...with is: y'=(2(2)-3)(e^((4-6+12)*ln8) y'=e^(10*ln8) The deivative of a^f(x) is a^f'(x) ln (a), where a is a consatnt. y=8^((x^2)-3x+12) y' = 8^((x^2)-3x+12) (2x-3) ln (8) y'= 8(2x-3) 8^((x^2)-3x+12) when x=2 y'=8(1)8^(4-6+12) =8 8^10 =8^11 lny=(x^2-3x+12)ln8 1/y(dy/dx) = (2x - 3)ln8 then you multiply by y, remembring that you had y=.. at the start an substituting that in dy/dx = 8^(x^2-3x+12)*(2x-3)ln8 so when x=2 dy/dx = 8^(4 - 6 +12) * ln8 dy/dx = 8^10*ln8 = 2232783354 to a whopping 10 s.f. but they usually just want the answer in terms of ln ln(a / b) does not equal ln(a) / ln(b), from the property of logs, split the log into two separate logs through subtraction: y = ln(x + 2) - ln(x - 1) Now take the derivative of each term: dy/dx = [1/(x + 2) * 1] - [1/(x - 1) * 1] dy/dx = 1 / (x + 2) - 1 / (x - 1) Optionally, you can make the denominators common and combine them into a single fraction: dy/dx = -3 / (x - 1)(x + 2) ln [base m] x = ln(x) / ln(m) This is how you convert log of any base to log of base e. log[base5] (x + 2) = ln(x+2) /ln(5) log[base7] { ln(x+2) /ln(5) } = ln (ln(x+2) /ln(5)) / ln(7) log[base3] { ln (ln(x+2) /ln(5)) / ln(7) } = ln ( ln (ln(x+2) /ln(5)) / ln(7) ) / ln(3) f(x) = [1/ln(3)] ln ( ln (ln(x+2) /ln(5)) / ln(7) ) let k = [1/ln(3)] Let ln (x+2) /ln(5) = u f(x) = k ln ( ln (u) /ln(7) ) f'(x) = k [1 / ( ln (u) /ln(7) ) ] d/dx[ ( ln (u) /ln(7) ) ---(1) d/dx [ ln (u) / ln(7) ] = 1/ln(7) (1/u) du/dx...
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...WAS THE POTENTIAL INDIRECT EFFECT OF THIS CATEGORY INVESTOR FAILURE? 7 DOES THE RESCUE OF INSTITUTIONS LABELLED “TOO BIG TO FAIL” 9 Strengthen the long term stability of financial services sector? If so, how? 9 Encourage excessive risk taking in the knowledge of an implicit “safety net”? If so, explain why 9 WAS THIS A CASE OF CRONY CAPITALISM? 10 REFERENCES: 11 WHAT ARE HEDGE FUNDS? Hedge funds are private investment funds that aim to make profits for their shareholders by trading securities. Hedge fund utilises a variety of financial instruments to reduce risks, enhance returns and minimise the correlation with equity and bond markets. They are flexible in their investment options and can use short selling, leverage, derivatives and arbitrage. Hedge funds are defined by their freedom from regulatory controls, stipulated by the Investment Company Act of 1940 or the Security Exchange Commission. Hedge funds do not have to disclose their activities to third parties, they offer a high degree of privacy for their investors and generally they take significant risks. They are actively managed investment portfolios holding position in publicly trading securities and...
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...Derivatives and Hedging Over recent years, the volatility in the financial markets has increased due to substantial changes domestically and internationally. This has given rise to increased financial price risks faced by both domestic and multi-national companies. Financial Derivatives are widely used by corporations to adjust to exposure to currency risk, interest rate risks, commodity price risks, and security holdings risk. Largely, companies are currently exposed to risks caused by unexpected movements in exchange rates and interest rates. Companies with a growing global presence are especially exposed to a wide range of financial risks, in particular foreign exchange risks and interest rate risk. Although, financial risks are the center of business operations of financial service firms, but they also impact the risk exposure of non-financial corporations. The management and supervision of these risks has become vital for the existence of companies in today’s unpredictable financial markets. The major financial risks that most firms are exposed to are interest rate risk, currency rate risk, commodity price risk, and security holdings risk. Interest rate risk is a very common type of risk, and result from a discrepancy in the sensitivity of a firms assets and liabilities to interest rate movements. On the other hand, currency risk exposure is virtually encountered by all firms, even if their exposure is not from a transaction or a translation risk. Many firms are...
