...Random Walks Charles N. Moore Department of Mathematics, Kansas State University Manhattan, KS 66506 U.S.A. Abstract. We discuss the classical theorem of P´lya on random walks on the integer lattice in o Euclidean space. This is the starting point for much work that has been done on random walks in other settings. We mention a tiny fraction of this work, and discuss in detail “random walks” which can be created using trigonometric functions. 1 P´lya’s Theorem o Consider the integers {. . . , −2, −1, 0, 1, 2, . . . }. Suppose you are standing at 0. Flip a coin. If the coin comes up heads, move to the right by one step. If it comes up tails, move to the left by one step. Flip the coin again. If it comes up heads, move a step to the right, if it comes up tails, move a step to the left. Repeat and continue this process. Must you come back to zero? Obviously, there is a very good chance of returning to zero: the first two flips could have been head then tail, or tail then head, and these both result in a return to zero. So of the four possible outcomes in the first two flips, half of these take you back to zero. So the probability of returning to zero is at least 1 2 . If you further consider that even if you fail to return to zero in two steps, that after some subsequent flips you might make it back to zero, then clearly the probability of returning to zero is greater than 1 . A natural question arises: 2 What is the probability of returning to zero? The answer was given by...
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...Sources of Short-term Finance And Its Comparative Analysis There are a number of sources of short-term finance which are listed below: 1. Trade credit 2. Bank credit – Loans and advances – Cash credit – Overdraft – Discounting of bills 3. Customers’ advances 4. Installment credit 5. Loans from co-operatives ------------------------------------------------- 1 . Trade Credit Trade credit refers to credit granted to manufactures and traders by the Suppliers of raw material, finished goods, components, etc. Usually business enterprises buy supplies on a 30 to 90 days credit. This means that the goods are delivered but payments are not made until the expiry of period of credit. This type of credit does not make the funds available in cash but it facilitates purchases without making immediate payment. This is quite a popular source of finance. ------------------------------------------------- 2 . Bank Credit Commercial banks grant short-term finance to business firms which is known as bank credit. When bank credit is granted, the borrower gets a right to draw the amount of credit at one time or in instalments as and when needed. Bank credit may be granted by way of loans, cash credit, overdraft and discounted bills. ( i ) Loans When a certain amount is advanced by a bank repayable after a specified period, it is known as bank loan. Such advance is credited to a separate loan account and the borrower has to pay interest on the whole amount of loan irrespective of...
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...Future, Option and Swap are three types of stocks bought and sold in the stock market. Future means trading an instrument in the future, options give buyers the right to trade security in future and swaps are derivatives where two parties agree to exchange one stream of cash flow with another. Future Trading The future trading consists of trading of futures where the future contracts are traded on the futures exchange. The trading of future contracts or normally termed, futures involves buying or selling of some underlying instruments sometime in the future where the future date is called the final settlement date or delivery date and the pre-set price is referred to as the futures price. The price set on the underlying asset at the day of delivery date is called settlement price in futures trading. Option Trading Options are basically the financial instruments that give the buyers the right to buy or sell the underlying security within a point of time in the future for a price, which is fixed at the time when the option is bought. The stock option buyers are called the holders and sellers are called writers in option trading terminology. The ‘call’ in option trading gives the owner of option a right but not an obligation to buy an underlying security within the specified time while the ‘put’ gives the owner a right but not the obligation to sell the underlying asset within the specified time at a pre-fixed price. The value of a stock option contract is determined by...
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...FIN425 Futures Project 2 In regards to price of the futures contracts over time, both the contracts we chose seemed to fluctuate between positive and negative price changes. The crude oil contract changed at a smaller ratio compared to the e-mini. As with the price of the futures contract, the price of the underlying assets changed at a similar rate. However, because of the dates we chose, the crude oil underlying asset increased at every interval. The underlying asset for the S&P 500 did not. The basis for the crude oil future is increasing at the end of the interval. This is a negative indicator because we are selling this future. The basis for the e-mini is a negative number that is fluctuating. The negative number is a positive indicator in this case because we are buying this contract. The margin account balance for E-mini S&P 500 future was $26,300. That was found by multiplying the initial maintenance fee of $5,060 by the number of E-mini contracts purchased, which is 5. The account balance experienced rise and fall trends, with four separate occasions that required a margin call in order to keep our maintenance margin above $23,000 ($4,600 marginal maintenance per contract times five contracts). We had to invest an additional $2.8 million in order to meet our margins. The Crude oil futures margin account balance began at $38,500, found by multiply the initial maintenance $3,850 per contract, and we signed on for 10 contracts of the crude oil futures. As for...
