Cdo Market Implosion and the Pricing of Subprime Mortgage-Backed
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Lecture 5 an Introduction to European Put Options. Moneyness
Lecture: 5 Course: M339D/M389D - Intro to Financial Math Page: 1 of 5 University of Texas at Austin Lecture 5 An introduction to European put options. Moneyness. 5.1. Put options. A put option gives the owner the right { but not the obligation { to sell the underlying asset at a predetermined price during a predetermined time period. The seller of a put option is obligated to buy if asked. The mechanics of the European put option are the following: at time−0: (1) the contract is agreed upon between the buyer and the writer of the option, (2) the logistics of the contract are worked out (these include the underlying asset, the expiration date T and the strike price K), (3) the buyer of the option pays a premium to the writer; at time−T : the buyer of the option can choose whether he/she will sell the underlying asset for the strike price K. 5.1.1. The European put option payoff. We already went through a similar procedure with European call options, so we will just briefly repeat the mental exercise and figure out the European-put-buyer's profit. If the strike price K exceeds the final asset price S(T ), i.e., if S(T ) < K, this means that the put-option holder is able to sell the asset for a higher price than he/she would be able to in the market. In fact, in our perfectly liquid markets, he/she would be able to purchase the asset for S(T ) and immediately sell it to the put writer for the strike price K. -
Treasury Yields and Corporate Bond Yield Spreads
Treasury yields and corp orate b ond yield spreads: An empirical analysis Gregory R. Du ee Federal Reserve Board Mail Stop 91 Washington, DC 20551 202-452-3055 gdu [email protected] First version January 1995 Currentversion May 1996 previously circulated under the title The variation of default risk with Treasury yields Abstract This pap er empirically examines the relation b etween the Treasury term structure and spreads of investment grade corp orate b ond yields over Treasuries. I nd that noncallable b ond yield spreads fall when the level of the Treasury term structure rises. The extentof this decline dep ends on the initial credit quality of the b ond; the decline is small for Aaa- rated b onds and large for Baa-rated b onds. The role of the business cycle in generating this pattern is explored, as is the link b etween yield spreads and default risk. I also argue that yield spreads based on commonly-used b ond yield indexes are contaminated in two imp ortant ways. The rst is that they are \refreshed" indexes, which hold credit ratings constantover time; the second is that they usually are constructed with b oth callable and noncallable b onds. The impact of b oth of these problems is examined. JEL Classi cation: G13 I thank Fischer Black, Ken Singleton and seminar participants at the Federal Reserve Board's Conference on Risk Measurement and Systemic Risk for helpful comments. Nidal Abu-Saba provided valuable research assistance. All errors are myown. The analysis and conclusions of this pap er are those of the author and do not indicate concurrence by other memb ers of the research sta , by the Board of Governors, or by the Federal Reserve Banks. -
Futures and Options Workbook
EEXAMININGXAMINING FUTURES AND OPTIONS TABLE OF 130 Grain Exchange Building 400 South 4th Street Minneapolis, MN 55415 www.mgex.com [email protected] 800.827.4746 612.321.7101 Fax: 612.339.1155 Acknowledgements We express our appreciation to those who generously gave their time and effort in reviewing this publication. MGEX members and member firm personnel DePaul University Professor Jin Choi Southern Illinois University Associate Professor Dwight R. Sanders National Futures Association (Glossary of Terms) INTRODUCTION: THE POWER OF CHOICE 2 SECTION I: HISTORY History of MGEX 3 SECTION II: THE FUTURES MARKET Futures Contracts 4 The Participants 4 Exchange Services 5 TEST Sections I & II 6 Answers Sections I & II 7 SECTION III: HEDGING AND THE BASIS The Basis 8 Short Hedge Example 9 Long Hedge Example 9 TEST Section III 10 Answers Section III 12 SECTION IV: THE POWER OF OPTIONS Definitions 13 Options and Futures Comparison Diagram 14 Option Prices 15 Intrinsic Value 15 Time Value 15 Time Value Cap Diagram 15 Options Classifications 16 Options Exercise 16 F CONTENTS Deltas 16 Examples 16 TEST Section IV 18 Answers Section IV 20 SECTION V: OPTIONS STRATEGIES Option Use and Price 21 Hedging with Options 22 TEST Section V 23 Answers Section V 24 CONCLUSION 25 GLOSSARY 26 THE POWER OF CHOICE How do commercial buyers and sellers of volatile commodities protect themselves from the ever-changing and unpredictable nature of today’s business climate? They use a practice called hedging. This time-tested practice has become a stan- dard in many industries. Hedging can be defined as taking offsetting positions in related markets. -
