DOCSLIB.ORG

Fineconslides2017

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Fineconslides2017 Introduction. Financial Economics Slides Howard C. Mahler, FCAS, MAAA These are slides that I have presented at a seminar or weekly class. The whole syllabus of Exam MFE is covered. For the new syllabus introduced with the July 2017 Exam. At the end is my section of important ideas and formulas. Use the bookmarks / table of contents in the Navigation Panel in order to help you find what you want. This provides another way to study the material. Some of you will find it helpful to go through one or two sections at a time, either alone or with a someone else, pausing to do each of the problems included. All the material, problems, and solutions are in my study guide, sold separately.1 These slides are a useful supplement to my study guide, but are self-contained. There are references to page and problem numbers in the latest edition of my study guide, which you can ignore if you do not have my study guide. The slides are in the same order as the sections of my study guide. At the end, there are some additional questions for study. SectionPages # Section Name A 1 9-17Introduction 2 18-31Financial Markets and Assets 3 32-53European Call Options B 4 54-86European Put Options 5 87-174Named Positions 6 175-224Forward Contracts C 7 225-243Futures Contracts 8 244-281Properties of Premiums of European Options 9 282-336Put-Call Parity 10 337-350Bounds on Premiums of European Options 11 351-369Options on Currency D 12 370-376Exchange Options 13 377-382Options on Futures Contracts 14 383-391Synthetic Positions E 15 392-438American Options 16 439-463Replicating Portfolios 17 464-486Risk Neutral Probabilities 18 487-494Random Walks F 19 495-559Binomial Trees, Risk Neutral Probabilities 20 560-579Binomial Trees, Valuing Options on Other Assets 1 My practice exams are also sold separately. SectionPages # Section Name A 21 580-596Other Binomial Trees 22 597-619Binomial Trees, Actual Probabilities 23 620-630Jensen's Inequality B 24 631-642Normal Distribution 25 643-654LogNormal Distribution 26 655-659Limited Expected Value C 27 660-735A LogNormal Model of Stock Prices 28 736-787Black-Scholes Formula 29 788-797Black-Scholes, Options on Currency 30 798-803Black-Scholes, Options on Futures Contracts 31 804-814Black-Scholes, Stocks Paying Discrete Dividends D 32 815-839Using Historical Data to Estimate Parameters of the Stock Price Model 33 840-860Implied Volatility 34 861-910Option Greeks E 35 911-921Delta-Gamma Approximation 36 922-946Profit on Options Prior to Expiration 37 947-960Elasticity 38 961-966Volatility of an Option F 39 967-972Risk Premium of an Option 40 973-981Sharpe Ratio of an Option 41 982-983Market Makers 42984-1028Delta Hedging 431029-1046Gamma Hedging 441047-1048Relationship to Insurance 45 Exotic Options 461050-1074Asian Options 471075-1113Barrier Options 481114-1147Compound Options 491148-1173Gap Options 501174-1187Valuing European Exchange Options 511188-1198Forward Start Options 521199-1211Chooser Options 531212-1224Options on the Best of Two Assets 541225-1234Lookback Options 551235-1250Cash-or-Nothing Options SectionPages # Section Name S 561251-1272Asset-or-Nothing Options 571273-1282Simulation 581283-1290Simulating Normal and LogNormal Distributions T 591291-1306Simulating LogNormal Stock Prices 601307-1315Valuing Asian Options via Simulation 611316-1346Improving Efficiency of Simulation 621347-1370Bonds and Interest Rates 631371-1381The Black Model U 641382-1399Interest Rate Caps 651400-1413Binomial Trees of Interest Rates V 661414-1466The Black-Derman-Toy Model 671467-1499Important Formulas and Ideas Chapter of Third Edition Derivatives Markets Sections of Study Guide 1 1, 2, 7 2.1-2.4 3, 4, 6 3 3-5, 9 52 6-7 9 8-15 103 16, 17, 19, 20 11.1 – 11.34 15, 18, 21-22 12.1-12.55 28-31, 33-34, 36-40 13 35, 41-44 146 45-53 18.1-18.57 24-27, 32 19.1-19.5 57-61 23.18 54-56 25.1, 25.4, 25.59 62-66 Appendix B.1 1 Appendix C 23 Unless otherwise stated chapter appendices are not included in the required readings from this text. 2 Sections 5.1-5.2, Section 5.3 (through the middle of p.136), Section 5.4 (through the top of p.143). 3 Excluding “Options on Commodities” on pages 315 and 316. 4 Including Appendix 11.A. 5 Including Appendices 12.A and Appendix 12.B. 6 Sections 14.1-14.3, Section 14.4 (through the bottom of p.419), Sections 14.5-14.6. 7 Including Appendix 18.A. 8 But with only those definitions in Tables 23.1 and 23.2 that are relevant to Section 23.1, including the top half of p.714 (Re: Lookback calls and puts). 