# Options

Words 4475
Pages 18
Chapter 3
The Time Value of Money

Solutions to Questions 1. A rate of return is the ratio of net cash inflows to net cash outflows produced by a financial contract. It is often expressed as a percentage. The ‘financial contract’ involved may be, for example, an investment in shares, land or bonds. An interest rate is a rate of return produced by debt of one form or another. Thus, an interest rate is one type of rate of return. Simple interest is a method of calculating interest in which the interest is computed on the basis of the original sum borrowed. Compound interest is a method of calculating interest in which interest is computed on the basis of the original sum borrowed plus interest owing but unpaid at the date of computation. The statement is true. The three different terms—‘present value’, ‘price’ and ‘principal’—all refer to the value of a financial contract at a given date (typically, today). ‘Present value’ tends to be used when the valuation is the result of a discounting procedure; ‘price’ tends to be used when the valuation is the result of a market transaction for a security and ‘principal’ tends to be used when the valuation refers to an amount lent by way of a standard loan. However, these circumstances are not independent; for example, a price may be offered and agreed to because a discounting procedure indicates to market participants that the price is the correct valuation. The term ‘nominal interest rate’ can mean an interest rate where interest is charged more frequently than the quoted period. For example, ‘6 per cent per annum payable quarterly’ is a nominal interest rate because interest is charged quarterly—that is, four times each year—but the quoted period is a year. The term ‘nominal interest rate’ can also mean an interest rate before taking out the effects of inflation. For example, if a lender receives interest at the rate of 5...

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#### Options

...be transferred from one party to other parties. Futures and options serve different needs in the capital market and will forever be important elements on their own in every well diversified portfolio. A futures contract is a standardized contract between two parties to buy or sell a specified asset of standardized quantity and quality for a price agreed upon today (the futures price or strike price) with delivery and payment occurring at a specified future date, the delivery date. The contracts are negotiated at a futures exchange, which acts as an intermediary between the two parties. The party agreeing to buy the underlying asset in the future, the "buyer" of the contract, is said to be "long", and the party agreeing to sell the asset in the future, the "seller" of the contract, is said to be "short". The terminology reflects the expectations of the parties—the buyer hopes or expects that the asset price is going to increase, while the seller hopes or expects that it will decrease in near future. Buyers of the futures contracts put up a fraction of the price of the underlying asset when the contract is entered upon. This upfront payment is like the down payment you pay when buying a house, which means that the futures contract itself does not come with a premium. Buyers and sellers of futures contracts are also obligated to fulfill the futures contract agreement upon expiration but not buyers and sellers of options contracts. Because of this obligation, both parties are......

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#### Real Options

...Options Theory Applied to Alternative Energy Industry Christina Clowdus Bus: 630 March 20, 2012 Dr. Shaw Introduction In life, you always have options. It is no different in capital investment. In today's unpredictable business world, managers recognize how risky the most valuable investment opportunities often are, and how useful a flexible strategy can be. That's why they want to know all their options. Yet many current financial assessment tools fail to identify what investors can do to capitalize on future uncertain events. “Managerial flexibility to adapt and revise future decisions in order to capitalize on favorable future opportunities or to limit losses has proven vital to long-term corporate success in an uncertain and changing marketplace” (Brennan, M.J. and E.S. Schwartz 1985, p. 15). Utilizing a real options strategy allows businesses to capture the value of managerial flexibility in adapting decisions in response to unexpected market developments. When used as a conceptual tool, real options allow management to characterize and communicate the strategic value of an investment project (Bjerksund, P. and S. Ekern 1990). Traditional methods (e.g. net present value, discounted cash flow) fail to accurately capture the economic value of investments in an environment of widespread uncertainty and rapid change. Using real options theory, managers can more effectively target crucial opportunities to redeploy, delay, modify, or even abandon capital-intensive......