Ice Crude Oil
ICE CRUDE OIL Intercontinental Exchange® (ICE®) became a center for global petroleum risk management and trading with its acquisition of the International Petroleum Exchange® (IPE®) in June 2001, which is today known as ICE Futures Europe®. IPE was established in 1980 in response to the immense volatility that resulted from the oil price shocks of the 1970s. As IPE’s short-term physical markets evolved and the need to hedge emerged, the exchange offered its first contract, Gas Oil futures. In June 1988, the exchange successfully launched the Brent Crude futures contract. Today, ICE’s FSA-regulated energy futures exchange conducts nearly half the world’s trade in crude oil futures. Along with the benchmark Brent crude oil, West Texas Intermediate (WTI) crude oil and gasoil futures contracts, ICE Futures Europe also offers a full range of futures and options contracts on emissions, U.K. natural gas, U.K power and coal. THE BRENT CRUDE MARKET Brent has served as a leading global benchmark for Atlantic Oseberg-Ekofisk family of North Sea crude oils, each of which Basin crude oils in general, and low-sulfur (“sweet”) crude has a separate delivery point. Many of the crude oils traded oils in particular, since the commercialization of the U.K. and as a basis to Brent actually are traded as a basis to Dated Norwegian sectors of the North Sea in the 1970s. These crude Brent, a cargo loading within the next 10-21 days (23 days on oils include most grades produced from Nigeria and Angola, a Friday). In a circular turn, the active cash swap market for as well as U.S. -
11 Option Payoffs and Option Strategies
11 Option Payoffs and Option Strategies Answers to Questions and Problems 1. Consider a call option with an exercise price of $80 and a cost of $5. Graph the profits and losses at expira- tion for various stock prices. 73 74 CHAPTER 11 OPTION PAYOFFS AND OPTION STRATEGIES 2. Consider a put option with an exercise price of $80 and a cost of $4. Graph the profits and losses at expiration for various stock prices. ANSWERS TO QUESTIONS AND PROBLEMS 75 3. For the call and put in questions 1 and 2, graph the profits and losses at expiration for a straddle comprising these two options. If the stock price is $80 at expiration, what will be the profit or loss? At what stock price (or prices) will the straddle have a zero profit? With a stock price at $80 at expiration, neither the call nor the put can be exercised. Both expire worthless, giving a total loss of $9. The straddle breaks even (has a zero profit) if the stock price is either $71 or $89. 4. A call option has an exercise price of $70 and is at expiration. The option costs $4, and the underlying stock trades for $75. Assuming a perfect market, how would you respond if the call is an American option? State exactly how you might transact. How does your answer differ if the option is European? With these prices, an arbitrage opportunity exists because the call price does not equal the maximum of zero or the stock price minus the exercise price. To exploit this mispricing, a trader should buy the call and exercise it for a total out-of-pocket cost of $74. -
The Promise and Peril of Real Options
1 The Promise and Peril of Real Options Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 [email protected] 2 Abstract In recent years, practitioners and academics have made the argument that traditional discounted cash flow models do a poor job of capturing the value of the options embedded in many corporate actions. They have noted that these options need to be not only considered explicitly and valued, but also that the value of these options can be substantial. In fact, many investments and acquisitions that would not be justifiable otherwise will be value enhancing, if the options embedded in them are considered. In this paper, we examine the merits of this argument. While it is certainly true that there are options embedded in many actions, we consider the conditions that have to be met for these options to have value. We also develop a series of applied examples, where we attempt to value these options and consider the effect on investment, financing and valuation decisions. 3 In finance, the discounted cash flow model operates as the basic framework for most analysis. In investment analysis, for instance, the conventional view is that the net present value of a project is the measure of the value that it will add to the firm taking it. Thus, investing in a positive (negative) net present value project will increase (decrease) value. In capital structure decisions, a financing mix that minimizes the cost of capital, without impairing operating cash flows, increases firm value and is therefore viewed as the optimal mix. -
