...Synthetic Forward and PutCallParity A synthetic long forward can be created by purchasing a call option and writing a put option with the same strike price and the same expiration date. Let’s say, that an investor buys a $500‐strike call option and sells a $500‐strike put option, both options have the same expiration time T. At T, the spot price will be equal to, above or below the strike price. If the spot price is above the strike price K, the investor will exercise the call option and buy the underlier for $500. The put will not be exercised. If the spot price is below the strike price the written put will be exercised against the investor, forcing him to buy the underlier at $500. The call will expire worthless. In either case, the underlier will be purchased at the strike price. The payoff of this combined position is max{0, S - K}- max{0, K - S} = S - K Call Put but this is actually the payoff of a long forward contract expiring at time T and with a forward price of $500. Be aware of the differences between an original long forward and a synthetic long forward: (i) the original long forward has no upfront premium payment while the synthetic long forward requires a net option premium (= abs[Call(K,T) – Put(K,T)] ) as upfront payment. (ii) At expiration at time T we pay the forward price with the original long forward, whereas with the synthetic long forward we pay the strike price. Let F0,T denote the “no‐arbitrage” forward price. This means you have to pay $0 today and at ...
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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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...10.2. What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum? The lower bound is [pic] Problem 10.3. What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum? The lower bound is [pic] Problem 10.4. Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second reason should apply even if interest rates are zero. Delaying exercise delays the payment of the strike price. This means that the option holder is able to earn interest on the strike price for a longer period of time. Delaying exercise also provides insurance against the stock price falling below the strike price by the expiration date. Assume that the option holder has an amount of cash [pic] and that interest rates are zero. When the option is exercised early it is worth [pic] at expiration. Delaying exercise means that it will be worth [pic] at expiration. Problem 10.5. “The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement. An American put when held in conjunction with the underlying stock provides...
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...service. In many cases these fees come from the difference between the bank´s bid and ask quotes -> called the bit/ask spread. 3) Exchange Rate Movements Prices and currencies can fluctuate. 3.1) Currency Appreciation and Depreciation Appreciate= a currency in value relative to other currencies. Depreciate= a currency decreases in value A purchasing power of one currency relative to another currency can appreciate or depreciate. 3.2) Measuring Fluctuations Exchange rate fluctuations are often presented in percentage terms, relative to some reference currency. 3.3) Why exchange rate change Purchasing Power Parity Purchasing Power Parity A well-known (and controversial) theory...
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...(except some complicated instruments), we can modify the fundamental formula in order to fit the specifications of the instrument that will be valued. An argument done by Black and Scholes which was based on the past proposition of Miller and Modigliani a well as assuming some ideal conditions, States that value of the firm is a sum of total value of debt plus the total value of common stock. As well as the fact that in the absence of taxes, the value of the firm is independent of its leverage and the change of debt has no effect on the firm value. V = E + Dm V: value of the firm. E: shareholders right (common stock values). Dm: market value of the debt. As the above equation impose that Equity (common stock values) can be viewed as a call option on the firm value (due to the shareholders limited liability and with consideration that firm debt can be represent as a zero-coupon bond), where exercising the option means that equity holders buy the firm at the face value of debt (which is in this case will be the exercise price of the option), on the liquidation date of the bond (maturity). The equity value can be represented as the option on the value of the firm (as the remaining after closing the debt on the expiration date) which is limited by the following boundaries: From the above equation the value of equity at the expiration date will be …. ET =...
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... TECHNICAL The Greeks are coming STEVE JAY RELEVANT TO PAPER 3.7 The new Paper 3.7 Syllabus includes far more detail on options than the old Paper 14. This article looks at the areas involved in the scope and benefits of financial engineering section of the syllabus. The reference to Greeks will become clear as we proceed. WHAT IS AN OPTION? The definition in finance is quite similar to that in every day language, i.e. an option is the right but not the obligation to perform a certain action. More specifically in finance it means that if we buy a call option we have the right but not the obligation to buy: a fixed amount; at a fixed time; at a fixed price; of the underlying instrument. On the other hand if we buy a put option we have the right but not the obligation to sell: a fixed amount; at a fixed time; at a fixed price; of the underlying instrument. TABLE 1: OPTION TERMINOLOGY Call option Put option Exercise price/Strike price In the money Out of the money American Option European Option Premium Traded Option Over the counter option Let us commence with a summary of the terminology surrounding options. This is given in Table 1 and many of the terms should be familiar from the foreign exchange and interest rate exposure sections of the syllabus. USES OF OPTIONS Options have two major uses on financial markets, speculation and hedging. Figure 1 gives an example of how speculators can use options to gamble on share price movements. It will be noted...
