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Topic: Convexity

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In the News (Sun 21 Jul 19)

 Convexity - Wikipedia, the free encyclopedia
Convexity may refer to one of the following.
The concepts of convexity and concavity are important in various fields, and in various fields the adjective "convex" has their own specific meanings.
This is a disambiguation page: a list of articles associated with the same title.
en.wikipedia.org /wiki/Convexity   (125 words)

 Wilmott Forums - What is convexity?   (Site not responding. Last check: 2007-10-21)
Convexity is a measure of the curvature in the relationship between bond prices and bond yields.
The degree to which the convexity increases the price (or decreases the yield) of a gamma position is directly linked to the market's perceived likelihood of such a large move.
Similarly, a long position in interest rate convexity, such as in a 25-year zero-coupon bond, when delta hedged by shorting a lower-convexity bond, provides an added return in the case of a large interest rate move, paid for by an inferior total return should rates not move so much.
www.wilmott.com /messageview.cfm?catid=19&threadid=13946   (2034 words)

 David Bremner's computational convexity bibliography
An algorithm for enumerating the vertices of a convex polyhedron.
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra.
Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental.
www.cs.unb.ca /profs/bremner/PolytopeBase/biblio/bibmain.html   (4008 words)

 SoA6, Mortgage Negative Convexity - Actuarial Outpost
Remember that the actual slope is an indication of the duration and that it is the rate of change of the slope that indicates the convexity.
Convexity is also a measure of rate of change of duration.
The simple mathematical explanation of negative convexity is a change in the curvature of the Price (y axis) vs. interest rate (x axis) curve.
www.actuarialoutpost.com /actuarial_discussion_forum/showthread.php?t=1380   (615 words)

 Convexity and concavity
The twin notions of concavity and convexity are used widely in economic theory, and are also central to optimization theory.
The notions of concavity and convexity are important in optimization theory because, as we shall see, the first-order conditions are sufficient (as well as necessary) for a maximizer of a concave function and for a minimizer of a convex function.
The inequalities in the definition of concave and convex functions are weak: such functions may have linear parts, as in the following figure.
www.chass.utoronto.ca /~osborne/MathTutorial/CV1.HTM   (1352 words)

 Duration   (Site not responding. Last check: 2007-10-21)
Convexity is a measure of the amount of "whip" in the bond's price yield curve (see above) and is so named because of the convex shape of the curve.
An easier way to think of it is that convexity is the rate of change of duration with yield, and accounts for the fact that as the yield decreases, the slope of the price - yield curve, and duration, will increase.
By using convexity in the yield change calculation, a much closer approximation is achieved (an exact calculation would require many more terms and is not useful).
www.finpipe.com /duration.htm   (647 words)

 TIFF Education Foundation: Convexity
Convexity remains a preoccupying phenomenon for bond investors.
[1] The reason bond specialists use the term convexity to describe this phenomenon is because graphing the price of a convex bond under varying interest rate conditions produces a convex line.
A rate increase from B to C may appear larger than a rate decrease from B to A but it is not: point B exactly bisects points A and C on the horizontal axis.
www.tiff.org /TEF/glossary/convexity.html   (389 words)

 Management of Meningiomas (File 13): CONVEXITY MENINGIOMAS
Convexity meningioma describes those tumors whose attachment does not occur on the dura of the skull base or does not involve the dural venous sinus or falx.
The tumor may arise from any area of the dura over the convexity, but they are more common along the coronal suture and near the parasagittal region.
I no longer do angiography for most patients with convexity meningiomas since blood supply is known and the procedure does not add any crucial information for planning the operation.
neurosurgery.mgh.harvard.edu /CranialBaseCenter/mening13.htm   (1026 words)

 Duration and Convexity
uration and convexity are factor sensitivities that describe exposure to parallel shifts in the spot curve.
Duration and convexity have traditionally been used as tools for asset-liability management.
delta and gamma Factor sensitivities used with derivatives that are analogous to duration and convexity.
www.riskglossary.com /articles/duration_and_convexity.htm   (1565 words)

 Re: Convexity limits
I was WRONG saying that convexity (further referred to as C) had nothing to do with parallel shifts.
In certain cases negative convexity might be a desireable property.
It might be problematic and confusing to monitor separate convexity limits in addition to duration limits.
www.contingencyanalysis.com /archive/archive03-4/00000440.htm   (248 words)