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...BFF9515 Options, Futures and Risk management Group assignment Semester 1, 2014 Due date: 16.05.2014 BFF5915 Group Assignment Part 1 1. Compute Beta * Method: First, compute the returns of each stocks and the return of the index. They can be calculated using excel with the formula: (current price / the previous price) – 1, Second, use covariance and variance function in excel to calculate the beta of each stock. Third, multiply each beta with the corresponding weight to calculate the portfolio beta. * The beta for each stocks and the beta for portfolio (see table 1.1) Details can be seen in sheet “EquityReturnData” in the data file “Data.xlsx”. Table 1.1 The Beta(s) of Stocks and Portfolio Name | Code | Weight | Beta | CROWN RESORTS | 51333T(RI) | 7.25% | 0.8039 | COMMONWEALTH BK.OF AUS. | 314054(RI) | 7.26% | 0.8950 | NATIONAL AUS.BANK | 901842(RI) | 3.74% | 1.1317 | COCHLEAR | 871051(RI) | 3.96% | 0.8402 | WESTFIELD GROUP | 912307(RI) | 2.56% | 0.7096 | TELSTRA | 871685(RI) | 4.60% | 0.5050 | MACQUARIE GROUP | 865438(RI) | 4.36% | 1.4238 | INVOCARE | 28047X(RI) | 3.87% | 0.7210 | FLIGHT CENTRE TRAVEL GP. | 871048(RI) | 4.28% | 1.0063 | CSL | 131775(RI) | 4.89% | 0.6488 | SLATER & GORDON | 50509L(RI) | 4.79% | 0.3001 | JB HI-FI | 27736M(RI) | 4.50% | 0.8261 | CARSALES.COM | 67967W(RI) | 4.54% | 0.8459 | WOOLWORTHS | 322714(RI) | 4.86% | 0.5500 | FORTESCUE METALS GP. | 314160(RI) | 7.15% | 1.8687 | The Portfolio...
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...very comfortable and familiar with being in leadership positions and providing community service. Therefore, an opportunity such as the Honors Leadership Development Scholarship is exactly what I have been searching for. In the past, I have participated in a plethora of leadership and community service activities, such as volunteering at Mercy Hospital, Villari’s Self Defense, and with the Cumberland County Sheriff’s Office. However, I would like to highlight two instances of being in leadership positions, which accentuate my energy, passion, and drive. These involvements were with my high school’s Future Options Fair committee and with my high school’s chapter of the National Honor Society....
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...Outline future options for Melbourne’s water resource Abstract Melbourne’s water reserves in the past 10 years have been exhausted; meanwhile climate change predictions indicate the pressure of water lack will be increasingly serious (Howe et.al 2005). This problem is not just for Melbourne, Australia and many other parts of the world also face to the water shortage problem. Since there is a grave water shortage in Melbourne, the policy of sustainable water management is becoming very important. In order to prevent further deterioration of water shortage in the future, the Victorian Government made a series of countermeasures. There are several projects to solve the scarcity of water problem in the future and work out Melbourne’s future water supply needs, such as water restriction in Melbourne; spending nearly 2 billion dollars to build one of the world’s biggest water desalination plants at South Melbourne; building catchment to collect and feed rain into eight of Melbourne’s reservoirs and protecting the water catchment area; establishing two large sewage treatment plants in east and west Melbourne. The other countries also did a lot to protect water resource such as Singapore used nearly half of the national area to build water reservoir; Moscow had developed high technology for Sewage treatment system. The Victorian Government dedicated in long-term water management to protect water security and in responding to Victoria's...