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...in 67 days, we must use 68 days since that is the option's time to expiration. 2. (Minimum Value of a Call) This would create an arbitrage opportunity. The call would be purchased and immediately exercised. For example, suppose S0 = 44, X = 40, and the call price is $3. Then an investor would buy the call and immediately exercise it. This would cost $3 for the call and $40 for the stock. Then the stock would be immediately sold for $44, netting a risk-free profit of $1. In other words, the investor could obtain a $44 stock for $43. Since everyone would do this, it would drive the price of the call up to at least $4. If the call were European, however, immediate exercise would not be possible (unless, of course, it was the expiration day), so the European call could technically sell for less than the intrinsic value of the American call. We saw, though, that the European call has a lower bound of the stock price minus the present value of the exercise price (assuming no dividends). Since this is greater than the intrinsic value, the European call would sell for more than the intrinsic value. Then at expiration, it would sell for the intrinsic value. 3. (Lower Bound of a European Call) The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of X. The cash received from the stock is greater than the cost of the call and bonds. Thus, there is a positive cash flow up front. The payoffs from the portfolio at expiration...
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...MARKET EFFICIENCY Efficiency with respect to an information set implies . . . that it is impossible to make abnormal profits by trading on the basis of that information set. 1. Prices in mkt reflect info about securities =>won’t be easy to find NPV>0 for financing i.e. under/overpriced securities is unlikely. 2. Market is efficient w/ respect to some info set if security prices would be unaffected by revealing that info to all participants. Weak Market reflects all info about past prices therefore can’t make abnormal profits based on past info. If it holds, Covariance (tomorrow’s abnormal return, today’s abnormal return) = 0, stock prices follow “random walk”. Test: transaction costs make technical trading not have a positive NPV. Semi Strong Weak plus - all publicly available info (i.e. rapid reaction time = can’t make money on the news) Test 1: active mgt funds in general perform worse than mkt. If info is already reflected in prices, extra costs of research & transaction of actively mgd fund vs tracker fund, incurred in vain Test 2: Study cumulative abnormal returns over time. Results show that info gets incorporated immediately (immediately rise (or fall) of prices), and starts to get incorporated before (insider’s info) Strong Semi Strong plus info NOT publicly available (inside info) Test: (Test 2 for semi), shows that there is insider’s trading or info leakage, also regulation Implications of mkt efficiency: - Expected return on a stock is exactly...
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...Prof. Dr. Streitferdt International Financial Management Winter semester 2015/16 1. Prologue 1. Prologue 2. Foreign exchange markets 3. Foreign exchange exposure management 4. Financial management of multinational corporations 5. Financial management of multinational corporations 6. Corporate Governance 7. Mergers & Acquisitions 8. Risikomanagement Prof. Dr. Streitferdt: International Financial Management 1 1. Prologue Discounting Calculating present value 0 t=1 t=2 t=3 2,000 t=0 4,500 3,000 t=4 t=5 3,500 6,000 How much would you be willing to pay for this stream of future cash flows, if the interest is at i = 5.65%? Why is the result today’s value of the future cash flows? What are the assumptions of this calculation? Prof. Dr. Streitferdt: International Financial Management 2 1. Prologue Discounting Calculating present value 10/28 10/14 6,000 0 How much would you be willing to pay for this stream of future cash flows, if the two week Euribor is at i = 5.65%? What makes this calculation different from the last slide’s calculation? How many days has a year? Prof. Dr. Streitferdt: International Financial Management 3 1. Prologue Discounting Interests for investments with less than one year maturity Interests are always quoted for one year: A company has in 2012 an overdraft credit of 100,000 €...
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...FRE 6123 Final Solutions May 7, 2009 This final was 50% of your grade. Here was the distribution of results: You can pick up your graded final exam from me on Monday if you want. But perhaps you don’t need to. Here are the solutions. 1. (5 points) Basics a. (2 points) Under the Capital Asset Pricing Model: A. Every investor holds the risk free asset only, and none of the market portfolio. B. Every investor holds the market portfolio only, and none of the risk free asset. C. Every investor holds a portfolio with a beta of one. D. None of the above. CIRCLE ONE: A B C D Solution: D. Investors can hold any combination of the riskfree asset and the market portfolio, depending on their particular risk aversion, etc.; so A and B are false. C is false because, for example, an investor holding just the riskfree asset holds a portfolio with a beta of zero. b. (1 point) Asset A has a correlation of 80% with the market, but asset B only has a correlation of 50% with the market. Therefore, asset A has a higher beta to the market than asset B. CIRCLE ONE: TRUE FALSE Solution: FALSE. The beta is the correlation times the asset volatility divided by the market volatility. If asset A has e.g. half the volatility of asset B, then asset A would have a lower beta. c. (2 points) There are 100 different assets. You plot their means and standard deviations, and painstakingly figure out the efficient frontier. You plot the risk free asset and find the tangency portfolio. Now, you...
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...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 returns? Writing puts because the most you can earn is your premium and premium of puts is lower than that of calls. • Which one of the strategies offers the greatest downside potential? Writing calls since when stock price reaches really high, your potential loss is infinite. • Which one of the strategies offers the least downside potential? Buying puts because the most you can lose is...