 Convexity, Roughness   (Site not responding. Last check: 2007-10-21)
A convex hall is defined as an imaginary elastic string, stretched around the object.
The Convexity describes how convex the outline of the object is. It is equal to the ratio of the outline area divided by the convex area:
Convex objects like rectangles or ellipses have this value equal to 1.
www.imagewarp.com /help/convexity.htm   (131 words)

 Exercises on convexity and concavity for functions of many variables   (Site not responding. Last check: 2007-10-21)
The function C of many variables and the function D of a single variable are both convex.
Show that f is a convex function (without assuming that C and D are differentiable).
The function f (of n variables) is concave, and the function g (of n variables) is convex.
www.chass.utoronto.ca /~osborne/MathTutorial/CVNX1.HTM   (336 words)

 Advanced Bond Concepts
A bond with greater convexity is less affected by interest rates than a bond with less convexity.
Convexity is the final major concept you need to know for gaining insight into the more technical aspects of the bond market.
Understanding even the most basic characteristics of convexity allows the investor to better comprehend the way in which duration is best measured and how changes in interest rates affect the prices of both plain vanilla and callable bonds.
www.investopedia.com /university/advancedbond/advancedbond6.asp   (854 words)

 SSRN-Duration, Convexity and Higher Order Hedging (Revisited) by Andrew Jeffrey
Here the concepts of Duration and Convexity are studied when the term structure at a single point in time generally cannot be summarized by a finite number of state variables.
In this paper definitions of Duration and Convexity are provided that circumvent this problem and consistency with traditional measures is shown.
Convexity additionally requires a model of how this volatility will change over time.
papers.ssrn.com /sol3/papers.cfm?abstract_id=250791   (241 words)

 Vanderbilt Capital Advisors
  Until the concept of convexity was developed, it had been a mystery why some bonds gained value more slowly when rates declined and lost value more quickly when rates rose.
The second statement is accurate since the final bond principal payment (at maturity) has the most convexity and the cash flow of a zero is entirely composed of its final payment.
A negatively convex portfolio will provide an investor with a higher initial yield than that of a positively convex portfolio.
www.vcallc.com /mailings/1999/convexity.htm   (1103 words)

 Articles - Convex   (Site not responding. Last check: 2007-10-21)
The definition of a convex set and a convex hull extends naturally to non-Euclidean geometry by defining a convex set to contain the geodesics joining any two points in the set.
The notion of convexity in the Euclidean space may be generalized by modifying the definition in some or other aspects.
The notion of convexity may be generalised to other objects, if certain properties of convexity are selected as axioms.
www.newmirror.com /articles/Convex   (684 words)

As yields increase (decrease) the convexity decreases (increases).
Neither convexity nor duration alone are good approximations of bond price changes when yield changes are large.
Two bonds that have equal duration but different convexity, the bond with the greater convexity will be more valuable because no matter whether yields increase or decrease the bond will have a higher price.
www.umsl.edu /~busahanc/DURATION.htm   (399 words)

 [No title]   (Site not responding. Last check: 2007-10-21)
Convexity is always greater than duration and also grows much more rapidly with maturity than duration.
In this context, convexity is desirable not only when yields are volatile ( EMBED Equation.3 ) but also at times when one has large changes in predicted yields no matter the sign of predicted yield changes.
Of course, negative convexity is not realistic for option free bonds so only the part of this curve where convexity is positive is realistic for option free bonds.
price.ou.edu /finance_CFS/finance_CFS_body/data/0504.doc   (4897 words)

 Image Restoration by Ordinary Kriging with Convexity   (Site not responding. Last check: 2007-10-21)
As kriging is a non-convex estimation technique and negative kriging weights applied to, image data can give estimates outside the range of pixel values.
Convexity is therefore required in this image analysis to ensure nonnegative weights.
Experiments on an image degraded with different levels of Gaussian white noise are given to illustrate the effectiveness of the proposed approach.
csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/icpr/2000/0750/03/0750toc.xml&DOI=10.1109/ICPR.2000.903552   (158 words)

In a convex figure, if you pick any two points, the points between them are also a part of the figure.
If you can assemble convex figure B from n copies of figure A, then figure A is n-convex.
The last is the only other class of n-vex convex pentagon I was able to find.
www.mathpuzzle.com /convex.html   (344 words)

 CAS Discussion Forums: Convexity
The CAS answer uses t=1,2,3,4 and then divides the duration by 2 and the convexity by 2^2 since the payments are every six months.
My manual and my seminars also fully discussed and worked questions in which we both calculated and used convexity a number of times, including the use of a shortcut method that I recommended to be used on the exam in place of the textbook formula because of its ease and speed.
By no means do I think Richard is perfect and even in context the convexity note seemed to me to be brushing convexity aside (which I did not do).
www.casact.org /forum/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=12&t=000108   (1863 words)