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#### Options

...Dear Professor Bhattacharya, This is our written brief of case 1. As we misunderstood the instructions of question 5, we tried again to finish the problem properly. We just didn’t want to miss the great opportunity to practice our knowledge of the class so we worked on it independently. Thank you so much for your time and understanding. Best regards, Xiaolin Li, Shengyu Zhang, Riley David and Strick Jacob CASE 1 BY GROUP 1 Xiaolin Li, Shengyu Zhang, Riley David and Strick Jacob QUESTION 1 #1: Buying Calls * If ST < \$55, we won’t exercise the call, and lose the premium of\$2.875; * If ST > \$55, we will exercise the call and the net profit will be ST - \$55 - \$2.875 = ST - \$57.875 #2: Writing Calls * If ST < \$55, the call buyer will not exercise the call, thus we earn the premium of \$2.875; * If ST > \$55, the call buyer will exercise the call and our net profit is \$2.875 + \$55 – ST = \$57.875 - ST #3: Buying Puts * When ST > \$55, we won’t exercise the put and will lose the premium of \$2.625; * When ST < \$55, we begin to earn money (\$55 - ST – \$2.625) #4: Writing Puts * When ST > \$55, keep our premium of \$2.625; * When ST < \$55, need to purchase the stock, payoff is ST - \$55 + 2.625 QUESTION 2 • Which one of the strategies offers the greatest upside return? Buying calls since it can provide infinite profit as stock price grows. • Which one of the strategies offers the least upside......

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#### Futures and Options

...| Futures & Options Report | | | | | | a) Our portfolio consists of five stocks, one put option and one futures contract. The five stocks we have are Exxon Mobil (XOM), Johnson & Johnson (JNJ), Google (GOOG), Ford (F), and Amazon (AMZN). These stocks are all traded on the NASDAQ stock market. We have purchased ten shares of each of the five stocks below. Below is a graph with shows when we purchased the stocks and how much it cost at that time.   | Stock P | Date | Time | AMZN | \$179.97 | 3/5/2012 | 1:28pm | XOM | \$86.67 | 3/5/2012 | 1:29pm | GOOG | \$614.70 | 3/5/2012 | 1:28pm | F | \$12.48 | 3/5/2012 | 1:29pm | JNJ | \$64.67 | 3/5/2012 | 1:28pm | The table below now shows the results of how the stock performed from 3/5/12 to 3/16/12: We will discuss some stock analysis and the gain/loss later in this report.   | Current | Date | Time | AMZN | 185.05 | 3/16/2012 | 1:28pm | XOM | 86.44 | 3/16/2012 | 1:29pm | GOOG | 625.4 | 3/16/2012 | 1:28pm | F | \$12.51 | 3/16/2012 | 1:29pm | JNJ | \$65.12 | 3/16/2012 | 1:28pm | Other than having five stocks, we have a put option for Procter & Gamble and a futures contract of Gold. b) Analyzing the futures contract of gold we bought at the beginning, March 2, 2012, it closed at \$1,698 which meant our initial value was at \$10,125 with a margin call at \$7500. If it drops below that price then we would have to borrow money to bring it back up to the initial margin. On March 3...

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#### Options Market

...Options Markets Options Markets Prepared By: Daniel Bielewicz Jomark Manglicmot Juan Mendez December 1, 2014 Prepared By: Daniel Bielewicz Jomark Manglicmot Juan Mendez December 1, 2014 Table of Contents Page Introduction 2 Options Market 2 Market Makers 4 Equity Market 6 Conclusion 9 Works Cited 10 Introduction The options market is directly linked to the U.S. economy in many ways. It plays a huge role in various markets and institutions and is reflective of its underlying assets. In this case we will discuss the various issues regarding the options market and how it affects U.S. markets and institutions. This includes a breakdown of the options market, the market makers’ role, and how the options market affects the equity market. Options Market Nowadays, many investors’ portfolios include investments such as mutual funds, stocks, and bonds. But that is not all there is for investors to invest in. Another method of investment is called options, and it brings a world of opportunities for investors. However, options are complex securities and can be extremely risky.  Options, as the name implies, give the option to the buyer to either sell or buy a stock for a given price. The right to buy stock at a given price is called a “call option” and the right to sell it is called “put option”. Options were designed to take advantage of the volatility in the market and are used by investors to......

