...Option Pricing: A Simplified Approach† John C. Cox Massachusetts Institute of Technology and Stanford University Stephen A. Ross Yale University Mark Rubinstein University of California, Berkeley March 1979 (revised July 1979) (published under the same title in Journal of Financial Economics (September 1979)) [1978 winner of the Pomeranze Prize of the Chicago Board Options Exchange] [reprinted in Dynamic Hedging: A Guide to Portfolio Insurance, edited by Don Luskin (John Wiley and Sons 1988)] [reprinted in The Handbook of Financial Engineering, edited by Cliff Smith and Charles Smithson (Harper and Row 1990)] [reprinted in Readings in Futures Markets published by the Chicago Board of Trade, Vol. VI (1991)] [reprinted in Vasicek and Beyond: Approaches to Building and Applying Interest Rate Models, edited by Risk Publications, Alan Brace (1996)] [reprinted in The Debt Market, edited by Stephen Ross and Franco Modigliani (Edward Lear Publishing 2000)] [reprinted in The International Library of Critical Writings in Financial Economics: Options Markets edited by G.M. Constantinides and A..G. Malliaris (Edward Lear Publishing 2000)] Abstract This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived...
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...values through hedging by reducing taxable income, agency cost and the cost of financial distress. This report provides a qualitative and quantitative analysis of corporate risk management for the company Air New Zealand. We uses a time series OLS regression model. The fair value of derivatives is used as dependent variable to measure the extent of financial instrument usage. The result shows that the use of derivatives by Air NZ fails to add value to the company. FINA781 Report Page 1 1. Introduction Air New Zealand Limited is the national airline and flag carrier of New Zealand. Based in Auckland, New Zealand, the airline operates scheduled passenger flights to 56 destinations locally and internationally. Air New Zealand is a member of the Star Alliance global airline alliance, having joined in 1999. Air New Zealand originated in 1940 as Tasman Empire Airways Limited (TEAL), a flying boat company operating trans-Tasman flights between New Zealand and Australia. TEAL became wholly owned by the New Zealand government in 1965, whereupon it was renamed Air New Zealand. The airline was largely privatized in 1989, but returned to majority government ownership in 2001 after a failed tie up with Australian carrier Ansett Australia. As of 2008, Air New Zealand carries 11.7 million passengers annually. Do hedging create firm value has been a popular topic argued through decades. In this report we are going to identify whether Air New Zealand create value through hedging. In this...
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...J. of Multi. Fin. Manag. 13 (2003) 123 Á/139 www.elsevier.com/locate/econbase Foreign-denominated debt and foreign currency derivatives: complements or substitutes in hedging foreign currency risk? William B. Elliott a,*, Stephen P. Huffman b, Stephen D. Makar b a Department of Finance, Oklahoma State University, 224 Business, Stillwater, OK 74078, USA b University of Wisconsin Oshkosh, Oshkosh, WI, USA Received 30 June 2001; accepted 20 April 2002 Abstract Using a unique dataset, this study examines the relationship between foreign-denominated debt (FDD), foreign currency exposure and foreign currency derivative (FCD) use, for a sample of US multinational corporations. We find a positive relationship between the exposure to foreign currency risk and the level of FDD, indicating that this debt may be used as a hedge. Moreover, FDD is negatively related to the use of FCD. We interpret this as further evidence that FDD is used as a hedge, and substitutes for the use of FCD in reducing currency risk. # 2002 Elsevier Science B.V. All rights reserved. Keywords: F23 Keywords: Hedging; Foreign debt; Currency derivatives 1. Introduction US multinational corporations (MNCs) employ a variety of financial and nonfinancial techniques to reduce or hedge their exposure to changing exchange rates (e.g. Bodnar et al., 1998; Marshall, 2000). Financial techniques include foreign- * Corresponding author. Tel.: '/1-405-744-8639; fax: '/1-405-744-5180 E-mail address: elliowb@okstate...