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...$2331000 of accrued wages. The wages were all earned within the past 2 weeks, and no single employee is due more than $2000. Long-term bank loans actually consist of two different loans: $5 million in straight unsecured debt, plus another $4563000 in loans that are subordinate to the $5 million loan. In recent times, with the financial markets strengthening up, more and more people entering this financial market as players, there arises the need to further increase the scope of the financial markets which primarily dealt in stocks and debt. This lead to the rise of the product: derivatives. Derivatives are those financial instruments which derive its value from its underlying asset, the asset can be anything. The scope of derivatives has been really widening. So, this assignment also focuses on some of the derivatives like futures, options, forward rate agreements and swaps. These derivatives were earlier designed to cover the risks from uncertain conditions, or rather for the purpose of hedging; however they have been widely used for further purposes like speculation, different forms of trading, arbitraging, etc. Of course, future cash flows cannot be predicted with certainty. The greater the banks confidence in a companys future cash flow, the more it will be willing to lend against it. A critical part of a credit officers expertise is to make judgments about the relative risks to a companys cash flow posed by unforeseen events, both external to the company (changes...
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...should help you in this test, you must recognize that the format of an electronic assignment does not enable certain types of questions to be asked. Therefore, you need to prepare for different types of questions in addition to those you encounter in assignments. This is especially true in view of the fact that, for instance, it is difficult in an e-assignment to ask for intermediate work in obtaining a derivative starting with its definition – namely using a limit. In the following I will attempt to give a flavour of how some questions may be worded.] There will be 4 questions of equal weight, drawn from various topics. It is entirely possible that a topic found in the text but not appearing below may appear in your test, i.e. what appears below does not constitute an exhaustive list of examinable topics. 5 possible questions are presented below. lim trig expression involving a&h Q. a) If a and b are constants, evaluate h→0 trig expression involving b&h A correct answer without detailed reasoning will be given little merit. b) Something involving related rates. Q. Obtain the derivative of the following functions, and simplify as far as possible: … functions not shown…say two different part questions involving log,...
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...BUSINESS INTELLIGENCE USING SAS PROJECT ON “PUT CALL PARITY ON NIFTY INTRADAY DATA” AT INSTITUTE OF MANAGEMENT TECHNOLOGY, HYDERABAD BY ADITI GUPTA SHIWANI SHARMA SWATI TOMAR TULIKA CHAMADIA APPROVED BY DR. CHAKRAPANI (ASSOCIATE PROFESSOR) DATE OF SUBMISSION 15th October, 2013 ACKNOWLEDGMENT We would like to thank several people for their support and encouragement during the project without which this project would not have been a success. At first, we would like to extend my thanks to our Project Mentor/Guide Dr. Chakrapani, Associate Professor at Institute of Management Technology, Hyderabad, who gave us such a nice subject and project to work on which helped us to get the insight on the subject. Apart from this he always helped and guided us at every point of time of the project. He has been a continuous guide for putting in the correct efforts as well as how to improvise on the quality in time. He has been a great support in bringing this project to the desired format. At last we would also like to extend a special thanks to the other project members, friends and family who always supported us throughout the project. Table of Contents ACKNOWLEDGMENT 2 1. INTRODUCTION 4 OPTION CONTRACT 4 TYPES OF OPTION CONTRACT 4 OPTION PRICING 4 INTEREST RATES AND DIVIDENDS 5 PUT-CALL PARITY 6 2. PUT-CALL PARITY INTRADAY ON INDEX DATA 6 OBJECTIVE 6 METHODOLOGY 6 FINDINGS 7 CONCLUSION: 9 PROGRAM: 9 1. INTRODUCTION OPTION...
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...Futures, Options, Swaps Financial Derivatives Commodity Derivatives 1 Derivatives – Overview • Financial instrument or security whose payoffs depend on another instrument or security • Price of instrument a derivative of underlying security – Farmer who sows a crop in June, faces uncertainty over the price received at harvest time in September – Merchant/ consumer faces a price in September as well – Farmer, merchant negotiate on a price in June for settlement in September • Chicago Board of Trade 1848 • Yodoya rice futures in 1650 • Forwards, Futures, Options, Swaps 2 Derivatives - Definitions • Forwards – involves a contract initiated at one time, performance in accordance with the terms of the contract occurs at a subsequent future time • Futures – type of forward contract with standardized and closely specified contract terms – – – – Traded in organized exchange Standardized, specific quantity, delivery date, mechanism Performance guaranteed by clearinghouse Margins – good faith deposit with the exchange • Option – the right to purchase underlying good at a specific price until a specific date – Calls and Puts • Swaps – Agreement between two or more parties to exchange sequence of cash flows over a period in the future 3 Derivatives - Applications • Price risk elimination • Speculation • Market completeness • Information efficiency • Trading efficiency 4 Derivatives - Markets • Commodity Derivatives: underlying asset a commodity –...
