Economics curves

Yield curve

In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. According to finance scholar Dr. Frank J. Fabozzi, investors use yield curves to price debt securities traded in public markets and to set interest rates on many other types of debt, including bank loans and mortgages. Shifts in the shape and slope of the yield curve are thought to be related to investor expectations for the economy and interest rates. Ronald Melicher and Merle Welshans have identified several characteristics of a properly constructed yield curve. It should be based on a set of securities which have differing lengths of time to maturity, and all yields should be calculated as of the same point in time. All securities measured in the yield curve should have similar credit ratings, to screen out the effect of yield differentials caused by credit risk. For this reason, many traders closely watch the yield curve for U.S. Treasury debt securities, which are considered to be risk-free. Informally called "the Treasury yield curve", it is commonly plotted on a graph such as the one on the right. More formal mathematical descriptions of this relationship are often called the term structure of interest rates. (Wikipedia).

Yield curve
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How to draw the slope field and sketch the particular equation

Learn how to create slope fields and sketch the particular solution to a differential equation. Slope fields are tools used to graphically obtain the solutions to a differential equation. It is the estimation of the graphical representation of a differential equation using the slopes of th

From playlist Differential Equations

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How to sketch the slope field

Learn how to create slope fields and sketch the particular solution to a differential equation. Slope fields are tools used to graphically obtain the solutions to a differential equation. It is the estimation of the graphical representation of a differential equation using the slopes of th

From playlist Differential Equations

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This video introduces slope fields and shows how to graph a slope field

From playlist Introduction to Differential Equations (Calculus I)

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This lesson explains how to graph a line given a point on the line and the slope of the line. The concept of slope is emphasized. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)

From playlist Graphing a Linear Equations in Slope-intercept form: y=mx+b

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Using the partial derivatives of a multivariable function to construct its gradient vector.

From playlist Advanced Calculus / Multivariable Calculus

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A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.

From playlist Advanced Calculus / Multivariable Calculus

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Graphing a linear equation in slope intercept form

👉 Learn how to graph linear equations given the slope and the y-intercept. When given the slope and the y-intercept of a linear graph, we first plot the y-intercept and using the slope, we can determine the rise and the run of the required line and then be able to plot the next point from

From playlist ⚡️Graph Linear Equations Using Slope and Y-intercept

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Graphing a linear equation in slope intercept form

👉 Learn how to graph linear equations given the slope and the y-intercept. When given the slope and the y-intercept of a linear graph, we first plot the y-intercept and using the slope, we can determine the rise and the run of the required line and then be able to plot the next point from

From playlist ⚡️Graph Linear Equations Using Slope and Y-intercept

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Par yield

The yield (aka, yield to maturity, YTM) is the single rate that correctly prices the bond; it impounds the spot rate curve. For each coupon bond, there is a different implied yield. The PAR YIELD is the yield (YTM) for a bond that happens to price at par, and therefore is equal to this bon

From playlist Bonds: Yields

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👉 Learn how to graph linear equations given the slope and the y-intercept. When given the slope and the y-intercept of a linear graph, we first plot the y-intercept and using the slope, we can determine the rise and the run of the required line and then be able to plot the next point from

From playlist ⚡️Graph Linear Equations Using Slope and Y-intercept

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Fixed Income: Twists are steepening or flattening of the yield curve (FRM T4-23)

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From playlist Valuation and RIsk Models (FRM Topic 4)

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Fixed Income: Yield to Maturity (FRM T4-29)

Financial Risk Manager (FRM, Topic 4: Valuation and Risk Models, Fixed Income, Bruce Tuckman Chapter 3, Returns, Spreads and Yields). Yield to maturity (aka, yield) is the single rate that discounts a bond's cash flows to a present value that matches the bond's traded (observed) price. Dis

From playlist Valuation and RIsk Models (FRM Topic 4)

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Why par yields are the best interest rate measure

Par yields are the best interest rate because they summarize the spot rate term structure into a single yield measure. I also show the so-called "coupon effect" which is also an argument in favor of par yields. But I think the better reason is their information content. Yield to maturity (

From playlist FRM applications

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BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology

From playlist BEM1105x Course - Prof. Jakša Cvitanić

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FRM: Comparison of spot curve, forward curve and bond yield

A simple comparison using a 2.5 year $100 par 6% semiannual coupon bond. Spot rate: the yield for each cash flow that treats the cash flow as a zero-coupon bond. A coupon-paying bond is a set of zero-coupon bonds. Forward rate: the implied forward rates that make an investor indifferent to

From playlist Bonds: Introduction

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FRM: Bootstrapping the Treasury spot rate curve

The theoretical spot rate curve is different than the par yield curve. Here is how to bootstrap the spot rate. For more financial risk videos, visit our website! http://www.bionicturtle.com

From playlist Bonds: Introduction

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Introduction to the yield curve | Stocks and bonds | Finance & Capital Markets | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/stock-and-bonds/bonds-tutorial/v/introduction-to-the-yield-curve Introduction to the treasury yield curve. Created by Sal Khan. W

From playlist Stocks and bonds | Finance and Capital Markets | Khan Academy

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The yield curve | Stocks and bonds | Finance & Capital Markets | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/economics-finance-domain/core-finance/stock-and-bonds/bonds-tutorial/v/the-yield-curve Annual Interest Varying with Debt Maturity. Created by Sal Khan. Watch the next

From playlist Stocks and bonds | Finance and Capital Markets | Khan Academy

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From playlist Determining Rate of Change and Slope

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Norm (mathematics) | Cox–Ingersoll–Ross model | Heath–Jarrow–Morton framework | LIBOR market model | Interpolation | Geometric mean | Supply and demand | Basis point | Bessel process | Interest rate risk | Arbitrage pricing theory | Yield to maturity | Risk-free rate | Nelson-Siegel | TED spread | Bootstrapping (finance) | Short-rate model | Zero interest-rate policy | Interest rate swap | Kernel (statistics) | Leverage (finance) | Spline (mathematics) | Ornstein–Uhlenbeck process | Federal funds rate | Curve fitting | Linear programming | Hull–White model | Multi-curve framework