OPTION-BASED EQUITY STRATEGIES Roberto Obregon
MEKETA INVESTMENT GROUP BOSTON MA CHICAGO IL MIAMI FL PORTLAND OR SAN DIEGO CA LONDON UK OPTION-BASED EQUITY STRATEGIES Roberto Obregon MEKETA INVESTMENT GROUP 100 Lowder Brook Drive, Suite 1100 Westwood, MA 02090 meketagroup.com February 2018 MEKETA INVESTMENT GROUP 100 LOWDER BROOK DRIVE SUITE 1100 WESTWOOD MA 02090 781 471 3500 fax 781 471 3411 www.meketagroup.com MEKETA INVESTMENT GROUP OPTION-BASED EQUITY STRATEGIES ABSTRACT Options are derivatives contracts that provide investors the flexibility of constructing expected payoffs for their investment strategies. Option-based equity strategies incorporate the use of options with long positions in equities to achieve objectives such as drawdown protection and higher income. While the range of strategies available is wide, most strategies can be classified as insurance buying (net long options/volatility) or insurance selling (net short options/volatility). The existence of the Volatility Risk Premium, a market anomaly that causes put options to be overpriced relative to what an efficient pricing model expects, has led to an empirical outperformance of insurance selling strategies relative to insurance buying strategies. This paper explores whether, and to what extent, option-based equity strategies should be considered within the long-only equity investing toolkit, given that equity risk is still the main driver of returns for most of these strategies. It is important to note that while option-based strategies seek to design favorable payoffs, all such strategies involve trade-offs between expected payoffs and cost. BACKGROUND Options are derivatives1 contracts that give the holder the right, but not the obligation, to buy or sell an asset at a given point in time and at a pre-determined price. -
Default & Returns on High Yield Corporate Bonds
Soluzioni Innovative: (Private) & Public Debt Crediamo nella supremazia della Conoscenza. Dr. Edward Altman Crediamo nelle forza delle Idee. Co-Founder & Senior Advisor Classis Capital Sim SpA Crediamo nell’Ispirazione. 1 Turin, April 12, 2017 Agenda . Current Conditions and Outlook in Global Credit Markets . Assessing the Credit Health of the Italian SME Sector . Minibond Issuers 2 Major Agencies Bond Rating Categories Moody's S&P/Fitch Aaa AAA Aa1 AA+ Aa2 AA Aa3 AA- A1 A+ A2 A A3 A- Baa1 BBB+ Baa2 Investment BBB Baa3 Grade BBB- Ba1 High Yield BB+ Ba2 ("Junk") BB Ba3 BB- B1 B+ B2 B B3 B- High Yield Caa1 CCC+ Market Caa CCC Caa3 CCC- Ca CC C C D 3 Size Of High-Yield Bond Market 1978 – 2017 (Mid-year US$ billions) $1.800 $1,624 $1.600 Source: NYU $1.400 Salomon Center $1.200 estimates US Market using Credit $1.000 Suisse, S&P $800 and Citi data $ (Billions)$ $600 $400 $200 $- 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 1994 – 2016 (Mid-year € billions)* 500 468€ 471 Western Europe Market 418 400 370 ) 300 283 Source: Credit 200 194 Suisse Billions ( 154 € 108 100 81 61 70 89 84 81 79 80 77 0 2 5 9 14 27 45 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 *Includes non-investment grade straight corporate debt of issuers with assets located in or revenues derived from Western Europe, or the bond is denominated in a Western European currency. -
Derivative Securities
2. DERIVATIVE SECURITIES Objectives: After reading this chapter, you will 1. Understand the reason for trading options. 2. Know the basic terminology of options. 2.1 Derivative Securities A derivative security is a financial instrument whose value depends upon the value of another asset. The main types of derivatives are futures, forwards, options, and swaps. An example of a derivative security is a convertible bond. Such a bond, at the discretion of the bondholder, may be converted into a fixed number of shares of the stock of the issuing corporation. The value of a convertible bond depends upon the value of the underlying stock, and thus, it is a derivative security. An investor would like to buy such a bond because he can make money if the stock market rises. The stock price, and hence the bond value, will rise. If the stock market falls, he can still make money by earning interest on the convertible bond. Another derivative security is a forward contract. Suppose you have decided to buy an ounce of gold for investment purposes. The price of gold for immediate delivery is, say, $345 an ounce. You would like to hold this gold for a year and then sell it at the prevailing rates. One possibility is to pay $345 to a seller and get immediate physical possession of the gold, hold it for a year, and then sell it. If the price of gold a year from now is $370 an ounce, you have clearly made a profit of $25. That is not the only way to invest in gold. -