9 Section 25.1 (through the bottom of p.754), Section 25.4 (through the middle of p.773), Section 25.5 (through the middle of p.781). Author Biography: Howard C. Mahler is a Fellow of the Casualty Actuarial Society, and a Member of the American Academy of Actuaries. He has taught actuarial exam seminars and published study guides since 1994. He spent over 20 years in the insurance industry, the last 15 as Vice President and Actuary at the Workers' Compensation Rating and Inspection Bureau of Massachusetts. He has published many major research papers and won the 1987 CAS Dorweiler prize. He served 12 years on the CAS Examination Committee including three years as head of the whole committee (1990-1993). Mr. Mahler has taught live seminars and/or classes for Exam C, Exam MFE, CAS Exam S, CAS Exam 5, and CAS Exam 8. He has written study guides for all of the above. [email protected] www.howardmahler.com/Teaching Exam MFE Financial Economics Seminar Style Slides prepared by Howard C. Mahler, FCAS Copyright 2017 by Howard C. Mahler. Howard Mahler [email protected] www.howardmahler.com/Teaching 2017 Financial Economics, HCM 3/26/17, Page 1 Introduction Continuously Compounded Risk Free Rate: r as used by McDonald is what an actuary would call the force of interest. The discount factor is: exp[-t r]. In contrast, an effective annual rate is what an actuary would call the rate of interest. The discount factor is: 1 / (1 + r)t. 2017 Financial Economics, HCM 3/26/17, Page 2 A derivative is an agreement between two people that has a value determined by the price of something else. A call is an option to buy. A put is an option to sell. 2017 Financial Economics, HCM 3/26/17, Page 3 A forward contract is an agreement that sets the terms today, but the buying or selling of the asset takes place in the future. For example, Clark agrees to sell Lois 100 shares of ABC stock for $60 per share one year from now. The purchaser of an option has bought the right to do something in the future, but has no obligation to do anything. In contrast, in a forward contract both parties are obligated to fulfill their parts of the contract. 2017 Financial Economics, HCM 3/26/17, Page 4 Futures contract is similar to forward contract except: • Typically traded on an exchange. • Marked to market periodically. € • The buyer and the seller post margin. € € 2017 Financial Economics, HCM 3/26/17, Page 5 Continuous Dividends: We often assume that dividends are paid at a continuous rate δ. So that if one buy a share of stock at time 0, and reinvests the dividends in the stock, at time T one would have eTδ shares of the stock. 2017 Financial Economics, HCM 3/26/17, Page 6 Continuously Compounded Returns: Let St and St+h be the stock prices at times t and t+h. Then the continuously compounded return on the stock between time t and t+h is: ln[St+h / St]. On an annual basis, this return is: ln[St+h / St] / h. For example, if the stock price is $80 at time 0 and $90 at time 2 years, then the continuously compounded return from time 0 to 2 is: ln[90 / 80] = 11.78%. On an annual basis, this return is: 11.78% / 2 = 5.89%. 2017 Financial Economics, HCM 3/26/17, Page 7 Long and Short Positions: Entering into a long position is buying. Entering into a short position is selling or writing. A position is long with respect to an underlying asset (stock or commodity) if it becomes more valuable when the price of the underlying increases. A position is short with respect to an underlying asset if it becomes less valuable when the price of the underlying increases. 2017 Financial Economics, HCM 3/26/17, Page 8 Selling Short: If we sell a stock short, then we borrow a share of stock and sell it for the current market price. At the designated time in the future, we will return a share of stock to the person from whom we borrowed it. We also must pay the person from whom we borrowed the stock any stock dividends they would have gotten on the stock, when they would have gotten them. 2017 Financial Economics, HCM 3/26/17, Page 9 Ozzie borrows 1000 shares of stock from Harriet and sells them. The stock pays dividends at a continuously compounded annual rate of 1%. If Ozzie agreed to return the shares in six months, then he would return to Harriet 1000 e1%/2 = 1005 shares. 2017 Financial Economics, HCM 3/26/17, Page 10 Arbitrage: If there is a possible combination of buying and selling with no net investment that has no risk but generates nonnegative cashflows, this is an arbitrage opportunity.
