature to commercial applicability. With the traditional concepts, the margins for additional improvements have become rather small after years of continuous research and development. Thus further progress may be confined to minor improvements of individual process steps, catalysts and equipment design. 

This is a very malty and smooth barley wine. You must have patience to allow this a long time to mature — at least 6-8 months. It will really be at its best after 1 year. This beer won first place in the 1991 American Homebrewers Association National Competition. A subsequent batch won third place in the 1992 Dixie Cup. This original recipe was first brewed with my good friend, John Hood. 

Quicklime was traditionally hydrated on the small scale by sprinkling water on to a pile of lime until no more water was absorbed. The lime was left for some time to mature and was then passed over fine sieves to remove grit. However, such a product was of poor and variable quality and required a high labour input. 

In most large organizations, these measures are already in place, but organizations are not yet comfortable with them. They will take time to mature, but the future is pushing these two strange bedfellows closer together, so mature they must. 

The forward rate function/at time t is not static and is a function of the short-rate r at time f, the time t and the time to maturity T. The Hull-White model can be calibrated in terms of the forward rate /. That is, at time t the information (parameters) required to implement this are the short-rate r(t), the standard deviation a of the short-rate, the forward rate / and the standard deviations Bj t, T)a t) of the forward rates at time t. If the forward rates are known in a form that allows their first differential to be calculated with respect to t, using the other information, it is possible to calculate the function Bj, the derivative of this function and thereby the value for a f), using the relationship in Equation (3.56) ... 

Like the bond price function, the yield on a zero-coupon bond is a function of the short-rate r and follows a normal distribution the yield curve is a function of the short-rate r, the time t and the time to maturity T. The Imig-run average future interest over the time to maturity (t, T) is normally distributed and given by ... 

The Vasicek, Cox-Ingersoll-Ross, Hull-White and other models incorporate mean reversion. As the time to maturity increases and as it approaches infinity, the forward rates converge to a point at the long-run mean reversion level of the current short-rate. This is the limiting level of the forward rate and is a function of the volatility of the current short-rate. As the time to maturity approaches zero, the short-term forward rate converges to the same level as the instantaneous short-rate. In the Merton and Vasicek models, the mean of the short-rate over the maturity period T is assumed to be constant. The same constant for the mean, or the drift of the interest rate, is described in the Ho-Lee model, but not the extended Vasicek or Hull-White model. 

FIGURE 8.6 The effect of leverage, variance and time to maturity on credit spread. (Reproduced from Merton (1974).)... 

Like Black and Cox s work, the authors find spreads similar to the market spreads. Moreover, they find a correlation between credit spread and interest rate. In fact, they illustrate that firms with similar default risk can have a different credit spread according to the industry. The evidence is that a different correlation between industry and economic environment affects the yield spread on corporate bonds. Then, the duration of a corporate bond changes following its credit risk. For high-yield bonds, the interest-rate sensitivity increases as the time to maturity decreases. 

The findings show that by increasing time to maturity, bonds with high ratings have an increasing/flat credit spread curve, while low rated bonds have a hump-shaped credit curve. Moreover, the credit spread becomes wider as the value of w increases. 

Theta measures the change of the option value to the change of time to maturity. 

Index duration is usually equal to the time until the next reset date, whereas spread duration is equal to a modified duration of a bond paying fixed coupon, with same coupon payments and time to maturity. Therefore, conventionally floaters have lower index duration and higher spread duration. 

Mortgage Type Interest-only mortgages that are not linked to a repayment vehicle will have the base case default probability increased by a factor up to 1.33, dependent on the time to maturity of the loan. 

Options on Euro-BUND futures (OGBL). The BUND future is a contract on a notional long-term instrument issued by the German Federal Government with a remaining time to maturity between 8.5 and 10.5 years, bearing a 6% coupon. 

Here, i is the market observation index with time to maturity of tj, and R t) represents the interest rate corresponding to maturity t, where < t < j. The formula can be used to derive any swap rate between two market observations R(fi) and i). 

Although newcomers to the market commonly consider duration, much as Macaulay did, a proxy for a bond s time to maturity, this interpretation misses the main point of duration, which is to measure price volatility, or interest rate risk. Using the Macaulay duration can derive a measure of a bond s interest rate price sensitivity, i.e., how sensitive a bond s price is to changes in its yield. This measure is obtained by applying a mathematical property known as a Taylor expansion to the basic equation. 

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. 

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