Chapter 21 . Options
Chapter 21 : Options-1 CHAPTER 21 . OPTIONS Contents I. INTRODUCTION · BASIC TERMS II. VALUATION OF OPTIONS A. Minimum Values of Options B. Maximum Values of Options C. Determinants of Call Value D. Black-Scholes Option Pricing Model (1973, BSOPM) E. Put-Call Parity III. EXERCISE FOR PAYOFF DIAGRAM IV. ASSIGNED PROBLEMS FROM THE TEXTBOOK V. SELF-EXERCISE PROBLEMS I. INTRODUCTION · BASIC TERMS 1. Option : right to buy (or sell) an asset at a fixed price on or before a given date Right ® buyer of option has no obligation, seller of option is obligated Call ® right to buy Put ® right to sell Note: Option may be written on any type of asset => most common is stock 2. Exercising the option - buying or selling asset by using option 3. Strike (or exercise) price - price at which asset may be bought or sold 4. Expiration date - last date on which option may be exercised 5. European option - may be exercised only at expiration date 6. American option - may be exercised on or before expiration date 7. In-the-money - positive cash flow if exercised ® call [put] =? 8. Out-of-the-money - negative cash flow if exercised ® call [put] = ? Chapter 21 : Options-2 9. At-the-money - zero cash flow if exercised ® call [put] = ? Chapter 21 : Options-3 II. VALUATION OF OPTIONS A. Minimum Values of Options 1. Minimum Value of Call A call option is an instrument with limited liability. If the call holder sees that it is advantageous to exercise it, the call will be exercised. If exercising it will decrease the call holder's wealth, the holder will not exercise it. -
Bond Risk, Bond Return Volatility, and the Term Structure of Interest Rates
Bond Risk, Bond Return Volatility, and the Term Structure of Interest Rates Luis M. Viceira1 Forthcoming International Journal of Forecasting This draft: January 2010 Abstract This paper explores time variation in bond risk, as measured by the covariation of bond returns with stock returns and with consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yield on long-term bonds and short-term bonds forecasts positively future excess returns on bonds at varying horizons, and that the short-term nominal interest rate forecasts positively stock return volatility and exchange rate volatility. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component, and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with larger discount rate risk for bonds. The short rate forecasts only the discount rate component of bond beta. JEL classification:G12. 1Graduate School of Business Administration, Baker Libray 367, Harvard Univer- sity, Boston MA 02163, USA, CEPR, and NBER. Email [email protected]. Website http://www.people.hbs.edu/lviceira/. I am grateful to John Campbell, Jakub Jurek, André Per- old, participants in the Lisbon International Workshop on the Predictability of Financial Markets, and especially to two anonymous referees and Andréas Heinen for helpful comments and suggestions. -
Introduction to Options Mark Welch and James Mintert*
E-499 RM2-2.0 01-09 Risk Management Introduction To Options Mark Welch and James Mintert* Options give the agricultural industry a flexi- a put option can convert an option position into ble pricing tool that helps with price risk manage- a short futures position, established at the strike ment. Options offer a type of insurance against price, by exercising the put option. Similarly, the adverse price moves, require no margin deposits buyer of a call option can convert an option posi- for buyers, and allow buyers to participate in tion into a long futures position, established at favorable price moves. Commodity options are the strike price, by exercising the call option. The adaptable to a wide range of pricing situations. option buyer also can sell the option to someone For example, agricultural producers can use com- else or do nothing and let the option expire. The modity options to establish an approximate price choice of action is left entirely to the option buyer. floor, or ceiling, for their production or inputs. The option buyer obtains this right by paying the With today’s large price fluctuations, the financial premium to the option seller. payoff in controlling price risk and protecting What about the option seller? The option seller profits can be substantial. receives the premium from the option buyer. If the option buyer exercises the option, the option What is an Option? seller is obligated to take the opposite futures An option is simply the right, but not the position at the same strike price. Because of the obligation, to buy or sell a futures contract at seller’s obligation to take a futures position if the some predetermined price within a specified option is exercised, an option seller must post a time period.