Load more

Recommended publications
  • Up to EUR 3,500,000.00 7% Fixed Rate Bonds Due 6 April 2026 ISIN
    Up to EUR 3,500,000.00 7% Fixed Rate Bonds due 6 April 2026 ISIN IT0005440976 Terms and Conditions Executed by EPizza S.p.A. 4126-6190-7500.7 This Terms and Conditions are dated 6 April 2021. EPizza S.p.A., a company limited by shares incorporated in Italy as a società per azioni, whose registered office is at Piazza Castello n. 19, 20123 Milan, Italy, enrolled with the companies’ register of Milan-Monza-Brianza- Lodi under No. and fiscal code No. 08950850969, VAT No. 08950850969 (the “Issuer”). *** The issue of up to EUR 3,500,000.00 (three million and five hundred thousand /00) 7% (seven per cent.) fixed rate bonds due 6 April 2026 (the “Bonds”) was authorised by the Board of Directors of the Issuer, by exercising the powers conferred to it by the Articles (as defined below), through a resolution passed on 26 March 2021. The Bonds shall be issued and held subject to and with the benefit of the provisions of this Terms and Conditions. All such provisions shall be binding on the Issuer, the Bondholders (and their successors in title) and all Persons claiming through or under them and shall endure for the benefit of the Bondholders (and their successors in title). The Bondholders (and their successors in title) are deemed to have notice of all the provisions of this Terms and Conditions and the Articles. Copies of each of the Articles and this Terms and Conditions are available for inspection during normal business hours at the registered office for the time being of the Issuer being, as at the date of this Terms and Conditions, at Piazza Castello n.
    [Show full text]
  • Tracking and Trading Volatility 155
    ffirs.qxd 9/12/06 2:37 PM Page i The Index Trading Course Workbook www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page ii Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Aus- tralia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Wiley Trading series features books by traders who have survived the market’s ever changing temperament and have prospered—some by reinventing systems, others by getting back to basics. Whether a novice trader, professional, or somewhere in-between, these books will provide the advice and strategies needed to prosper today and well into the future. For a list of available titles, visit our web site at www.WileyFinance.com. www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page iii The Index Trading Course Workbook Step-by-Step Exercises and Tests to Help You Master The Index Trading Course GEORGE A. FONTANILLS TOM GENTILE John Wiley & Sons, Inc. www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page iv Copyright © 2006 by George A. Fontanills, Tom Gentile, and Richard Cawood. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com.
    [Show full text]
  • (NSE), India, Using Box Spread Arbitrage Strategy
    Gadjah Mada International Journal of Business - September-December, Vol. 15, No. 3, 2013 Gadjah Mada International Journal of Business Vol. 15, No. 3 (September - December 2013): 269 - 285 Efficiency of S&P CNX Nifty Index Option of the National Stock Exchange (NSE), India, using Box Spread Arbitrage Strategy G. P. Girish,a and Nikhil Rastogib a IBS Hyderabad, ICFAI Foundation For Higher Education (IFHE) University, Andhra Pradesh, India b Institute of Management Technology (IMT) Hyderabad, India Abstract: Box spread is a trading strategy in which one simultaneously buys and sells options having the same underlying asset and time to expiration, but different exercise prices. This study examined the effi- ciency of European style S&P CNX Nifty Index options of National Stock Exchange, (NSE) India by making use of high-frequency data on put and call options written on Nifty (Time-stamped transactions data) for the time period between 1st January 2002 and 31st December 2005 using box-spread arbitrage strategy. The advantages of box-spreads include reduced joint hypothesis problem since there is no consideration of pricing model or market equilibrium, no consideration of inter-market non-synchronicity since trading box spreads involve only one market, computational simplicity with less chances of mis- specification error, estimation error and the fact that buying and selling box spreads more or less repli- cates risk-free lending and borrowing. One thousand three hundreds and fifty eight exercisable box- spreads were found for the time period considered of which 78 Box spreads were found to be profit- able after incorporating transaction costs (32 profitable box spreads were identified for the year 2002, 19 in 2003, 14 in 2004 and 13 in 2005) The results of our study suggest that internal option market efficiency has improved over the years for S&P CNX Nifty Index options of NSE India.