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...PART 1 Introduction Objective – The objective is to protect the capital value of the stock positions, while having a short term cautiously bullish view on the stock but also concerned about the fall in the price. Hence a combination of collar strategy and protective put was adopted, as they are more appropriate for a short term period. Only one stock was shorted. Also we seek a target return of 10% annualized. Benefits & Risks - Our profit potential is not limited, so if the share price rise, we still benefit from increase in value of share. The strategy being effective for a short period. The options chosen were of shorter time period as the time decay works in our favour which have been written, time erodes faster when option approaches expiry. Also out of the money options were chosen as there was an expectation that calls would not be realised as the stock price would reasonably grow. This led to increase participation in share price rise while the trade-off is on premium received which is lower for out of money options. A detailed explanation has been provided in APPENDIX A. Portfolio Construction A portfolio of 6 stocks from ASX200 and their related options was constructed on 03rd Sep’15 to be held for 2 weeks and then squared off at the end of the period. The top performing stocks from well diversified sectors were identified based on fundamental and market analysis. 1) Energy sector - AGL Energy Limited (AGL) 2) Healthcare sector -Sonic Healthcare...
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...and faster growth of financial industry, Foreign Exchange high-frequency trading has become substantially more prominent to today’s market players, especially to bankers and market makers. This research aims at introducing today’s FX high-frequency trading structure and discussing how a market maker can effectively reduce downside risk when market faces a huge upward or downward stress. An Exponential Moving Average operator is introduced and implemented using a Matlab software for tick-by-tick data analysis. Simulation framework for market high-frequency data and client trading flow is also introduced and implemented using the Matlab software. Real-time P&L calculation is introduced and used to determine the performance of a proposed risk hedging strategy. On the other hand, due to the financial crisis we experienced in 2007, 2008, and 2009, we analyze the tail risk of foreign exchange market. Extreme Value Theory (EVT) has been applied to real EUR/USD data, which contains eight-year daily closing exchange rate. An extension of from EVT to Value-at-Risk (VaR) calculation is introduced. We also consider the volatility clustering issue in asset returns and demonstrate how GARCH model can be applied for VaR calculation. Lastly, we propose a method of using VaR as a...
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...LECTURE 7: BLACK–SCHOLES THEORY 1. Introduction: The Black–Scholes Model In 1973 Fisher Black and Myron Scholes ushered in the modern era of derivative securities with a seminal paper1 on the pricing and hedging of (European) call and put options. In this paper the famous Black-Scholes formula made its debut, and the Itˆ calculus was unleashed upon the world o 2 of finance. In this lecture we shall explain the Black-Scholes argument in its original setting, the pricing and hedging of European contingent claims. In subsequent lectures, we will see how to use the Black–Scholes model in conjunction with the Itˆ calculus to price and hedge all manner of o exotic derivative securities. In its simplest form, the Black–Scholes(–Merton) model involves only two underlying assets, a riskless asset Cash Bond and a risky asset Stock.3 The asset Cash Bond appreciates at the short rate, or riskless rate of return rt , which (at least for now) is assumed to be nonrandom, although possibly time–varying. Thus, the price Bt of the Cash Bond at time t is assumed to satisfy the differential equation dBt (1) = rt Bt , dt whose unique solution for the value B0 = 1 is (as the reader will now check) t (2) rs ds . Bt = exp 0 The share price St of the risky asset Stock at time t is assumed to follow a stochastic differential equation (SDE) of the form (3) dSt = µt St dt + σSt dWt , where {Wt }t≥0 is a standard Brownian motion, µt is a nonrandom (but not necessarily...
