Derivatives tend to be an intricate topic in accounting. So to begin, a basic understanding of derivatives is that they are a binding contract between two or more parties. The contract is for a future transaction of some underlying financial asset. The purpose for companies to implement derivatives are to aide them in managing risk by using a type of financial forwards, futures, options, or swaps. For example, a forward contract is when Company A believes Company B’s stock price will substantially increase over the next year. However, Company A does not have the resources to purchase the stock today. Therefore, Company A and B enter a contract for delivery of 10,000 shares of Company B in one year at an agreed upon price. Furthermore, this…
proportional constant (often negligible), hv is photon energy, EQD is bandgap energy, n based on the transition type (n = 1/2 for direct allowed transitions), and α is absorption coefficient. Kubelka-Munk Equation (3): approximation of α .5 f(R)=(1-R)2/R=k/s (3) Where R is reflectance, k is the molar absorption coefficient, and is scattering coefficient. However, this method…
Once the model was created the formula was used. Finally, a formula was created that could remove the risk from investments. Many financial derivatives were invented to exploit the BS formula. So after the academics received the Nobel price, LTCM (long term capital management) was created (smart guys going to the market). In 1995 the hedge fund LTCM (long term capital management) was created. The Nobel prize winners had no problem raising the capital and became what could be the team of the…
For the application of Hopf’s bifurcation theory to the system (29) (see [Marsden J.E., M. Mckracken, 1976]), it is required to satisfy the following transversality condition (34) Substituting , and into (31), and calculating the derivatives with respect to , we obtain (35) where Since , we have , and . Hence there is a Hopf bifurcation at . We have the following result: Theorem 13. Suppose holds. Then the system (29) undergoes a Hopf…
The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
isomeric forms 1, 2, 3-triazole and 1,2,4-triazol with common molecular formula C2H3N3,and both have 69.06 molecular weight. [2]] 1, 2, 4-triazole derivatives simply exist in solid forms. 3, 4, 5-substituted 1, 2, 4-triazole derivatives melts on thermolysis when heated at high temperature3160C for half an hour. 1, 2, 4-Triazole derivatives are easily soluble in polar solvents and slightly soluble in non-polar solvents. However the solubility in non-polar solvents can be enhanced by substitution…
What are the factors affecting the prices of options? Explain the assumptions in the Black-Scholes model. In order to understand the factors that affect the prices of options, we need to understand what options are and how they work. Options are derivative assets. According to a California-based company called Optionetics (website: www.optionetics.com), "options are the most versatile trading instruments ever invented". This means, that you aren 't limited to making a profit only when the market…
On 1705, Newton’s career was known by everyone and he was knighted by Queen Anne of England. He died on March 31, 1727. Back to the Fundamental Theorem of Calculus. This theorem is a simple theorem that establishes the relationship between the derivative and the integral and as we said before has two parts. The first part that talks about the relationship between the derivative and the integrals and the second part that tells us how to calculate a definite integral. The easiest way to…
According to Hull, J (Options, Futures and other derivatives: page 7); Options are traded both on exchanges and in the over-the-counter markets. There are two types of option; there is a Call Option and Put Options. The Call Option gives the owner the ability to trade a specified amount of products at a fixed price; and the put option is option which gives the owner the right to sell the underlying asset by a certain date for a certain price. And there are styles of options: American Options and…
(40) deduces the result. Other assertions follow in a similar way. Note that all D i need to be bounded for convergence as a consequence of this theorem. Theorem 3.2. Suppose that u ∈ Cp+1(Ω); s = 1; 2;∞;Ω ⊂ R2 and that uh ∈ Wh on a quasi-uniform family {Qh} of meshes on Ω into quadrilaterals. Then a necessary condition for ∥u − uh∥ Ls(Ω) = O(hp+1) is for uh to be Wp+1 s smooth. In particular, for ∥u − uh∥ L∞(Ω) = O(hp+1) a necessary condition is that all the kth partial derivatives at xi ∈ T…