    [Show full text]
  • Margin Requirements Across Equity-Related Instruments: How Level Is the Playing Field?
    Fortune pgs 31-50 1/6/04 8:21 PM Page 31 Margin Requirements Across Equity-Related Instruments: How Level Is the Playing Field? hen interest rates rose sharply in 1994, a number of derivatives- related failures occurred, prominent among them the bankrupt- cy of Orange County, California, which had invested heavily in W 1 structured notes called “inverse floaters.” These events led to vigorous public discussion about the links between derivative securities and finan- cial stability, as well as about the potential role of new regulation. In an effort to clarify the issues, the Federal Reserve Bank of Boston sponsored an educational forum in which the risks and risk management of deriva- tive securities were discussed by a range of interested parties: academics; lawmakers and regulators; experts from nonfinancial corporations, investment and commercial banks, and pension funds; and issuers of securities. The Bank published a summary of the presentations in Minehan and Simons (1995). In the keynote address, Harvard Business School Professor Jay Light noted that there are at least 11 ways that investors can participate in the returns on the Standard and Poor’s 500 composite index (see Box 1). Professor Light pointed out that these alternatives exist because they dif- Peter Fortune fer in a variety of important respects: Some carry higher transaction costs; others might have higher margin requirements; still others might differ in tax treatment or in regulatory restraints. The author is Senior Economist and The purpose of the present study is to assess one dimension of those Advisor to the Director of Research at differences—margin requirements.
    [Show full text]
  • Are Defensive Stocks Expensive? a Closer Look at Value Spreads
    Are Defensive Stocks Expensive? A Closer Look at Value Spreads Antti Ilmanen, Ph.D. November 2015 Principal For several years, many investors have been concerned about the apparent rich valuation of Lars N. Nielsen defensive stocks. We analyze the prices of these Principal stocks using value spreads and find that they are not particularly expensive today. Swati Chandra, CFA Vice President Moreover, valuations may have limited efficacy in predicting strategy returns. This piece lends insight into possible reasons by focusing on the contemporaneous relation (i.e., how changes in value spreads are related to returns over the same period). We highlight a puzzling case where a defensive long/short strategy performed well during a recent two- year period when its value spread normalized from abnormally rich levels. For most asset classes, cheapening valuations coincide with poor performance. However, this relationship turns out to be weaker for long/short factor portfolios where several mechanisms can loosen the presumed strong link between value spread changes and strategy returns. Such wedges include changing fundamentals, evolving positions, carry and beta mismatches. Overall, investors should be cognizant of the tenuous link between value spreads and returns. We thank Gregor Andrade, Cliff Asness, Jordan Brooks, Andrea Frazzini, Jacques Friedman, Jeremy Getson, Ronen Israel, Sarah Jiang, David Kabiller, Michael Katz, AQR Capital Management, LLC Hoon Kim, John Liew, Thomas Maloney, Lasse Pedersen, Lukasz Pomorski, Scott Two Greenwich Plaza Richardson, Rodney Sullivan, Ashwin Thapar and David Zhang for helpful discussions Greenwich, CT 06830 and comments. p: +1.203.742.3600 f: +1.203.742.3100 w: aqr.com Are Defensive Stocks Expensive? A Closer Look at Value Spreads 1 Introduction puzzling result — buying a rich investment, seeing it cheapen, and yet making money — in Are defensive stocks expensive? Yes, mildly, more detail below.
    [Show full text]
  • Evidence from SME Bond Markets
    Temi di discussione (Working Papers) Asymmetric information in corporate lending: evidence from SME bond markets by Alessandra Iannamorelli, Stefano Nobili, Antonio Scalia and Luana Zaccaria September 2020 September Number 1292 Temi di discussione (Working Papers) Asymmetric information in corporate lending: evidence from SME bond markets by Alessandra Iannamorelli, Stefano Nobili, Antonio Scalia and Luana Zaccaria Number 1292 - September 2020 The papers published in the Temi di discussione series describe preliminary results and are made available to the public to encourage discussion and elicit comments. The views expressed in the articles are those of the authors and do not involve the responsibility of the Bank. Editorial Board: Federico Cingano, Marianna Riggi, Monica Andini, Audinga Baltrunaite, Marco Bottone, Davide Delle Monache, Sara Formai, Francesco Franceschi, Salvatore Lo Bello, Juho Taneli Makinen, Luca Metelli, Mario Pietrunti, Marco Savegnago. Editorial Assistants: Alessandra Giammarco, Roberto Marano. ISSN 1594-7939 (print) ISSN 2281-3950 (online) Printed by the Printing and Publishing Division of the Bank of Italy ASYMMETRIC INFORMATION IN CORPORATE LENDING: EVIDENCE FROM SME BOND MARKETS by Alessandra Iannamorelli†, Stefano Nobili†, Antonio Scalia† and Luana Zaccaria‡ Abstract Using a comprehensive dataset of Italian SMEs, we find that differences between private and public information on creditworthiness affect firms’ decisions to issue debt securities. Surprisingly, our evidence supports positive (rather than adverse) selection. Holding public information constant, firms with better private fundamentals are more likely to access bond markets. Additionally, credit conditions improve for issuers following the bond placement, compared with a matched sample of non-issuers. These results are consistent with a model where banks offer more flexibility than markets during financial distress and firms may use market lending to signal credit quality to outside stakeholders.
