In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation, or getting access to otherwise hard-to-trade assets or markets.
Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges.
Derivatives are one of the three main categories of financial instruments, the other two being equity (i.e., stocks or shares) and debt (i.e., bonds and mortgages). The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed in 1936, are a more recent historical example.
Hey there. So during break, I'm going to try and refreshen up what I have learned over the summer on Calculus for next semester. I downloaded the M.I.T video lecture series for Calculus I with David Jerison. The lecture series is good, however I have a question. In his first lecture, he starts...
1. Find the derivatie of y, dy when e/\(y) cos x=1 + sin (xy)
---
dx
2. I don't know of any Relevant equations
3. The first time i tried the problem i got e/\(y) cos X+ y cos (xy)...
Homework Statement Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates, r = \sqrt{(x^{2}+ y^{2}})
show that \frac{\partial T}{\partial x} = \frac{x}{r} \frac{dT}{dr}
Just a quick question...
To calculate a directional derivative of f(x,y) at the point \vec{u} in the direction \hat{v}, can I just use the formula...
\nabla f(\vec{u}) . \hat{v}?
It would be so easy.
V_{a;b} = V_{a,b} - \Gamma^d_{ad}V_d
Now take the second derivative...
V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{ac}V_{f;b} - \Gamma^f_{bc}V_{a;f}
But I have no idea how to get the parts with the Christoffel symbols.
V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{(a;b)c}V_{af} = (V_{a;b})_{,c} -...
Homework Statement
I've been given equations that have derivatives as initial conditions, rather than things like u(0,t)=u(L,t)=0
Things like this:
http://img444.imageshack.us/img444/5082/mathu.th.jpg
Uploaded with ImageShack.us
Homework Equations
The Attempt at a...
Hi!
Please can anyone help me to understand what exactly Integration & derivatives are.
Please don't tell in form of limits & continuity. But tell in details of , what we exactly do when we use these functions. Please explain with a practicle example.
I will appreciate your efforts...
Homework Statement
Using Maple, I'm asked to create a quintic function, in the form of ax^5+bx^4+cx^3+dx^2+ex+f given the following data:
It will pass through the points (-5,15), (-5/2, 100), and (10, -5)
-f'(5)=(-1)
-f''(5)=1
Homework Equations
How would I go about doing this? I'm allowed to...
Hi, I'm a new member to the forum, and I'm currently studying Calculus.
Basically, derivatives can be written as (dy/dx) in Leibniz's notation, but I remember my teacher saying that it's just a symbol and shouldn't be used like two variables (dy and dx)...
However, when there's some integral...
In statistical mechanics we express partial derivatives of functions, keeping some variables fixed. But these variables are functions of the other variables (which are not fixed).
I'm just confused by this, what is the convention for taking these derivatives? For example, if we have S as a...
I try to understand how to calculate derivatives of functions, which contain matrices.
For a start I am looking at derivatives by a single variable.
I have x=f(t) and I want to calculate \frac{dx}{dt}. The caveat is that f contains matrices, that depend on t. Can I use the ordinary chain rule...
In short, I need to know how do you do them.
I missed class, and our textbook is so bad that it might as well be written in a foreign language. I understand how to do dy/dx of an equation not in the form y =... ex. y^2 = x^3 + 2x + 5, (y'=(3x^2 +2)/2y) for example, but how would you take the...
Homework Statement
What are the upper derivative and lower derivative of the characteristic function of rationals?
Homework Equations
The Attempt at a Solution
I think they are : upper derivative = 0
lower derivative = negative infinity
Homework Statement
What is the relationship with a function's rising, falling, high point or low point to it's derivative?
The Attempt at a Solution
I have plotted my graphs, I can see that they intersect at the high and low points. But what is the relationship
Also on another...
I need to use partial derivatives to prove that
u(x,t)=f(x+at)+g(x-at)
is a solution to:
u_{tt}=a^{2}u_{xx}
I'm stuck on how I'm supposed to approach the problem. I'm lost as to what order I should do the derivations in. I tried making a tree diagram, and I came out like this. The arrow...