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#### Option Pricing

...to determine the option price when the stochastic volatility is independent of stock price. The second case is to determine the option price when the stochastic volatility is correlated with the stock price. This paper provides a solution in series form for the stochastic volatility option, in addition to a discussion about the numerical methods that are used to examine pricing biases, and an investigation about the occurrence of the biases in the case of stochastic volatility. As for the results obtained, this paper presents interesting results for each of the two cases. When the stochastic volatility is independent of stock price, the results show that the price calculated using Black-Scholes equation is overestimated for at-the-money options and underestimated for deep in-and out-of-the-money options. This overpricing takes place for stock prices within about ten percent of the exercise price. Moreover, it is shown that the degree of the pricing bias can be up to five percent of the Black-Scholes price. For the second case when the stock price is positively correlated with the volatility, the results show that the Black-Scholes formula overprices in-the-money options and underprices out-of-the-money options. On the other hand, when the stock price is negatively correlated with the volatility, the Black-Scholes formula overprices out-of-the-money options and underprices in-the-money options. Although these results are obtained for European call option, they can be......

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#### Share Option

...美国股票期权案例 股票期权始于本世纪70年代，是西方近二十年来兴起的一种用来激励经理人员的报酬制度。以期权计划为代表的长期激励机制在美国已得到广泛的推行，股票期权创造性的以股票升值所产生的差价作为对企业经营人员人力资本的一种补偿，成功地将经营人员的个人目标与公司的长期利益结合起来。      股票期权就是公司给予员工未来一段时间内以现在的一个价格购买公司股票的权利。一般来说，管理者是以该权利被给予时的价格即行权价，在期权到期时购买公司股票的。该期权的年限一般是5-10年，也就是说持有该权利的管理者在持续经营企业一段时间后，才能行使该权利。如果该期权到期时的股票价格高于授权时的股票价格，说明他保证了公司资本和企业市值的不断升值，这是符合股东利益的。对管理者来说，在期权到期时行使该权利的结果将为他带来丰厚的收入。当然，如果期权到期时的股票价格低于授权时的价格，管理者不但享受不到该期权的收益，而且还意味着他是一个失败的管理者。     如何借鉴国外成熟的经验，结合自己的国情，探索我国的经营者持股激励机制，对于现阶段培育经理人市场，造就高素质企业家队伍，有十分重要的现实意义。对美国一些著名公司的股票期权实施情况进行分析，也许能够为目前国内正在积极探索并实践股权激励的上市公司提供一些参考。      微软公司  微软员工的薪酬主要有三部分构成，一部分是工资，另一部分就是公司股票认购权，最后一部分是奖金。微软通常不付给员工很高的薪酬，但是有高达15%的一年两度的奖金、股票认购权以及工资购买股票时享受的折扣。每一名微软雇员工作满十八个月就可获得认股权中的25%的股票，此后每六个月可获得其中的12.5%,10年内的任何时候员工都可以兑现全部认购权。微软每两年还配发一次新的认股权，雇员可用不超过10%的工资八五折优惠价格购买公司的股票。      去年互联网发展的高峰中，作为软件界巨头，就像其他成熟的技术公司一样，微软的管理人员和工程师也纷纷跳槽到互联网新创企业和风险投资企业。微软公司为了留住顶尖人才，最近又悄悄推出一系列新的奖励制度，包括超过往常数量的员工股票期权和额外的休假等。在新的奖励制度中，股票期权计划分配给高级管理人员和重要的软件工程师，最多可达200，000股。据知情人士透露，微软最近提拔的30多名副总裁中，有些人就有资格享受该项奖励。      Intel公司  Intel 公司从1984年开始面向公司的高层管理人员授予股票期权，主要用于对高层管理人员的年度管理绩效的奖励。1999年Intel对经过管理部门的推荐或者公司补偿委员会的批准对高级管理人员授予股票期权。股票期权授予数量取决于以下几个公司内部因素如：前一次赠与的数量、过去几年中的工作贡献和工作范围等。一般而言，最初授予的股票期权在授予5年后才可以行权。Intel公司在1984年的股票期权计划中提出公司会在非经常情况下对主要高级管理人员和其他高级员工赠与额外的股票期权，以认可他们在未来领导公司前进中的潜力。这类股票期权的授予等待期一般要长于普通股票期权的授予等待期。公司在1999年的股票期权计划中开始实施不仅包括其主要高级管理人员的股票期权制度，并且开始进行全体员工的股票期权计划。      Motorola公司  1993年Motorola提出了一个包括其CEO在内的高级管理人员最小股票持有指引方案，该指引方案规定，如果CEO所拥有的股票少于其基本工资的4倍，或者其他高级管理人员所拥有的股票少于其基本工资的3倍，则这些高级管理人员必须保留50%从1993年12月起开始...