    [Show full text]
  • 307439 Ferdig Master Thesis
    Master's Thesis Using Derivatives And Structured Products To Enhance Investment Performance In A Low-Yielding Environment - COPENHAGEN BUSINESS SCHOOL - MSc Finance And Investments Maria Gjelsvik Berg P˚al-AndreasIversen Supervisor: Søren Plesner Date Of Submission: 28.04.2017 Characters (Ink. Space): 189.349 Pages: 114 ABSTRACT This paper provides an investigation of retail investors' possibility to enhance their investment performance in a low-yielding environment by using derivatives. The current low-yielding financial market makes safe investments in traditional vehicles, such as money market funds and safe bonds, close to zero- or even negative-yielding. Some retail investors are therefore in need of alternative investment vehicles that can enhance their performance. By conducting Monte Carlo simulations and difference in mean testing, we test for enhancement in performance for investors using option strategies, relative to investors investing in the S&P 500 index. This paper contributes to previous papers by emphasizing the downside risk and asymmetry in return distributions to a larger extent. We find several option strategies to outperform the benchmark, implying that performance enhancement is achievable by trading derivatives. The result is however strongly dependent on the investors' ability to choose the right option strategy, both in terms of correctly anticipated market movements and the net premium received or paid to enter the strategy. 1 Contents Chapter 1 - Introduction4 Problem Statement................................6 Methodology...................................7 Limitations....................................7 Literature Review.................................8 Structure..................................... 12 Chapter 2 - Theory 14 Low-Yielding Environment............................ 14 How Are People Affected By A Low-Yield Environment?........ 16 Low-Yield Environment's Impact On The Stock Market........
    [Show full text]
  • 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.
    [Show full text]
  • Black-Scholes Equations
    Chapter 8 Black-Scholes Equations 1 The Black-Scholes Model Up to now, we only consider hedgings that are done upfront. For example, if we write a naked call (see Example 5.2), we are exposed to unlimited risk if the stock price rises steeply. We can hedge it by buying a share of the underlying asset. This is done at the initial time when the call is sold. We are then protected against any steep rise in the asset price. However, if we hold the asset until expiry, we are not protected against any steep dive in the asset price. So is there a hedging that is really riskless? The answer was given by Black and Scholes, and also by Merton in their seminal papers on the theory of option pricing published in 1973. The idea is that a writer of a naked call can protect his short position of the option by buying a certain amount of the stock so that the loss in the short call can be exactly offset by the long position in the stock. This is standard in hedging. The question is how many stocks should he buy to minimize the risk? By adjusting the proportion of the stock and option continuously in the portfolio during the life of the option, Black and Scholes demonstrated that investors can create a riskless hedging portfolio where all market risks are eliminated. In an efficient market with no riskless arbitrage opportunity, any portfolio with a zero market risk must have an expected rate of return equal to the riskless interest rate.
