...Jon M. Huntsman School of Business Master of Science in Financial Economics August 2013 Pricing and Hedging Asian Options By Vineet B. Lakhlani Pricing and Hedging Asian Options Table of Contents Table of Contents 1. Introduction to Derivatives 2. Exotic Options 2.1. Introduction to Asian Options 3.1. Binomial Option Pricing Model 3.2. Black-Scholes Model 3.2.1. Black-Scholes PDE Derivation 3.2.2. Black-Scholes Formula 1 2 3 4 4 5 6 7 3 3. Option Pricing Methodologies 4. Asian Option Pricing 4.1. 4.2. 4.3. 4.4. Closed Form Solution (Black-Scholes Formula) QuantLib/Boost Monte Carlo Simulations Price Characteristics 8 8 10 11 14 5. Hedging 5.1. Option Greeks 5.2. Characteristics of Option Delta (Δ) 5.3. Delta Hedging 5.3.1. Delta-Hedging for 1 Day 5.4. Hedging Asian Option 5.5. Other Strategies 6. Conclusion 16 17 17 19 20 22 25 26 27 32 34 Appendix i. ii. iii. Tables References Code: Black-Scholes Formula For European & Asian (Geometric) Option 1 Pricing and Hedging Asian Options 1. Introduction to Derivatives: Financial derivatives have been in existence as long as the invention of writing. The first derivative contracts—forward contracts—were written in cuneiform script on clay tablets. The evidence of the first written contract was dates back to in nineteenth century BC in Mesopotamia...
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...Giddy | Hedging 1 Hedging Techniques Dr. Ian Giddy New York University Techniques of Hedging A brief comparison of hedging tools Forwards, futures, swaps Asset-liability matching Pricing and linkages among the tools Uses and abuses of options When to use, and when not to use Copyright ©2009 Ian H Giddy 4 Giddy | Hedging 2 What Hedging Instruments? What Protection Needed? Volatility & Direction Direction Complex risks Or arbitrage Exotics, Hybrids, structured notes OTC options, Caps and Floors Forwards, Futures, Swaps Copyright ©2009 Ian H Giddy 5 Tools for Hedging Petrobras has to pay for equipment from Japan, in Japanese yen, in 3 months Borrow and pay now? Use a forward contract/FX swap? Pay later at spot? Copyright ©2009 Ian H Giddy 6 Giddy | Hedging 3 Forward Contracts, Futures and Money Market Hedging Money market hedging: match currency of assets and liabilities Forwards: Agreement to exchange currencies at certain exchange rate in the future Futures: Exchange-traded contracts for notional future delivery, minimizing default risk via marking-tomarket Currency swap: match payments on foreign-currency debt Interest-rate swap: change floating cost to fixed Copyright ©2009 Ian H Giddy 7 A Typical Forward Exchange Contract We agree today to pay a certain price for a currency in the future JPY Sony Sony B of A B of A Copyright ©2009 Ian H Giddy 8 Giddy | Hedging 4 Forward Quotations ...
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...Tutorial Answers 6 1. Transaction Exposure. Fischer Inc., exports products from Florida to Europe. It obtains supplies and borrows funds locally. How would appreciation of the euro likely affect its net cash flows? Why? ANSWER: Fischer Inc. should benefit from the appreciation of the euro, because it should experience a strong demand for its products when the euro has more purchasing power (can obtain dollars at a low price). 2. Transaction Exposure. Aggie Co. produces chemicals. It is a major exporter to Europe, where its main competition is from other U.S. exporters. All of these companies invoice the products in U.S. dollars. Is Aggie’s transaction exposure likely to be significantly affected if the euro strengthens or weakens? Explain. If the euro weakens for several years, can you think of any change that might occur in the global chemicals market? ANSWER: If the euro strengthens, European customers can purchase Aggie’s goods with fewer euros. Since Aggie’s competitors also invoice their exports in dollars, Aggie Company will not gain a competitive advantage. Nevertheless, the overall demand for the product could increase because the chemicals are now less expensive to European customers. If the euro weakens, European customers will need to pay more euros to purchase Aggie’s goods. Since Aggie’s competitors also invoice their exports in dollars, Aggie Company may not necessarily lose some of its market share. However, the overall...