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#### Stock Options

...Stock Options Stock options are a privilege given to an employee to purchase shares of company stock. They give the employee the right to buy common stock from the company at an agreed upon price, also known as the “strike price.” If the value of the stock increases above the agreed upon price, the employee gains additional profit, other than their compensation, from the sale of the option. The purpose of stock options is to give the holder a certain bind to the company’s success. Stock options are very popular as more than 10 million Americans own them today. Stock options meet the objectives of an effective compensation program. Effective compensation programs are ones that motivate employees to high levels of performance, help retain executives and allow for recruitment of new talent, base compensation on employee and company performance, maximize the employee’s after-tax benefit and minimize the employee’s after-tax cost and use performance criteria over which the employee has control. GAAP now requires that stock options be expensed, however GAAP previously required that the excess of the market price of the stock over its exercise price measure compensation cost at the grant date. The company would therefore not recognize any compensation expense related to the options because at the grant date, the market price and the exercise price were the same. If a company has a stock option plan, compensation expense should be recorded during the period(s) in which......

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#### Covered Call Options

...world market for a profit. Some countries even have an immediate market for their minerals like oil and gold. Almost all LDCs and a number of the other countries that needed bail out funds, have these resources that can be sold for profit. However in a situation where quick funds are needed, selling these resources would take a considerably long period of time which is not available at that instance. This can be remedied by the sell of long term covered call options on the resources of the different countries that need the funds. An options strategy is when an investor holds a long position (owns the asset: in our case mineral) in an asset and writes (sells) call options on that same asset in an attempt to generate increased income from the asset. This strategy is often employed when an investor has a short-term neutral view on the asset and for this reason holds the asset long and simultaneously have a short position via the option to generate income from the option premium.By selling Long term covered call options, the country makes money that not only can be used to fund bailouts but can also be used for other budgetary expenditures. To expand on this...

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#### Option Strategies

...Option Trading Strategies and Their Effectiveness in the Indian Market The project starts with introduction to: * Overview of Derivatives and mainly Options. * The working and mechanics of options and how they help in hedging and trading. * History of Options with respect to Global & Indian Markets. * The advantages of Options The project mainly aims to cover the conceptual and theoretical background of the study including option terminology, option payoffs, payoff profiles of long & short underlying & long and short call and put options followed by options theory, knowledge and outline of the various possible trading and hedging strategies with options that are widely known including : * When to use the strategy * Basic legs involved * Other derivatives/underlying used with the strategy * The payoff profile of the strategy * The risk and reward * Breakeven points and profit and loss analysis Some of the strategies intended to be covered are: Long Call, Short Call, Synthetic Long Call, Long Put, Short Put, Covered Call, Straddles, Strangles, Collars, Spreads, Butterflies and Condors The various strategies are individually analysed with the help of detailed examples and then further studied taking real life examples of hypothetical positions from past data of Indian Derivatives market, mainly from the historical data archives of NSE as given on website of NSE. (Preferably recent month expiry contracts) Drawing......

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#### Option Valuation

...Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price – exercise price for a put option: exercise price – stock price the intrinsic value for out-the-money or at-themoney options is equal to 0 time value of an option = difference between actual call price and intrinsic value as time approaches expiration date, time value goes to zero 21-2 Determinants of Option Values Call + – + + + – Put – + + + – + Stock price Exercise price Volatility of stock price Time to expiration Interest rate Dividend rate of stock 21-3 Binomial Option Pricing consider a stock that currently sells at S0 the price an either increase by a factor u or fall by a factor d (probabilities are irrelevant) consider a call with exercise price X such that dS0 < X < uS0 hence, the evolution of the price and of the call option value is uS0 Cu = (uS0 – X) C S0 dS0 Cd = 0 21-4 Binomial Option Pricing (cont.) now, consider the payoff from writing one call option and buying H shares of the stock, where Cu − Cd uS0 − X H= = uS0 − dS0 uS 0 − dS0 the value of this investment at expiration is Up Down Payoff of stock HuS0 HdS0 Payoff of calls –(uS0 – X) 0 Total payoff HdS0 HdS0 21-5 Binomial Option Pricing (cont.) hence, we obtained a risk-free investment with end value HdS0 arbitrage argument: the current value of this investment......