    [Show full text]
  • Volatility Uncertainty and the Cross-Section of Option Returns*
    Volatility Uncertainty and * the Cross-Section of Option Returns [December 24, 2019] Jie Cao The Chinese University of Hong Kong E-mail: [email protected] Aurelio Vasquez ITAM E-mail: [email protected] Xiao Xiao Erasmus University Rotterdam E-mail: [email protected] Xintong Zhan The Chinese University of Hong Kong E-mail: [email protected] Abstract This paper studies the relation between the uncertainty of volatility, measured as the volatility of volatility, and future delta-hedged equity option returns. We find that delta-hedged option returns consistently decrease in uncertainty of volatility. Our results hold for different measures of volatility such as implied volatility, EGARCH volatility from daily returns, and realized volatility from high-frequency data. The results are robust to firm characteristics, stock and option liquidity, volatility characteristics, and jump risks, and are not explained by common risk factors. Our findings suggest that option dealers charge a higher premium for single-name options with high uncertainty of volatility, because these stock options are more difficult to hedge. * We thank Peter Christoffersen, Christian Dorion, Bjorn Eraker, Stephen Figlewski, Amit Goyal, Bing Han, Jianfeng Hu, Kris Jacobs, Inmoo Lee, Lei Jiang, Neil Pearson, and seminar participants at The Chinese University of Hong Kong, Erasmus University Rotterdam, Korea Advanced Institute of Science and Technology, HEC Montréal, Wilfrid Laurier University, and University of Hong Kong. We have benefited from the comments of participants at the 2018 Canadian Derivatives Institute (CDI) Annual Conference, the 2018 China International Conference in Finance, the 2018 Northern Finance Association Annual Conference, and the 2018 SFS Cavalcade Asia-Pacific.
    [Show full text]
  • Basic Financial Derivatives
    An Introduction to Lecture 3 Mathematical Finance UiO-STK-MAT3700 Autumn 2018 Professor: S. Ortiz-Latorre Basic Financial Derivatives The valuation of financial derivatives will be based on the principle of no arbitrage. Definition 1. Arbitrage means making of a guaranteed risk free profit with a trade or a series of trades in the market. Definition 2. An arbitrage free market is a market which has no opportunities for risk free profit. Definition 3. An arbitrage free price for a security is a price that ensure that no arbitrage opportunity can be designed with that security. The principle of no arbitrage states that the markets must be arbitrage free. Some financial jargon will be used in what follows. One says that has/takes a long position on an asset if one owns/is going to own a positive amount of that asset. One says that has/takes a short position on an asset if one has/is going to have a negative amount of that asset. Being short on money means borrowing. You can take a short position on many financial assets by short selling. Example 4 (Short selling). To implement some trading strategy you need to sell some amount of shares (to get money and invest in other assets). The problem is that you do not have any shares right now. Then, you can borrow the shares from another investor for a time period (paying interest) and sell the borrowed shares in the market to get the money you need for your strategy. To close this position, at the end of the borrowing period you must buy again the shares in the market and give them back to the lender.
    [Show full text]
  • Copyrighted Material
    Index Above par 8 Bear spread 169 Accounting for dividends 88–90 Below par 8 Agreements 1, 2, 8, 34–41, 199, 321 Bermudan option 151 American option 151, 155–6 Bermudan swaption 195 early exercise boundary 156–8, 224 ‘Best of’ option 209 pricing 158–9 Beta, volatility Annual bond 23 estimation 357–9 Annual compounding factor 5 mapping 356–7 Annual coupons 10 Binary option 152, 214 Annual equivalent yield 29 Binomial option pricing model 138, 148–51 Annual rate 3 Binomial tree 148, 244 Arbitrage pricing 82, 87–8, 92–3, 144, 224 BIS Quarterly Review 73 Arbitrageurs 87 Bivariate GARCH model 262 Arithmetic Brownian motion 139, 141, 291 Black-Scholes-Merton (BSM) formula 137, Arithmetic process 18 139, 173, 176, 179 Asian option 208, 221–4 Black-Scholes-Merton (BSM) model 173–85 Asset management, factor models in 326 assumptions 174 Asset-or-nothing option 152 implied volatility 183, 231–42 ATM option 154, 155, 184, 190, 238, 239, interpretation of formula 180–3 240, 318 partial differentiatial equation (PDE) 139, At par 8 175–6 At-the-money (ATM) option 154, 155, 18, prices adjusted for stochastic volatility 190, 238, 240, 318 http://www.pbookshop.com183–5 Average price option 208, 222–4 pricing formula 178–80 Average strike option 208, 221–4 underlying contract 176–8 Black–Scholes–Merton Greeks 186–93 Bank of England forward rate curves 57–8 delta 187–8 Banking book 1, 47 gamma 189–90 Barrier option 152,COPYRIGHTED 219–21 static MATERIAL hedges for standard European options Base rate 8 193–4 Basis 68, 95 theta and rho 188–9 commodity 100–1
    [Show full text]