Now I understand the basic concept that if one derivative's velocity you get acceleration and if you integrate velocity you will get the distance. But what about in this case?Homework Statement
Homework Equations
The Attempt at a Solution
Homework Statement
Using logarithmic differentiation calculate the derivative of y=e^(x^x)
The Attempt at a Solution
y=e^x^x
LNy=LNe^x^x
LNy=x^xLNe
...
Stuck!
This seems to be the only way you can do it, but once I get to that part I'm not sure what else there is to do. I...
I need to find the derivative of the square root of (2x+1) (not sure how to do square root symbol here, sorry)
I understand that the square root of (2x+1)= (2x+1)^(1/2), but I am getting a little confused on how to continue from there.
sorry folks i don't even have an idea to this question`s solution so i hope u people may like to help me. i`m stuck to it since last week nd i hope its from partial derivative... please suggest me a book or a hint or the solution.
Let a long circular cylinder of unit radius be placed in a large...
For example, if I want to show that there is no real # solution to
x2 + 24x2 = -1
is it correct to show that
d2/dx2( x4 + 24x2 ) = d2/dx2(-1)
---> 12x2+48 = 0
And since x^2 is >0 or =0, 12x2+48 ---> 0 + 48 \neq 0
Therefore, there is no real number solution to x2 + 24x2 = -1...
Homework Statement
find the dy/dx
of y = Sin4 x2 - Cos4 x2
Homework Equations
derivatives and identities
factoring
dy/dx (Sinx) = Cosx
dy/dx (Cosx) = -Sinx
The Attempt at a Solution
y = (Sin2 x2 - Cos2 x2) (Sin2 x2 + Cos2 x2)
im stuck at this part i don't know how to...
Homework Statement
y=(sin2x)(cos2)
Homework Equations
Product Rule for Derivatives
identities:
derivatives of
Sinx = Cosx
Cox = -Sinx
The Attempt at a Solution
i used the product and chain rule for derivatives then do the identities
y = sin2x*cos2x
dy/dx = (Cos2x)(2)...
Homework Statement
A straight line is drawn from the point (0,a) to horizontal axis, and then back to (1,b). Prove that the total length is shortest when the angles \alpha and \beta are the same.
2. Homework Equations /graphs
[PLAIN]http://dl.dropbox.com/u/23215/Graph.jpg
The...
Homework Statement
Show that the expression A,
T(dP/dT)|V - P
is equal to expression B,
T^2 * [d(P/T)/dT]|V
Also, show that expression C,
-[d(P/T)/d(1/T)]|V
is also equal to expression B
Homework Equations
A: temperature * (dPresure/dTemperature at constant volume) -...
Homework Statement
is the derivativethe same thing as the slope of the function for which we're finding the derivative?
Homework Equations
The Attempt at a Solution
Homework Statement
Find y'' if y=1/3(1+cos^2(√x))
Homework Equations
The Attempt at a Solution
Now I believe I got the first derivative right since the teacher marked ir right, but my real question here is what do I do with the 1/3? Is it ok to throw away the constant when I...
Homework Statement
find the largest distance and shortest distance from the origin to the conic whose equation is
6x2 + 4xy +3y2 - 28=0
and hence determine the lengths of the semi axes of this conic
Homework Equations
Lagrange identity
F= f + λφ = 0
distance = d2 =x2+ y2+...
Homework Statement
Find the absolute maximum and minimum values of f on
the set D.
f(x,y) = 1+4x-5y
D is the closed triangular region with vertices (0,0) (2,0) (0,3)
Homework Equations
To find the absolute maximum and minimum values of a continuous function
on a closed, bounded set :
1. Find...
Homework Statement
Show that there is a polynomial function f of degree n such that:
1. f('x) = 0 for precisely n-1 numbers x
2. f'(x) = 0 for no x, if n is odd
3. f'(x) = 0 for exactly one x, if n is even
4. f'(x) = 0 for exactly k numbers, if n-k is odd
Homework Equations
The...
