Combining pdf curves

View 1 excerpt, references background. Marginal abatement cost MAC curves, relationships between tonnes of emissions abated and the CO2 or greenhouse gas GHG price, have been widely used as pedagogic devices to illustrate simple … Expand.

Marginal abatement cost curves for policy making — expert-based vs. Legal commitments to reduce CO2 emissions require policy makers to find cost-efficient means to meet the obligations. Marginal abatement cost MAC curves have frequently been used in this context to … Expand. Legal commitments to reduce CO 2 emissions require policy makers to find cost-efficient means to meet the obligations.

Marginal abatement cost MAC curves have frequently been used in this context … Expand. Marginal abatement cost curves: a call for caution. Legal commitments to reduce CO2 emissions require policy makers to find cost-efficient means to meet these obligations. Marginal abatement cost MAC curves, which illustrate the economics associated … Expand. View 2 excerpts, references background. Least-cost greenhouse planning : supply curves for global warming abatement.

Abstract The paper presents a methodology for comparing the cost-effectiveness of different technical options for the abatement of greenhouse gas emissions. The methodology also allows a … Expand. Marginal abatement cost curves MACCs are a favorite instrument to analyze international emissions trading.

View 2 excerpts, references background and methods. Marginal abatement curves MACs are often used heuristically to demonstrate the advantages of emissions trading. View 1 excerpt, references methods. The iterative contribution and relevance of modelling to UK energy policy. A bottom-up decomposition analysis of energy-related CO2 emissions in Greece.

According to Ngugi et al. This was driven by the requirement of International Accounting Standard IAS 39, which requires that there should be a standard yield curve to facilitate investors in fixed income instruments to value their portfolios at fair market values. However, the market participants identified limitations in prices reported on the NSE and decided not to use the yield curve created at the time to value their portfolios.

It was then agreed that the yield rates applied to the market were to be derived from a cross-section of key market players. The yield curve, which was primarily available through Reuters, which is a media channel dedicated to providing market data in the international financial market and disseminating that information locally.

Unfortunately, logarithmic linear interpolation has a tendency of implying discontinuities in the forward rate curve, a weakness depicted by all variations of linear interpolation methods, as shown by Hagan and West [1]. We intend to construct a yield curve for the NSE by overcoming the limitations experienced by the group working on the yield curve in To improve on this, we will use raw bond data from CBK, which is the primary issuer of the bonds in Kenya.

This way, we will construct a yield curve which is based on clean bond prices without accruals of interest and so forth, as is the case in secondary market. In addition, we intend to use an interpolation method which has been verified as being superior to the variations of linear interpolation methods, and that is an im- provement of monotone preserving r t t method.

The Yield Curve A yield curve is a graphical representation of relationship between return yield of same type of financial in- struments and its day to maturity. In other words, all the differences in terms of types, credit risks and liquidity are removed from bonds and just the path of interest rates according to maturity rate is represented in yield curves.

Yield curves can be grouped into two in terms of coupons: namely coupon bearing yield curves and zero coupon yield curve. A coupon bearing yield curve is obtained from an observable market bonds at various times to maturity with the bonds having the same coupon rate. Most of the government securities having long maturity dates usually have coupons.

A zero cou- pon bond yield curve is the yield curve between zero coupon bond yield and maturity dates. Zero coupon yields are the difference between the purchasing price and face value of bonds since the bonds do not pay any coupon until maturity date. Yield curves can also be grouped into nominal yield curves, spot yields curves, and forward yield curves. Nominal yield curves take place in primary bond markets, and it is the graph of yields of bonds which are trans- acted at nominal prices.

Spot yield curve is another definition of zero coupon yield curve. Forward yield curve is the curve representing the connection between the forward rate and its corresponding maturity where the for- ward rate is the interest rate implied by the zero coupon rates for periods of time in the future.

Shapes of Yield Curves The yield curves reflect the market expectations and may take one of the three main patterns: normal, flat or in- verted curves. Each shape includes different information for market. Normal Yield Curve As the name indicates, this is the yield curve shape that forms during normal market conditions.

Normal market conditions occur when investors generally believe that there will be no significant changes in the economy, such as in inflation rates, and that the economy will continue to grow at a normal rate.

During such conditions, inves- tors expect higher yields for fixed income securities with long-term maturities that occur farther into the future. To invest in one instru- ment for a longer period of time, an investor needs to be compensated for undertaking the additional risk. Flat Yield Curve These curves indicate that the market environment is sending mixed signals to investors, who are interpreting interest rate movements in various ways.