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...Essays in Banking and Risk Management by James Ian Vickery B.Ec.(Hons), University of New South Wales (1997) Submitted to the Department of Economics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2004 c ° James Ian Vickery, MMIV. All rights reserved. The author hereby grants to Massachusetts Institute of Technology permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Department of Economics August 15 2004 Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ricardo Caballero Ford International Professor of Economics Thesis Supervisor Accepted by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Temin Elisha Gray II Professor of Economics Chairperson, Department Committee on Graduate Studies Essays in Banking and Risk Management by James Ian Vickery Submitted to the Department of Economics on August 15 2004, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics Abstract This thesis consists of...
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...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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...Essays in Banking and Risk Management by James Ian Vickery B.Ec.(Hons), University of New South Wales (1997) Submitted to the Department of Economics in partial fulllment of the requirements for the degree of Doctor of Philosophy in Economics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2004 c ° James Ian Vickery, MMIV. All rights reserved. The author hereby grants to Massachusetts Institute of Technology permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Department of Economics August 15 2004 Certied by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ricardo Caballero Ford International Professor of Economics Thesis Supervisor Accepted by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Temin Elisha Gray II Professor of Economics Chairperson, Department Committee on Graduate Studies Essays in Banking and Risk Management by James Ian Vickery Submitted to the Department of Economics on August 15 2004, in partial fulllment of the requirements for the degree of Doctor of Philosophy in Economics Abstract This thesis consists of three essays at the intersection...
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...Financial Institutions Center Derivatives and Corporate Risk Management: Participation and Volume Decisions in the Insurance Industry by J. David Cummins Richard D. Phillips Stephen D. Smith 98-19 THE WHARTON FINANCIAL INSTITUTIONS CENTER The Wharton Financial Institutions Center provides a multi-disciplinary research approach to the problems and opportunities facing the financial services industry in its search for competitive excellence. The Center's research focuses on the issues related to managing risk at the firm level as well as ways to improve productivity and performance. The Center fosters the development of a community of faculty, visiting scholars and Ph.D. candidates whose research interests complement and support the mission of the Center. The Center works closely with industry executives and practitioners to ensure that its research is informed by the operating realities and competitive demands facing industry participants as they pursue competitive excellence. Copies of the working papers summarized here are available from the Center. If you would like to learn more about the Center or become a member of our research community, please let us know of your interest. Anthony M. Santomero Director The Working Paper Series is made possible by a generous grant from the Alfred P. Sloan Foundation Derivatives and Corporate Risk Management: Participation and Volume Decisions in the Insurance Industry By J. David Cummins Wharton School, University...
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...will beat the other major airlines. Compare this to Walmart, it is possible to find an item Walmart sells for a lower price somewhere else but not often and not without considerable effort. Most people believe it is easier and cheaper to just shop at Walmart instead of hunting around for that occasional deal elsewhere. Continuing the everyday low price model is an important tenet of Southwest Airlines. Management has used this pricing model for the entire forty-three years history of the company and will continue to do so into the future. This pricing model can only be sustained by the company keeping the cost of doing business down. Some of the methods Southwest has employed to keep their overhead costs low include long term fuel price hedging, a simpler bag check and ticketing process which allows for faster loading times and a reduced number of employees needed. Southwest Airlines’ premier cost saving and efficiency measure is there use of only one airframe, Boeing’s 737-800. Use of one airframe allows cost saving when it comes to maintenance, pilot training and rest rotations. Channels of Distribution Southwest Airlines only uses a few simple and straight forward...
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...FIN 535 – International Finance COURSE DESCRIPTION Presents international financial tools, applications, and concepts used in formulating effective financial management strategies. Examines fundamental international financial relationships and transactions among firms, foreign exchange rate determination and forecasting, foreign exchange risk and exposure, balance of payment accounting, and evolution of the international monetary system. Analyzes special topics such as working capital management strategies, capital budgeting, cost of capital, and optimal capital structure in the context of international operations. INSTRUCTIONAL MATERIALS Required Resources Madura, J. (2012). International financial management (11th ed.). Mason, OH: South-Western, Cengage Learning. Supplemental Resources Al Nasser, O.M. (2010). How does foreign direct investment affect economic growth? The role of local conditions. Latin American Business Review 11, 111-139. Kornecki, L. & E. M. Ekanayake. (2011). Inward FDI stock in the U.S. economy and state based determinants. Advances in Management, 4(6), 13-24. Ranjan, V. & Agrawal, G. (2011). FDI inflow determinants in BRIC countries: A panel data analysis. International Business Research, 4(4), 255-263. United Nations. (2011). Foreign Direct Investments in LDCs: Lessons learned from the decade 20012010 and the way forward. United National Conference on Trade and Development. COURSE LEARNING OUTCOMES 1. Compare multinational financial management...