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...date in the future. Derivatives are used to control risk. They can be used to reduce risk (known as hedging), or to increase risk (known as speculation) in order to enhance returns. 1 Futures Introduction A futures contract is a standardised, legally binding, marketable agreement to trade a specified asset on a specified date in the future at a specified price. The futures contract will specify the details of the transaction, with particular regard to: • Price • delivery date • type of asset to be delivered • quantity of asset to be delivered • minimum quality of asset to be delivered o this factor is important for commodity futures Note that, the ‘price’ of the future is the specified amount that is paid by the buyer to the seller on the delivery date. No money passes from the buyer to the seller at outset. Types of futures contracts Futures contracts were originally based on commodities (e.g. sugar, wheat, gold), and have been traded since the 18th Century. However, financial futures have been traded on the Chicago Board of Trade (CBOT) since 1972 and London International Financial Futures and Options Exchange (LIFFE) since 1982. In practice, futures contracts are settled ‘for cash’, rather than by the delivery of the underlying asset. The cash settlement is the difference between the price of the underlying asset at the delivery date and the price agreed at the outset of the contract. The seller of a futures contract is...
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...........................7 1.4.1 1.4.2 CHAPTER 2: DEFINITIO NS OF BASIC DERIVATIVES ............................................................... 8 2.1 FORWARDS...............................................................................................................................8 Settlement of forward contracts ............................................................................................................9 Default risk in forward contracts .........................................................................................................10 2.1.1 2.1.2 2.2 2.3 FUTURES................................................................................................................................11 O PTIONS................................................................................................................................12 Call option...
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...Chapter 9 Derivatives: Futures, Options, and Swaps Chapter Overview This chapter provides an introduction to derivatives, and examines both their uses and abuses. Reading this chapter will prepare students to: * Explain derivatives. * Understand how derivatives can be used to transfer risk. * Analyze the pricing of derivatives. Chapter Outline I. The Basics: Defining Derivatives A. Derivatives are financial instruments whose value depends on (i.e., is derived from) the value of some other underlying financial instrument or asset (these include stocks or bonds as well as other assets). B. A simple example is an interest rate futures contract, which is an agreement between two investors that obligates one to make a payment to the other depending on the movement in interest rates over the next year. C. Such an arrangement is very different from the purchase of a bond for two reasons: a. Derivatives provide an easy way for investors to profit from price declines, as opposed to the purchase of a bond, which is a bet that its price will increase. b. In a derivatives transaction, one person’s loss is always the other person’s gain. D. Derivatives can be used to speculate on future price movements, but because they allow investors to manage and reduce risk, they are indispensable to a modern economy. E. The purpose of derivatives is to transfer risk from one person or firm to another, providing a kind of insurance...
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...Project Report on Derivatives | Introduction to Futures & Options 1.0INTRODUCTION In recent times the Derivative markets have gained importance in terms of their vital role in the economy. The purpose of this report to get an orientation to the derivatives and develop a basic understanding of what it is and how does it work. Derivatives are financial instruments, which derive their value from an underlying asset. The underlying asset can be bullion, index, share, bonds, currency, interest, etc. Derivatives are likely to grow even at a faster rate in near future. The emergence of the market for derivatives products, most notably futures and options, can be tracked back to the willingness of risk-averse economic agents to guard themselves against uncertainties arising out of fluctuations in asset prices. By their very nature, the financial markets are marked by a very high degree of volatility. Through the use of derivative products, it is possible to partially or fully transfer price risks by locking-in asset prices. As instruments of risk management, these generally do not influence the fluctuations in the underlying asset prices. However, by locking-in asset prices, derivative product minimizes the impact of fluctuations in asset prices on the profitability and cash flow situation of risk-averse investors. However, the use of F&O has grown into other segments like leveraged trading and arbitrage. 2.0 OBJECTIVES OF THE REPORT: ...