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...Computer Corporation – Share Repurchase Program Questions: 1. Why do companies use stock options to compensate employees? What are the advantages of stock options relative to cash compensation? What, if any, are their disadvantages? 2. What, if any, risks do Dell’s shareholders face from Dell’s stock option program? Draw terminal payoff diagrams to illustrate the risk. Is this risk something that shareholders of Dell expect to bear when investing in Dell? 3. How does Dell remove, or hedge, the perceived risk of the stock options program for shareholders? Draw terminal payoff diagrams to illustrate. 4. Why does Dell transact in both call and put options? Use put-call parity to reformulate the put and call positions that Dell takes in terms of Dell’s stock and borrowing. What effectively does Dell’s call and put positions accomplish? Is risk management the primary motivation for Dell’s actions? A stock option is an offer by a company that gives employees the right to buy a specified number of shares in the company at an agreed upon price (usually lower than market) by a specific date. The benefit of granting options to employees is viewed as a good thing because it (theoretically) aligned the interests of the employees (normally the key executives) with those of the common shareholders. If a material portion of a CEO's salary were in the form of options, she or he would be incited to manage the company well, resulting in a higher stock price over the long...
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...BEA3001 Financial Management 2012-2013 Option Pricing Dr Bill Peng, CFA Today • Describe the basic characteristics of financial options • Develop the Binomial Option Pricing Model • Discuss the Put-Call Parity theorem • Introduce and apply Black-Scholes Option Pricing Model BP BEA3001 Financial Management 2 Coursework Test 1 Directions • Reminder: CW Test 2 [4pm Wed 20th Mar 2013] • CW Test 1: 6pm on Monday 26th November • Students entitled to extra time: STC/C • Surnames starting with letters “A” to “K” (inclusive): Amory Moot Room • Surnames starting with letters “L” to “W” (inclusive): STC/A • Surnames starting with letters “X” to “Z” (inclusive): STC/B BP BEA3001 Financial Management 3 Coursework Test 1 Directions cont’d • Everyone should arrive in the corridor outside either Amory Moot Room or STC A/B/C by 6:15pm and wait QUIETLY to be called into a test room • We will aim to get you settled and started as soon as possible and you will be free by 8:00pm at the latest, if all of you could kindly follow the instructions • Fair-play: breach of exam rules will be punished • You should have with you your student ID card, a note of your 2012-2013 candidate number, pencils, erasers, pens and a calculator BP BEA3001 Financial Management 4 Coursework Test 1 Directions cont’d • You should take a seat where a test paper (together with an answer booklet) has been placed, but DO NOT touch the test paper or the answer booklet until told to do...
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...20.1 Option Basics • Financial Option: A contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price as some future date • Call Option: A financial option that gives its owner the right to buy an asset • Put Option: A financial option that gives its owner the right to sell an asset • Option Writer: The seller of an option contract • Exercising an Option: When a holder of an option enforces the agreement and buys or sells a share of stock at the agreed-upon price • Strike Price (Exercise Price): The price at which an option holder buys or sells a share of stock when the option is exercised • Expiration Date: The last date on which an option holder has the ri p g p ght to exercise the option Ameri can Option: Options that allow their holders to exercise the option on any date up to, and including, the expiration date • European Option: Options that allow their holders to exercise the option only on the expiration date Note: The names American and European have nothing to do with the location where the options are traded. The option buyer (holder): Holds the right to exercise the option and has a long position in the contract • The option seller (writer): Sells (or writes) the option and has a short position in the contract • Because the long side has the option to exercise, the short side has an obligation to fulfill the contract if it is exercised. The buyer pays the writer a premium. Stock options are traded...
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...Limited 23-1 Chapter Outline 23.1 Options 23.2 Call Options 23.3 Put Options 23.4 Selling Options 23.5 Stock Option Quotations 23.6 Combinations of Options 23.7 Valuing Options 23.8 An Option-Pricing Formula 23.9 Stocks and Bonds as Options 23.10 Capital-Structure Policy and Options 23.11 Mergers and Options 23.12 Investment in Real Projects and Options 23.13 Summary and Conclusions McGraw-Hill Ryerson © 2005 McGraw Hill Ryerson Limited 23-2 23.1 Options Many corporate securities are similar to the stock options that are traded on organized exchanges. Almost every issue of corporate stocks and bonds has option features. In addition, capital structure and capital budgeting decisions can be viewed in terms of options. McGraw-Hill Ryerson © 2005 McGraw Hill Ryerson Limited 23-3 23.1 Options Contracts: Preliminaries An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset on (or perhaps before) a given date, at prices agreed upon today. Calls versus Puts Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today. When exercising a call option, you call in the asset. Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset at some time in the future, at prices agreed upon today. When exercising a put, you put the asset to someone. McGraw-Hill Ryerson © 2005 McGraw...
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