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...average price put 17 References 20 Chapter 1- Introduction Asian option is one type of options where the payoff is determined by the average underlying stock price over a period of time. This differs from the usual European and American options where the payoff depends on the price of the underlying instrument at exercise. Therefore, the Asian options are one of the forms of exotic options. Asian options have a lower volatility and hence rendering them cheaper relative to their European counterparts. They were originally used in 1987 when Banker's Trust Tokyo office used them for pricing average options on crude oil contracts; and hence the name "Asian" option. The popularity of these derivatives arises from their usefulness in hedging, and other...
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...HOW TOTAL WEALTH OF THE CEO AFFECTS THE RISK POLICY OF FIRM OLD DOMINION UNIVERSITY FIN 863 FINAL PROJECT BY SONIK MANDAL CHARLIE SWARTZ INTRODUCTION Agency theory states that the goals of the owners and the managers of a firm diverge in a way that the managers take less risk since their ownership of the company is much less compared to the owners of the firm who have a much bigger stake in the company. Thus managers being risk averse, they forego profitable ventures if they anticipate them to be risky (Guay, 1999, Jensen & Meckling, 1976). Making the salary structure more convex by introducing more option-based compensation and stock awards is one way owners try to align the goals of the managers with the owners. But managerial wealth attached to the firm is only a fraction of their total personal wealth in the portfolio. Other components of manager’s total wealth could be stocks owned in other companies, real estate portfolio, and other debt related securities. A lot of research has been done in the past explaining how managerial compensation structure (options, stock awards etc.) affect his risk taking abilities (Knopf et al. 2002, Rogers, 2002, etc.). But not much research has been done showing how manager’s outside wealth affects his risk taking in the firm. As far as we know, the only paper that has looked at this relationship is by Elsila et al. 2013 but that paper only looked at the Swedish listed firms...
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...Journal of Banking & Finance 25 (2001) 535±554 www.elsevier.com/locate/econbase Eciency of the Dojima rice futures market in Tokugawa-period Japan Shigeru Wakita * Faculty of Economics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo, 192-0397 Japan Received 21 May 1998; accepted 20 December 1999 Abstract Co-integration analysis is applied to historical data (1760±1864) from the worldÕs ®rst well-established futures market, in rice at Dojima (in Osaka, Japan). The market shows a strong seasonal character. The summer market was strongly characterized by producersÕ hedging behavior, and may be called a ``commodity-oriented futures market''. On the other hand, the spring and autumn markets in the middle of Tokugawa era were ``®nancial'' markets, characterized by the unbiasedness hypothesis from the theory of rational expectations. Ó 2001 Elsevier Science B.V. All rights reserved. JEL classi®cation: G13; N25 Keywords: Futures market; Market eciency; Cointegration; Osaka 1. Introduction In Tokugawa-period Japan (1603±1867), the rice trading center was Osaka, a city called the ``kitchen for the country''. It was there that clan governments (Han) across the land shipped much of the rice they collected as land tax in lieu of cash. In Dojima, the site of the rice trading activities, a rice futures market * Tel.: +81-426-77-2307; fax: +81-426-77-2304. E-mail address: wakita@bcomp.metro-u.ac.jp (S. Wakita). 0378-4266/01/$ - see front matter Ó 2001...
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