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...Risk management has developed into business segments that differ from the traditional insurance applications. Georgia Pacific (GP) has more than 400 locations and 61,000 employees in North America and Europe. Risk management applications in the areas of foreign currency and political issues need to be addressed to be a success in the international market. Risk management is ultimately the economic impact on the company, so methods have been developed companies have used to adapt to the changing business environment. Financially GP uses a credit line and bonds for funds when cash flow is unable to cover capital requirements. The line of credit is at 2.3% but has restrictions on debt ratios that must be followed to maintain this low rate (GP Proxy Statement). In the last few years GP has struggled in the sluggish economy and has had net losses from 1999 to 2002 so bonds have been used to replace some of the credit line because the ratios needed to keep the credit line may not be maintainable in the near future. In May, 2003 GP offered $500M in notes, with $350M at 7.375% due in 2008 and $150M at 8% due in 2014. The higher interest rates for the notes have to be paid because the debt ratios required by the credit line can not be maintained and there is a risk of default for the higher interest rates. Options are another risk management method GP utilizes. Options are guarantees to buy or sell a stock at a specified value by a given date. One method used to valuate options...
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...the United Kingdom banking and financial services industries. The BBA defines LIBOR as: The rate at which an individual Contributor Panel bank could borrow funds, were it to do so by asking for and then accepting inter-bank offers in reasonable market size, just prior to 11:00 [a.m.] London time. We can also define LIBOR as an indicative average interest rate at which a selection of banks (the panel banks) are prepared to lend one another unsecured funds on the London money market. Investors around the world use the LIBOR to calculate the interest rate on myriad forms of debt, from home mortgages and credit cards to municipal bonds and derivatives contracts. The Commodity Futures Trading Commission, which doggedly pursued the wrongdoing and brought the scandal to light, estimates that some $350 trillion worth of derivatives and $10 trillion worth of loans are based on LIBOR. LIBOR CALCULATION The LIBOR interest rates are not based on actual transactions. On every...
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...a. They can go public through an IPO Baderman Island Resort is a self-contained resort, surrounded by Kelsey Island. It is all inclusive resort that offers almost unlimited activities for entertainment as well as relaxation. The resort has plenty of opportunity for expansion but they have to decide which option is best for their organization. One option is through an IPO (Initial Public Offering). A SWOT analysis is the best way to investigate this option. Strengths: An IPO brings new capital quickly for expansion in order to make the resort more profitable and offer more activities for the visitors. It also makes the stock more valuable for the investors. Expansion of the resort makes the resort more appealing to the public which will in turn make more money for the resort and the investors. Weaknesses: With investors, there are more splits in the profits as well as more red tape to make decisions within the company. Although the organization is making more profits, it has to be divided amongst the investors and the company. On top of that, the organization has to answer to a board of directors in order to make changes or expansions to the property. There has to be a vote before a decision can be made to any of the existing or future amenities that the resort holds. Opportunities: With an IPO, there is opportunity to make changes to the resort. Expansion is an option which gives the company more value. This gives more stock options which in turn brings in more money. Once...
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...============================================= Forex Risk Management in International Banking – Case study # 2 ============================================= Sleeper Pty Ltd manufacture bedroom furniture. On 30th March you call to see their financial director to discuss renewal of their banking facilities and you are given to understand that the Company has signed a contract with German suppliers to purchase sufficient materials to cover the next 6 months requirement. The Company has agreed to buy 10,000 loads of timber at $ 100 a load and payment will be effected in two equal amounts on the 30th June and on 30th September. The rates of exchange for AD/DEM on the day of your visit are as follows: Buy Sell 30th March 1.4410 1.4108 Forward Margins (Assume a discount) 1 month .0108 .0133 3 months .0320 .0345 6 months .0606 .0634 The financial director tells you of his pleasure at having obtained an AUD contract as opposed to one where the payment would have to have been in Deutschemarks. The Director feels that the company has benefited because the cost of timber was originally quoted as DEM 1,450,000 (AUD 1 = DEM 1.45) where as the Company will only be paying AUD 1,000,000. You discuss the matter fully with your customer and explain that you would have been able to have arranged forward cover for the Company within its existing facilities without a strain on its resources. During the meeting you discuss whether or not there...