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#### Real Options Assignment

...FIN 855 – FINANCIAL MANAGEMENT, SPRING 2014 Real Options Assignment Multiple Choice Questions (3 points each) 1. The following are the main types of real options: (I) The option to expand if the immediate investment project succeeds (II) The option to wait (and learn) before investing (III) The option to shrink or abandon a project (IV) The option to vary the mix of output or the firm’s production methods A) I only B) I and II only C) I, II, and III only D) I, II, III, and IV only 2. The opportunity to invest in a project can be thought of as a three-year real option on an asset which is worth \$500 million (PV of the cash flows from the project) with an exercise price of \$800 million (investment needed). Calculate the value of the option given that, N(d1) = 0.3 and N(d2) = 0.15. Assume that the interest rate is 6% per year. A) \$150 million B) \$49 million C) \$30 million D) None of the above. 3. The DCF approach must be: A) Augmented by added analysis if there are no embedded options. B) Augmented by added analysis if a decision has significant embedded options. C) Jettisoned if there are any embedded options. D) Computed carefully to identify the options. 4. The following are examples of expansion options: (I) A mining company may acquire rights to an ore body that is not worth developing today but could be profitable if product prices increase (II) A film producing company acquiring the rights to a novel to produce a film based on the novel...

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#### Currency Option

...Currency—Currency Options Let’s based on Figure 1.1 Option Chain for NASDAQ OMX call option below, we will do a call option example. Figure 1.1: Option Chain for NAZDA OMX Group Inc. (Taken and Compiled from Figure 1.2: Option Chain for NASDAQ OMX Group Inc. (NDAQ) in Appendix A) Both calls and puts option will be based on the option of striking price at 32 cent/AUD, expires on September 2013 and a contract size is AUD10,000. 1.1 Call Option Premium price=2 cents/AUD Supposed that the spot rate at expiration (in cents), ST = 40 cents/AUD Exercise value = ST– Strike price = 40 – 32 = 8 cents per contract or \$800. Thus, the call owner will be able to purchase AUD10,000 worth \$4,000 (=AUD10,000 X \$0.40) in the spot market, for \$3, 200 (=AUD10,000 X \$0.32). But if the Spot rate at the expiration is lower than the strike price, and causing a negative exercise value, the caller buyer has no obligation to exercise as it will be a disadvantage. He/she can either let it expire or zero value. Below in Diagram 1.1 graph illustrates the 32 Sept AUD call option from the buyer’s perspective at the expiration. As shown above, in the buyer’s perspective, he/she should not lose any amount over the premium when the Spot rate is higher than the Strike price and in theory the buyer will have an infinite gains. When it reaches the spot rate at expiration which is ST = E+p = 32+2 = 34 cents/AUD, both the buyer and the writer have gain or lose. 1.2......

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#### Option Greeks

...Option Greeks 1. Delta Definition: Delta measures the sensitivity of the option price to the change in the price of the underlying asset. * Delta is the amount an option price is expected to move based on a 1 unit change in the underlying asset (assuming no changes in other variables). * In other words delta is approximation of the chance of an option expiring in the money as delta of calls and puts are closely related for same Strike price (Put–Call Parity) and depending on Theta and Vega of the option. * Delta is sensitive to changes in volatility and time to expiration If expiry time or volatility is more there is less certainty about whether the option will be ITM or OTM at expiration, and is reflected by delta of their call and put options. * As time passes, the delta of in-the-money options increases and the delta of out-of-the-money options decreases. As volatility falls, the delta of in-the-money options increases and the delta of out-of-the-money options decreases. * Delta may be more sensitive to time until expiration and volatility the further in the money or out of the money the option is. * The rate of increase for delta of in the money option is more than the rate of decrease of delta of out of the money option. Graph: Call and Put option Delta Value Delta of Call options: * Value ranges from 0 to 1. * It is equal to slope of the price curve (payoff diagram of the call option). * Direct relationship...

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