Hi,
I have a coupled system of ODE like:
w1'' = A w2'' + B w1 + C w2
w2'' = D w1'' + E w1 + F w2
I need to solve it analytically but it seems it cannot be solved using eigenvalue method. My concern is first that if this system have sufficient equations and if so how it can be solved...
Ok, I just had a lecture recently the attached picture is what it was about. I understand it all, however at the end it says we havnt proven it yet - just wondering how DO you prove it then?
Thanks,
Owen
Homework Statement
I have no homework problem to ask, but rather a general question.
Ill give and example of a potential function V = 3x^2 + 2y^2
i know to find Fx i have to differentiate 3x^2 with respect to x and 2y^2 with respect to y. But i have seen cases where someone takes the...
Homework Statement
Show, with appropriate examples, that the conditions g(x) < f(x) < h(x) and derivative(g(x0))=derivative(h(x0)) = m does not imply derivative(f(x0)) = m or even exists. And with some additional condition.
Homework Equations
derivative g(x) = lim(h tends to zero)...
Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers!
Let f(x)=−3x+6 if x<-3
= 15 if x > -3
Find the average rate of change of f(x) on the interval −5<x<5 .
The average rate of...
Homework Statement
calculate the derivative of the following functions?
f(x,y,z,t) = (x-1)(2-y)z + (t^3 - 1)xyz
g(x,y) = 1/(1 + exp(-(ax + by + c))
h(x,y,z) = (x-1)^2 exp(x) + (y-2)^3 * z^3
The Attempt at a Solution
the way i was thinking was may be split the problem into...
Hi there. Well, I wanted to know how to find the second derivatives of a function using implicit differentiation. Is it possible? I think it is. I think I must use the chain rule somehow, but I don't know how... I'm in multivariable calculus since the function I'm going to use could be seen as a...
Homework Statement
proving the nth derivative of x to the n power is n factorial
Homework Equations
The Attempt at a Solution
proving it for n=1
d^(1)x^1/dx = 1!=1 (a)
d/dx x^1 =1 (b)
a=b therefore at n=1 it is true
supposing it is true for n=k
then d^(k)x^k/dx = k...
Homework Statement
The problem is : take the derivative of (x - a)
Homework Equations
Power Rule : f '(x) = r x^(r-1)
Difference Rule : f '(x) = g '(x) - h '(x)
The Attempt at a Solution
This is such a simple problem but I don't understand how my solutions manual and Wolfram...
I'm having issue with one problem. We're asked to break down the problem into partial fractions to solve for the integral.
Well, I'm stuck on one. I'm being asked for the values of A, B, and C for the following problem.
∫((9x^2+13x-83)/((x-3)(x^2 + 16)))dx
I can get it worked down...
Homework Statement
The function given to me is F(x) = A + Bx.
x is the displacement, F(x) is the force as a function of that displacement, and A and B are constants.
From the function, I'm supposed to find the velocity of the function as a function of x.
We also know that the items...
Homework Statement
f(x) = 10(sin(x))^x ----> find f '(1)
The Attempt at a Solution
I have tried several different approaches, but still get stuck with a wrong answer every time
f(x) = 10(sin(x))^x let f(x) = y so y=10(sin(x))^x then ln y = ln10(sin(x))^x...
I have a question about these two. I have a direction derivative at a in the direction of u defined as:
f'(a;u) = lim [t -> 0] (1/t)[f(a + tu) - f(a)]
And the partial derivative to be defined as the directional derivative in the direction of u = e_i.
My text, Analysis on Manifolds by...
Homework Statement
find the equation on the tangent plane of yz=ln(x+z) at point (0, 0, 1 )
Homework Equations
Tangent plane equation...
The Attempt at a Solution
I wasn't sure how to determine the partials on this equation. My attempt was to rearange as ln(x+z)-yz=0 so Fx =...