During such an environment, it is difficult for the market to determine whether interest rates will move significantly in either direction into the future. A flat yield curve usually occurs when the market is making a transition that emits different but simulta- neous indications of what interest rates will do.

In other words, there may be some signals that short term in- terest rates will rise and other signals that long-term interest rates will fall.

This condition will create a curve that is flatter than its normal positive trade off by choosing fixed-income securities with the least risk, or highest credit quality.

Inverted Yield Curve These yield curves form when the expectations of investors are completely the inverse of those demonstrated by the normal yield curve. In such abnormal market environments, bonds with maturity dates farther into the future are priced higher than the short-term bonds.

This means that the market expects yield of long term bonds to de- cline. An inverted yield curve indicates that investors interpret an inverted curve as an indication that the economy will soon experience a slowdown, which causes future interest rates to give even lower yields before a slow- down, thus creating a need to lock money into long-term investments at present prevailing yields, because it is expected that future yield will be even lower.

Zero-Coupon Yield Curves The zero-coupon yield curve is also known as the term structure of interest rates. It measures the relationship among the yields on default-free securities that differ only in the term to maturity.

In bond-valuation, the term structure of interest rates refers to the relationship between bond prices of differ- ent maturities in general. When interest rates of bonds are plotted against their maturities, this is called the yield curve. The term structure of interest rates and yield curves are used interchangeably in literature. Theories of the Yield Curves 1. Expectations Theory There are various versions of expectations theories. These theories place predominant emphasis on the expected values of future spot rates or holding-period returns.

Generally, this ap- proach is characterized by the following propositions 1 the return on holding a long term bond to maturity is equal to the expected return or repeated investment in a series of the short-term bonds, or 2 the expected rate of return over the next holding period in the same for bonds for all maturities [10]. The key assumption behind this theory is that buyers of bonds do not prefer bonds of one maturity over another, so they will not hold any quantity of a bond if its expected return is less than that of another bond with different maturity.

Bonds that have this characteristic are said to be perfect substitutes. Note that what makes long term bonds different from short term bonds are the inflation and interest rate risks. Therefore, this theory essentially assumes away inflation and interest rate risks [11]. Investors expect interest rates to rise in the future, which accounts for upward slope of the yield curve.

If the expectations hypothesis were correct, the slope of term structure could be used to forecast the future path of interest rates for example, if the yield curve were to slope upward at the short end, it would be because the interest rate is expected to rise. One problem with this version of the expectations hypothesis is that in fact, the yield curve slopes upward at the short end on average even though interest rates do not rise on the average.

One way to explain divergence is to assume that investors are simply wrong on average. Since bond prices do fluctuate over time, there is un- certainty even for default free bonds regarding the return from holding a long-term bond over the next period.

Moreover the amount of uncertainty increases with maturity period of the bond. If there were a risk premium associated with uncertainty, then the yield curve could slope upward on average without implying that interest rates increase on average.

If the risk premium were constant, the changes, in the slope of the yield curve would forecast changes in the future path of the interest rate.

For example, if the slope of the yield curve were to in- crease, then it would have to be because the path of futures interest rates is expected to be higher. This increase in the slope would imply that future bond yield would be higher. But there is a problem with this version of the hypothesis as well, according to a number of authors.

Another feature of the yield curve that the expectations has difficulty explaining is that the zero-coupon yield curves slopes downward on average at the long end, typically over the range of twenty to thirty years bond. In other words, the yield on a thirty-year zero-coupon bond is typically below the yield on a twenty-year bond.

The expectations hypothesis would suggest that that this slope is due to either 1 a persistently incorrect belief that the interest rate will begin to fall about 20 years from or 2 a decrease in the risk premium for bonds with matur- ities beyond twenty years, even though the uncertainty of the holding-period return for thirty-year bonds. Nei- ther of this reasons is sensible3. There is, however, a sensible explanation, for the persistent downward slope for the term structure at the long end.

The explanation has to do with uncertainty regarding the future-path of short-term rates. This uncertainty underlies the risk of holding bonds if there were no uncertainty regarding the future paths, there would be no risk of holding default-free bonds. Increases in this uncertainty lead to 1 increases in risk premia that increase the slope of the yield curve at the short end and 2 decreases in the slope of the yield curve at the long end via the effect of convexity. As a consequence, a symmetric increase in uncertainty about yield raises the average price of bonds, thereby lowering their current yields.

This effect is trivial at the short end of the yield curve where it plays no significant role, because it becomes noticeable and even dominant at the long end. The overall shape of the yield curve involves the trade-off between the competing effects of risk premia which cause longer term yields to be lower.