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...Question 1 What was the motivation to issue Nikkei-linked Eurobonds? The motivation for the European bank issuers of the Eurobonds, wasthe possibility to get U.S. dollar finance for a lower interest rate. Toachieve this, the issuer could sell the embedded put to Goldman Sachs. The profits from the put offset the difference between the 7%coupon they paid on the bonds and the desired LIBOR floating rate. The payment from the put covered the cost paid to the swapcounterparty for hedging the exposure to the Yen-Dollar exchangerate and swapping the LIBOR for a higher coupon rate. The European financial institution was left with a fully hedged U.S. dollar financing with a lower than normal coupon rate.Furthermore, due to some specific administrative regulation in Japan, the demand for these kind of coupons was high. In Japan,companies where not allowed to pay dividend out of capital gains. Moreover, dividend payments where an important factor in gaining an competitive advantage. Therefore, this bond construction allowed the Japanese life insurers (investors) to use the coupon rateto pay out dividend while still maintaining an exposure to the Nikkei. How are the puts embedded in the Nikkei-linked Eurobonds? A normal bond to Japanese institutions would pay a coupon rate lessthan 7%. The amount by which the 7% exceeded the normal couponrate can be seen as the put premium paid by the issuer. If, atmaturity, the Nikkei dropped below a pre-determined value (hencethe theoretical strike...
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...is about the branch of mathematics. For other uses, see Calculus (disambiguation). | It has been suggested that Infinitesimal calculus be merged into this article or section. (Discuss) Proposed since May 2011. | Topics in Calculus | Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus | Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities:Power rule, Product rule, Quotient rule, Chain rule | [show]Integral calculus | IntegralLists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order | [show]Vector calculus | Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem | [show]Multivariable calculus | Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian | | Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of...
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...COURSE: MATHEMATICS I (MTH 101) SYLLABUS I. Basic algebra: Linear and quadratic equations, Solving linear and quadratic equations, Application of equations: profit, pricing, savings, revenue, sales tax, investment, bond redemption, linear inequalities, applications of inequalities: profit, renting verses purchasing, leasing versus purchasing, revenue, current ratio, investment, Maple session on solving linear, quadratic and higher degree equations, solving inequalities II. Functions and Graphs: Introduction to functions, domain and range of a function, Applications: demand, supply and profit functions, demand and supply schedule, value of business, depreciation, Special functions: polynomial, rational, piecewise defined functions, Absolute value function, and evaluation of such functions. Combination of functions. Applications: cost, investment, sales, profit, business, Graphs of functions: linear, quadratic, piecewise defined functions, graphing of quadratic functions by finding vertex, Applications on graphs: inventory, debt payment, pricing, revenue and profit, demand and supply curves, Maple session on functions and graphs III. Lines and Systems: Equation of a straight line, slope and intercept of a line, parallel and perpendicular lines, Applications: price-quantity relationship, production levels, cost, revenue, demand and supply equations, isocost line, isoprofit line, depreciation, appreciation, systems of linear equations, solution of system...
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...Project Report On “DERIVATIVES – THE BEST TOOL IN INDIAN MARKET TO GET THE OPTIMUM RETURNS” ACKNOWLEDGEMENT We take this opportunity to place on record our grateful thanks & sincere gratitude to those who gave us valuable advice & inputs for our studies. Our study could not have been completed if we had not have been completed if we had not been able to get the reference material from the company. Whenever & whatever we present today has been made possible by true efforts & kind support of our project guide Mr. Akhilesh Rathi, Head, SNR Securities & Finance, Indore. We express our sincere regards & feel paucity of word to express our utmost gratitude toward him for providing us the necessary resources, worthwhile suggestions & constant guidance. We also like to express our thanks towards other staff members of SNR Securities & Finance who inspired us to put in our best efforts for the completion of the project. PREFACE Financial system is the mirror reflection of an economy. The performance of any economy to a large extent is dependent on the performance of the Financial Institution. Financial system plays an important role by mobilizing saving and allocating them to the most profitable activities, and enables society to make more productive use of its scarce resources. The Financial system consist of many institution, instruments, and markets. Financial Institution range from moneylender to banks, pension funds, insurance...
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