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...ERSTE GROUP Conference on European Economic Integration 2007 November 2007, Vienna Hedging exchange rate risks Veronika Lammer How big is your exchange rate risk? ERSTE GROUP − What is the net currency risk? - Not only receivables, but also liabilities can bear exchange rate risks as well as inventories, other assets and financing. - Cross correlations between currencies have to be assessed. - Bulk of cash flows with different currency risks at different times have to be taken into account. - Price sensitivity of goods to exchange rate fluctuations. - In the end, the important figure is the influence of exchange rate fluctuations on profits, not on sales. CEEI November 2007, Vienna Hedging exchange rate risks 2 Reducing currency risk ERSTE GROUP − Is currency risk a problem for your company? − Could you reduce your currency risk by changing your suppliers or employing a different financing strategy? − Do you want to hedge your currency risk - all the time, or just sometimes? - to the full amount, or just partly? - You should define rules for hedging, especially if you decide to hedge only sometimes or partly. CEEI November 2007, Vienna Hedging exchange rate risks 3 Change Financing ERSTE GROUP − One relatively simple method of reducing your currency risk is to take a loan in the currency in which you have the highest amount of receivables. - You can pay off the loan directly with receivables. - This protects you from a longer-term...
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...zero or in other words, reduce your risk to nothing not including the cost of the hedge. If a correlation is negative, as it was for the first three months, it means that investing in futures contracts was the right move because the cash flows are moving in opposite directions to minimize the risk. Another way to evaluate the performance of the hedging strategy is to compare the variance of unhedged cash flow and the hedged cash flow, expecting that that variance of the unhedged should be greater than the hedged cash flow. As seen in the table below, the variance of the unhedged is greater than the variance of the hedged when Link Technologies invested in currency futures contracts. Futures Variance | | Unhedged CF | 20,691,861,693.67 | Hedged CF | 2,774,199,924.92 | Difference | 17,917,661,768.75 | Even though, the hedging program was perfectly implemented, Mr. Lee strongly believed that investing in futures was the wrong approach because the company experienced a loss of half a million dollars during the first three months. So, he “suggested” that the firm should now invest in call options because the “downside risk was known; you could not lose more than what you paid for the call.” Following this decision, they yielded “a net...
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...Hedging by Executives: An Ethical Decision Nicole Jennings University of Maryland University College Introduction Hedging is a term used to describe the process of reducing risk exposure to a firm. Specifically, the use of derivatives, reduces this risk. A derivative is a tool whose value is based on something other than the market value of the firm (Ross, Westerfield, & Jaffe, 2013). Two of the most common derivatives are options and futures contracts. An option is a contract allowing the buyer to buy an asset on or before a certain date at a fixed price. A futures contract obligates the exchange to take place on a certain date for a specified price (Ross, Westerfield, & Jaffe, 2013). In today’s financial market, many executives of firms are given stock-based compensation. This serves as a positive reinforcement to the executive when the firm becomes more financially successful. It also serves as a negative reinforcement when the firm is doing poorly. While stock-based compensation may seem fairly logical, it results in an undiversified portfolio, which is not ideal as an investment because of unsystematic risk (Ross, Westerfield, & Jaffe, 2013). Hedging by executives has become a popular option for executives with stock-based compensation who want to reduce the risk of their portfolio (Dunham, Managerial Hedging and Firm Risk, 2010). The ethical dilemma of executive hedging has been a controversy in the corporate finance world for many decades. Some recent...
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...ACF 504: FINANCIAL MARKETS Coursework Assignment II GROUP 20 Definition of the Dataset (Word Count 1938) The dataset used in this report is derived from Thomson ONE Banker. The spreadsheet in Appendix contains the daily price of the TESCO and the FTSE All Share index during the period from 1 December 2014 to 30 November 2015. Each closing price includes 254 observations. We obtain 253 daily returns of the TESCO and 253 daily returns of FTSE index after calculating daily simple returns by using the following formula. = − −1 −1 The Capital Asset Pricing Model (CAPM) Before calculating the annualized standard deviation of daily stock returns and index returns, assuming that the expected return on the index is equal to the average of simple index returns, the expected return on the index equals to -0.002%. Since the number of sample of daily index returns is 253, we calculate the annualized expected return on the index as below. ((1 − 0.002%)253 − 1) = −0.606% The following formula is used to calculate the sample standard deviation: 253 1 S=√ ∑( − ̅ )2 253 − 1 =1 By using Excel function of STDEV.S, the sample standard deviation of daily index returns and of daily stock returns are 1.01% and 2.05% respectively. After multiplying by√253, the annualized sample standard deviation of daily index returns (S ) and of daily stock returns ( ) are 16.06% and 32.59%, respectively. The correlation of daily returns between the FTSE index...
