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.