Typically, the maximum yield occurs in the fifteen to twenty-five maturity range of the zero coupon yield. But a good theory should not imply that investors are wrong on average. Segments Market Theory This is the market segmentation hypothesis of Culbertson. Here it is asserted that individuals have strong matur- ity preferences, and that bonds of different maturities trade in separate markets.

This theory assumes that mar- kets for different-maturity bonds are completely segmented. The interest rate for each bond with a different ma- turity is then determined by the supply of and demand for the bond with no effects from the expected returns on other bonds and other maturities. In other words, longer maturity bonds that have associated with the inflation and interest rate risks are completely different assets than the shorter bonds. Download Download PDF. Translate PDF.

Malleret-Joinville BP Arcueil-Cedex, France Abstract properties and, second, partitioning the result into line seg- We present an algorithm that extracts curves from a ments [7]. After such a partitioning the problem remains set of edgels within a specific class in a decreasing or- to aggregate such segments into curves [13]. The algorithm inherits the percep- proposed methods that follow the edgels and recursively tual grouping approaches.

But, instead of using only local fits a curve until the fitting error is large. But, important cues, a global constraint is imposed to each extracted sub- difficulties remain: the extracted curves are highly depen- set of edgels, that the underlying curve belongs to a specific dent on the selected starting points, as well as the order of class.

In order to reduce the complexity of the solution, we the edgel linking. The approach we have explored tackles work with a linearly parameterized class of curves, func- such problem. This allows, first, to use a re- Other approaches have been motivated by the idea of cursive Kalman based fitting and, second, to cast the prob- perceptual grouping. The edgels are organized as nodes lem as an optimal path search in an directed graph.

Ex- of a graph, and linked to each other through arcs. Generally such cues correspond to some 1 Introduction intuitive measure of the local geometrical consistency as evaluated for each pair of nodes.

Measures such as align- Our study is motivated by the detection - via on-board ment, co-circularity, and saliency have been proposed [14]. The difficulty of finding road markings and bound- erties.

Different algorithms have been proposed to find aries stems from two main facts. They may also be ming and relaxation see [2, 1]. All such methods propose masked by shadows, light spots, be partially occluded, or cues based on pair-wise interactions between edgels, and even be physically fragmented.

Second, the extraction of seem difficult to extend when a more global constraint on markings must be performed in a reasonable time on a stan- the curve is needed. To alleviate these adverse conditions, we assume that In [10], the author proposes a method that finds the markings are ideally embedded into a family of smooth longest convex subgraph. Convexity proves to be a strong curves,.

A direct consequence of this modeling, is that enough constraint such that the computation can be per- we can now select edges based on their curve fitting perfor- formed by an exhaustive search. The main difficulties are in designing i a global acteristic of the features we seek to retrieve.

Indeed, the grouping technique that may result in a high combinato- existence of such curves in a typical image of a road, has a rial complexity, and ii a fitting technique for the family high probability to correspond to road boundaries or lane- that involves a large amount of computations. How- markings. Nowadays, the most widely used coordinate, and the vertical one. A set of edgels having a large is then clearly a network.

First, we describe the contrast amplitudes. The problem is now how to find such variational statement of our problem. Second, we define subsets. Ideally, this involves finding the partition F , of a simple edgel detector based on level-lines. We then we show, how we.

We want to select edges based on geometrical aspects. We define the putationally expensive. A large error indicates that the edgel set cannot be well represented by a curve in. Hence we introduce a measure.

To balance the fitting error, it is sufficient that. T The family of the shapes is a linearly parameteriz- T able subset of curves. The edgel set can be ordered. Therefore, the edgel graph is a connected acyclic directed graph.

Under these assumptions, we propose a new approach for an efficient partitioning which approximates the best solu- a b tion F maximizing 1. Our approach consists in finding the longest edgel subset first.

Then, to remove the found subset of the edgel set, and to iterate the optimal search for the next longest edgel subsets. With this partitioning approach, that we named Best-First Segmentation, the re- sulting subsets are ordered in decreasing energy. Both steps decrease the line segment detector for different values of the the number of resulting edgels, and in fact may remove minimal length b 8 pixels, c 16 pixels and d 32 useful information, as we explain below. Therefore the selection is harder on low- codes.

The list of directions on these connected edgels is contrast zone. As example, we show in Fig. The magnitude of the ing when a chain code of a list of connected edgels is a gradient along the light spot is so strong that the smoothing straight line or not [11, 16]. Using such algorithms al- removes the edge of the white lane-markings we want to lows us to construct a complete tree of possible straight detect.

Due to Thresholding. Therefore, smoothing and threshold steps, edgels in images are nu- this tree is a binary tree.