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...million. American Standard is: a) Hedging. b) Speculating. c) Locking in an arbitrage profit. Answer: Part a) Hedging is the correct answer. ------------------------------------------------- 2) American Standard Co. has a 90 day £62,500 receivable. American Standard’s bank, Bank of America, suggests a put option contract that matures in 90 days. American Standard purchases one put option contract, where one contract corresponds to a quantity of £62,500. American Standard is: a) Hedging. b) Speculating. c) Locking in an arbitrage profit. Answer: Part a) Hedging is the correct answer. Because in this case, the American Standard Co is sure about the money to be received and wants to hedge against the exchange rate risk which is hedging. ------------------------------------------------- 3) American Standard Co. has a 90 day £62,500 receivable. American Standard’s bank, Bank of America, suggests a call option contract that matures in 90 days. American Standard purchases one call option contract, where one contract corresponds to a quantity of £62,500. American Standard is: a) Hedging. b) Speculating. c) Locking in an arbitrage profit. Answer: Part a) Hedging is the correct answer and not locking in an arbitrage profit, because in this case, the American Standard Co is sure about the money to be received and wants to hedge against the exchange rate risk which is hedging. ------------------------------------------------- ...
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...such as a foreign exchange rate or a specified interest rate, for example, the London Interbank Offer Rate; It requires little or no initial net investment; and It is settled at a future date. 2. 3. Chapter 10 Page 1 TABLE 10.1 Examples of derivative instruments and their underlying Type of derivative instruments Options contract (call and put) Underlying Security price Used by Producers, trading firms. financial institutions and speculators Various companies Producers and consumers Financial institutions Forward contracts, e.g. foreign Foreign exchange rates exchange forward contracts Futures contracts, e.g. Commodity prices commodity futures Swaps. e.g. interest rate swap Interest rate Uses of Derivatives Generally, firms or individuals transact in derivatives to: 1. Manage market risks such as foreign exchange risk and interest rate risk; 2. 3. Reduce borrowing costs; or Profit from trading or speculation. Chapter 10 Page 2 Types of derivatives Ø Forward-type derivatives o Forward contract o Future contract o Swaps Ø Option-types derivatives o Option contract o Caps o Collars o Warrants Chapter 10 Page 3 Forward contract Forward contract is an agreement between two parties where by one party agrees to buy and other party agrees to sell a specified amount of an item (notational amount) at a fixed price (also called forward price or forward rate) for a delivery at...
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...Introduction: Overview of the hedging techniques: In the financial market, almost all of companies need to face the currency risk. In order to manage the currency risk, companies will use different hedging techniques, such as financial and operational hedging techniques. For example, money market, futures contracts, options and forwards contracts are commonly used by firms, as well as operational hedging techniques. All of 4 types of financial hedging techniques are short-term hedge. Money market is a part of financial markets for assets involved in short-term borrowing,lending, buying and selling. Its features are high liquidity, lower risk, such as treasury bills. Futures contracts are future transaction for buying or selling, and made by Futures exchange. The date and place of the transaction have been provided. There are some features of futures contracts. Quantity, commodity and quality have been limited, excepting the price. Also, it cannot be done over-the-counter. Options is a financial tool, which based on futures. If purchaser hold the options, he/she will has a right, not the obligation, to buy from or sell to the seller of the provided commodity in the future as the same price as the price agreed now. The last financial hedging technique, forwards contracts, is a non-standardization contact between two parties to sell or buy in the future. Curb-exchange and cash transaction are the feathers of forward contact. This essay will focus on two operational hedging techniques, market...
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...Global Financing and Exchange Rate Mechanisms Michael C. McGee MGT/448 November 6, 2012 Ian Finley Global Financing and Exchange Rate Mechanisms Globalization is ushering in tremendous business opportunities, competitive advantages, and greater profitability for companies that choose to set up operations in foreign countries. However, along with these opportunities come various risks to these companies. One of the main risks these companies will face is foreign currency exchange rate risk. Companies that plan to set up operations in a foreign country must exchange its domestic currency into the currency of the host nation to buy the necessary building materials, supplies, and other necessary resources that the operations will require (Hill, 2009). For example, if a U.S. company desires to set up operations in the country of China, it will have to exchange U.S. dollars currency into Chinese currency-the Yuan. If a company in Japan wants to set up operations in Spain or Italy, it would have to exchange its currency- the Yen into these countries’ currency, which is the Euro. The foreign currency exchange rates between these countries consistently fluctuate causing one to appreciate or depreciate against the other. The unpredictable movement of the foreign currency exchange rates can have adverse effects on a company’s investments, and profits that have operations in a foreign country. Foreign companies with operations in the U.S. normally convert the dollars it earns back...