 2004 Summer Research Conference on Gaussian Measure and Geometric Convexity
Remarkable advances have been made in several areas that involve aspects of Gaussian measure and the theory of convex bodies.
The conference will bring together researchers in convex geometry, probability, statistics, and the local/asymptotic theories of Banach spaces to discuss recent results and directions for future research.
Major themes will be (i) the role of probabilistic methods in understanding properties of convex bodies, especially in high dimensions; and (ii) the application of convex-geometric methods to the study of Gaussian processes.
www.ams.org /meetings/src-ball.html   (149 words)

 TheStreet.com: Practical Uses of Duration and Convexity for Bond Buyers
5/28/99 11:56 AM ET In this third and final installment of Fixed-Income Forum's miniseries on duration and convexity, we discuss basic practical uses of the two concepts for the individual investor.
As for convexity -- that feature that callable bonds don't have -- the implication for the individual bond investor is fairly simple.
In general, investors in bond mutual funds probably don't need to concern themselves to the same degree with duration and convexity.
www.thestreet.com /funds/bondforum/751721.html   (1080 words)

 Convexity of callable bond - Actuarial Outpost
it could be that convexity decreases in both cases andamp; that duration affects the price more....so without a numerical example, i am not sure.
Negative convexity will offset this change (like when a callable bond stops changing in price when it approaches the call price) and positive convexity will magnify the change further (a putable bond becomes much more valuable when rates drop).
Negative convexity will add to the negative change (a callable bond is more valuable when rates are rising - the option declines in value) and positive convexity will offset the negative price change (a putable bond stops changing in price when it falls below the put price).
www.actuarialoutpost.com /actuarial_discussion_forum/showthread.php?t=3787   (482 words)

 Wilmott Forums - CDS and convexity   (Site not responding. Last check: 2007-10-21)
For a simple model, say the CDS is worth the difference between the cash flows of a reference instrument discounted at the risk-free rate and the market price of the reference instrument.
Assuming the reference instrument has positive convexity, then you will have negative convexity with respect to a change in credit spread.
You will have positive convexity with respect to interest rate changes because the positive convexity on the reference cash flows discounted at the risk free rate will be larger (due to the longer duration coming from the smaller yield) than the positive convexity on the actual reference instrument (the one you are short).
www.wilmott.com /messageview.cfm?catid=3&threadid=9215   (220 words)

 Management of Meningiomas (File 18): CEREBELLAR CONVEXITY MENINGIOMA
One arises from the dura over the posterior convexity of the cerebellum and the other arises in the angle between the petrous and convexity dura and may include the wall of the sigmoid and lateral transverse sinuses (FIG.
Three of these lesions arose from the cerebellar convexity dura and three were over the sigmoid sinus.
A gross total removal was done in five and a radical subtotal removal in one, with tumor left in the wall of the sinus.
neurosurgery.mgh.harvard.edu /CranialBaseCenter/mening18.htm   (648 words)

 SSRN-Eurodollar Futures Convexity Adjustments in Stochastic Volatility Models by Vladimir Piterbarg, Marco Renedo
A formula that explicitly incorporates volatility smile, as well as a realistic correlation structure of forward rates, in computing Eurodollar futures convexity adjustments is derived.
The effect of volatility smile on convexity adjustments is studied and is found significant.
Piterbarg, Vladimir and Renedo, Marco Antonio, "Eurodollar Futures Convexity Adjustments in Stochastic Volatility Models" (February 4, 2004).
papers.ssrn.com /sol3/papers.cfm?abstract_id=610223   (181 words)

 Convexity and Jensen's inequality
Before introducing it, you need to know about convex and concave functions.
Pictorially, the function is convex if the function lies below the straight line segment connecting two points, for any two points in the interval.
One reason why we are interested in convex functions is that it is known that over the interval of convexity there is only one minimum.
www.engineering.usu.edu /classes/ece/7680/lecture2/node5.html   (373 words)

 New developments in convexity theory
S. Dragomir, On Hadamard's inequality for the convex mappings defined on a ball in the space and applications, Math.
C. Niculescu, Convexity according to the geometric mean, Math.
P. Roselli and M. Willem, A convexity inequality, Amer.
rgmia.vu.edu.au /inequalities2001/niculescu/niculescu.html   (223 words)

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