The Actuary’s Free Study Guide for Exam 3F / Exam MFE ...

1 The actuary 's free Study Guide for Exam 3F / Exam MFE Second Edition G. Stolyarov II. The actuary 's free Study Guide for Exam 3f / Exam MFE. Second Edition G. Stolyarov II, ASA, ACAS, MAAA, CPCU, ARe, ARC, API, AIS, AIE, AIAF. First Edition Published in February-May 2008. Second Edition Published in July 2014. 2008, 2014, G. Stolyarov II. This work is distributed under a Creative Commons Attribution Share-Alike Unported License. Permission to reprint this work, in whole or in part, is granted, as long as full credit is given to the author by identification of the author's name, and no additional rights are claimed by the party reprinting the work, beyond the rights provided by the aforementioned Creative Commons License.

2 In particular, no entity may claim the right to restrict other parties from obtaining copies of this work, or any derivative works created from it. Commercial use of this work is permitted, as long as the user does not claim any manner of exclusive rights arising from such use. While not mandatory, notification to the author of any commercial use or derivative works would be appreciated. Such notification may be sent electronically to 1. The actuary 's free Study Guide for Exam 3F / Exam MFE Second Edition G. Stolyarov II. Table of Contents Section Page Study Methods for Actuarial Exam 3F / Exam MFE 4. Section 1: Put-Call Parity 12. Section 2: Parity of Options on Stocks 15.

3 Section 3: Conversions and Reverse Conversions 19. Section 4: Parity of Options on Currencies 22. Section 5: Parity of Options on Bonds 25. Section 6: Generalized Put-Call Parity 28. Section 7: Classification of Calls and Puts 32. Section 8: Maximum and Minimum Option Prices 35. Section 9: Early Exercise on American Options 39. Section 10: Option Prices and Time to Expiration 43. Section 11: Option Prices for Different Strike Prices 46. Section 12: Strike-Price Convexity 49. Section 13: Exam-Style Questions on Put-Call Parity and Arbitrage 51. Section 14: Exam-Style Questions on Put-Call Parity and Arbitrage Part 2 56. Section 15: One-Period Binomial Option Pricing 59.

4 Section 16: Risk-Neutral Probability in Binomial Option Pricing 62. Section 17: Constructing Binomial Trees for Option Prices 64. Section 18: Multi-Period Binomial Option Pricing with Recombining Trees 66. Section 19: Binomial Option Pricing with Puts 70. Section 20: Binomial Option Pricing with American Options 73. Section 21: Binomial Pricing for Currency Options 78. Section 22: Binomial Pricing for Options on Futures Contracts 81. Section 23: Exam-Style Questions on Binomial Option Pricing 84. Section 24: Exam-Style Questions on Binomial Option Pricing for Actuaries Part 2 87. Section 25: Volatility and Early Exercise of American Options 91.

5 Section 26: Comparing Risk-Neutral and Real Probabilities in the Binomial Model 94. Section 27: Option Valuation Using True Probabilities in the Binomial Model 96. Section 28: The Random-Walk Model 99. Section 29: Standard Deviation of Returns and Multi-Period Probabilities in the Binomial Model 101. Section 30: Alternative Binomial Trees 103. Section 31: Constructing Binomial Trees with Discrete Dividends 106. Section 32: Review of Put-Call Parity and Binomial Option Pricing 109. Section 33: The Black-Scholes Formula 113. Section 34: The Black-Scholes Formula Using Prepaid Forward Prices 116. Section 35: The Black-Scholes Formula for Options on Stocks with Discrete Dividends 119.

6 Section 36: The Garman-Kohlhagen Formula for Pricing Currency Options 122. Section 37: The Black Formula for Pricing Options on Futures Contracts 125. Section 38: Exam-Style Questions on the Black-Scholes Formula 128. Section 39: Option Greeks: Delta 132. Section 40: Option Greeks: Gamma and Vega 135. Section 41: Option Greeks: Theta, Rho, Psi, and Greek Measures for Portfolios 138. Section 42: Option Elasticity and Option Volatility 141. Section 43: The Risk Premium and Sharpe Ratio of an Option 143. Section 44: The Elasticity and Risk Premium of an Option Portfolio 145. 2. The actuary 's free Study Guide for Exam 3F / Exam MFE Second Edition G.

7 Stolyarov II. Section 45: Calendar Spreads and Implied Volatility 147. Section 46: Revised Exam-Style Questions on Option Elasticity, Option Volatility, and the 151. Black-Scholes Formula Section 47: The Delta-Gamma Approximation 155. Section 48: The Delta-Gamma-Theta Approximation 157. Section 49: The Black-Scholes Partial Differential Equation 160. Section 50: The Return and Variance of the Return to a Delta-Hedged Market-Maker 162. Section 51: Exam-Style Questions on Market-Making and Delta-Hedging 164. Section 52: Asian Options 168. Section 53: Barrier Options 170. Section 54: Compound Options 173. Section 55: Pricing Options on Dividend-Paying Stocks 176.

8 Section 56: Gap Options 178. Section 57: Exchange Options 180. Section 58: Exam-Style Questions on Exotic Options 182. Section 59: The Basics of Brownian Motion 186. Section 60: The Basics of Geometric Brownian Motion 189. Section 61: The Basics of Mean-Reversion Processes 191. Section 62: Basics of Ito's Lemma for Actuaries 193. Section 63: Probability Problems Using Arithmetic Brownian Motion 195. Section 64: Probability Problems Using Geometric Brownian Motion 197. Section 65: Sharpe Ratios of Assets Following Geometric Brownian Motions 199. Section 66: Another Form of Ito's Lemma for Geometric Brownian Motion 201. Section 67: Multiplication Rules and Exam-Style Questions for Brownian Motion and Ito's 203.

9 Lemma Section 68: Conceptual Questions on Brownian Motion 207. Section 69: More Exam-Style Questions on Ito's Lemma and Brownian Motion 210. Section 70: The Vasicek Interest-Rate Model 214. Section 71: Exam-Style Questions on the Vasicek Interest-Rate Model 218. Section 72: The Cox-Ingersoll-Ross (CIR) Interest-Rate Model 225. Section 73: The Black Formula for Pricing Options on Bonds 229. Section 74: Forward Rate Agreements and Caplets 233. Section 75: Interest Rate Caps and Pricing Caplets Using the Black Formula 236. Section 76: Binomial Interest-Rate Models 238. Section 77: Basics of the Black-Derman-Toy (BDT) Interest-Rate Model 243.

10 Section 78: Pricing Caplets Using the Black-Derman-Toy (BDT) Interest-Rate Model 246. Section 79: Determining Yield Volatilities and the Basics of Constructing Binomial Trees in the 250. Black-Derman-Toy (BDT) Interest-Rate Model Section 80: Equity-Linked Insurance Contracts 254. Section 81: Historical Volatility 258. Section 82: Applications of Derivatives, the Garman-Kohlhagen Formula, and Brownian Motion 262. to International Business Contracts Section 83: Valuing Claims on Derivatives Whose Price is the Underlying Asset Price Taken to 267. Some Power Section 84: Assorted Exam-Style Questions and Solutions for Exam 3F / Exam MFE 271.