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...The American Institute for Foreign Study (AIFS) is an organization, which helps enable American students to travel abroad. The main service AIFS provides entails organizing educational and cultural exchange problems across the globe. As the case explains, AIFS has split their business into two major divisions that that serve American student’s studying abroad; the Study Abroad College division and the High School Travel division. The college division, which is controlled by Christopher Archer-Lock, sends American students all over the world on semester-long exchange programs. The high school division, which was founded as the American Council for International Studies (ACIS), is controlled by Becky Tabaczynski and sends high school students and their teachers on 1-4 week long trips. This nature of business involves a certain amount of bottom-line risk. AIFS focuses largely on American students studying abroad, therefore the majority of their revenue is in American Dollars (USD). However, AIFS costs’ are generally incurred in foreign currency (primarily Euros (EUR) and British Pounds (GBP)) because the services they arrange for happen abroad. Due to their business activities involving foreign currencies, an unfavorable change in the exchange rate could result in a higher cost base, and potentially a loss overall if the change is significant enough. Inherently, due to the nature of their business, AIFS is exposed to currency risk because they are dealing in multiple currencies...
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...................................................................................6 Introduction..............................................................................................................8 Summary ..................................................................................................................9 Part One The Growth in Mine Utilisation of Borrowed Gold ........................................11 The Case for Hedging ..........................................................................................15 Hedging Instruments – Their Development and Usage ................................19 Australia ................................................................................................................21 North America ....................................................................................................22 South Africa ..........................................................................................................23 Gold’s Price Decline in 1996/97 – Its impact on Hedging Strategies ..........25 Part Two The Supply of Leased Gold and Banking Risks in the Gold Forward Market ......................................................................................29 The Market...
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...against the dollar was observed from 1983 to 1993, there was evidence that the yen was overvalued against the dollar in 1993, and thus a distinct probability that the yen may eventually crash suddenly. Managing Tiffany’s yen-dollar exchange rate risk. The predicted depreciation of the yen would have a potentially negative impact on Tiffany’s financial results. There are three main types of foreign exchange exposures are (1) transaction (short-term), (2) economic (medium to long term) and (3) translation exposures. For a company like Tiffany which has sales in numerous countries, there are a continuing series of foreign currency receivables and payables. Thus, Tiffany should have a foreign currency hedging program to cover these foreign exchange exposures. The objective of hedging would be to stabilize product costs, over the short-term, despite exchange rate fluctuations. In the long-term, if exchange rate differences have significantly changed, it is possible to adjust retail prices when necessary to maintain its gross margin. To reduce exchange rate risk on its yen cash flow, Tiffany had two basic...
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...10 Business Snapshot 1.1 Hedge Funds CHAPTER 1 Hedge funds have become major users of derivatives for hedging, speculation, and arbitrage. A hedge fund is similar to a mutual fund in that it invests funds on behalf of clients. However, unlike mutual funds hedge funds are not required to register under U.S. federal securities law. This is because they accept funds only from ®nancially sophisticated individuals and do not publicly oer their securities. Mutual funds are subject to regulations requiring that shares in the funds be fairly priced, that the shares be redeemable at any time, that investment policies be disclosed, that the use of leverage be limited, that no short positions be taken, and so on. Hedge funds are relatively free of these regulations. This gives them a great deal of freedom to develop sophisticated, unconventional, and proprietary investment strategies. The fees charged by hedge fund managers are dependent on the fund's performance and are relatively highÐtypically 1 to 2% of the amount invested plus 20% of the pro®ts. Hedge funds have grown in popularity with over $1 trillion being invested throughout the world. ``Funds of funds'' have been set up to invest in a portfolio of other hedge funds. The investment strategy followed by a hedge fund manager often involves using derivatives to set up a speculative or arbitrage position. Once the strategy has been de®ned, the hedge fund manager must: 1. Evaluate the risks to which the fund is exposed. 2. Decide...
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