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...1. INTRODUCTION TO DERIVATIVES While, trading in derivatives products has grown tremendously in recent times, the earliest evidence of these types of instruments can be traced back to ancient Greece. Even though derivatives have been in existence in some form or the other since ancient times, the advent of modern day derivatives contracts is attributed to farmers’ need to protect themselves against a decline in crop prices due to various economic and environmental factors. Thus, derivatives contracts initially developed in commodities. The first “futures” contracts can be traced to the Yodoya rice market in Osaka, Japan around 1650. The origin of derivatives can be traced back to the need of farmers to protect themselves against fluctuations in the price of their crop. From the time it was sown to the time it was ready for harvest, farmers would face price uncertainty. Through the use of simple derivative products, it was possible for the farmer to partially or fully transfer price risks by locking-in asset prices. These were simple contracts developed to meet the needs of farmers and were basically a means of reducing risk. A farmer who sowed his crop in June faced uncertainty over the price he would receive for his harvest in September. In years of scarcity, he would probably obtain attractive prices. However, during times of oversupply, he would have to dispose off his harvest at a very low price. Clearly this meant that the farmer and his family were exposed...
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...Study Material on Derivatives, Options & Futures Content No. | Contents | Page No. | | Section 1: Derivatives | | 1.1 | Derivatives: History, Meaning and Definition | 3 | 1.2 | Classification of Derivatives | 4 | 1.3 | Features, Types and Players in Derivatives | 4 | 1.4 | Forwards: Meaning, Definition & Limitations | 6 | | Section 2: Futures | | 2.1 | Meaning | 8 | 2.2 | Terminologies | 8 | 2.3 | Payoff Profile | 10 | 2.4 | Numerical Examples | 11 | | Section 3: Options | | 3.1 | Meaning | 13 | 3.2 | Terminologies | 13 | 3.3 | Payoff Profile | 15 | 3.4 | Numerical Examples | 18 | | 1.0 Derivatives Introduction: Indian Financial Markets: Where does derivative fall? From the above chart we can see that derivatives fall under secondary market channel. 1.1 Derivatives History, Meaning and Definition History Derivatives have been a recent development in the Indian financial markets. But there have been derivatives in the commodities market. There are Cotton and Oilseed futures in Mumbai, Soya futures in Bhopal, Pepper futures in Cochin, Coffee futures in Bangalore etc. But the players in these markets are restricted to big farmers and industries, who need these as an input to protect themselves from the vagaries of agriculture sector. Globally too, the first derivatives started with the commodities, way back in 1894. Financial derivatives are a relatively late development, coming...
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...........................7 1.4.1 1.4.2 CHAPTER 2: DEFINITIO NS OF BASIC DERIVATIVES ............................................................... 8 2.1 FORWARDS...............................................................................................................................8 Settlement of forward contracts ............................................................................................................9 Default risk in forward contracts .........................................................................................................10 2.1.1 2.1.2 2.2 2.3 FUTURES................................................................................................................................11 O PTIONS................................................................................................................................12 Call option...
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...Chapter 8: Foreign currency derivatives Futures contracts Options Chapter 9: Interest rate and currency swap Interest rate risk management FRAs Interest rate futures (not examinable) Swaps 2 Foreign Currency Derivatives Financial management of the MNE in the 21st century involves financial derivatives. These derivatives, so named because their values are derived from underlying assets, are a powerful tool used in business today. These instruments can be used for two very distinct management objectives: Speculation – use of derivative instruments to take a position in the expectation of a profit Hedging – use of derivative instruments to reduce the risks associated with the everyday management of corporate cash flow 3 1 Foreign Currency Derivatives Derivatives are used by firms to achieve one of more of the following individual benefits: Permit firms to achieve payoffs that they would not be able to achieve without derivatives, or could achieve only at greater cost Hedge risks that otherwise would not be possible to hedge Make underlying markets more efficient Reduce volatility of stock returns Minimize earnings volatility Reduce tax liabilities Motivate management (agency theory effect) 4 Foreign Currency Derivatives What are they? Forward contracts Futures contracts Options Swaps 5 Foreign Currency Futures A foreign currency (FX) futures contract is an alternative to a forward contract that calls for future delivery of a standard amount of foreign...
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