## An Elementary Introduction to Mathematical Finance: Options and Other TopicsThis original text on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this second edition are: a new chapter on optimization methods in finance, a new section on Value at Risk and Conditional Value at Risk; a new and simplified derivation of the Black-Scholes equation, together with derivations of the partial derivatives of the Black-Scholes option cost function and of the computational Black-Scholes formula; three different models of European call options with dividends; a new, easily implemented method for estimating the volatility parameter. Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of California at Berkeley. He received his Ph.D. in statistics at Stanford University in 1968 and has been at Berkeley ever since. He has published nearly 100 articles and a variety of textbooks in the areas of statistics and applied probability including Topics in Finite and Discrete Mathematics (Cambridge University Press, 2000), An Introduction to Probability Methods, Seventh Edition (Harcourt Science snd Technology Company, 2000), Introduction to Probability and Statistics for Engineers and Scientists (Academic Press, 1999), A First Course in Probability, Sixth Edition (Prentice-Hall, 2001), Simulation, Third Edition (Academic Press, 2002), and Stochastic Processes (John Wiley & Sons, 1982). He is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, a fellow of the Institute of Mathematical Statistics, and a recipient of the Humboldt U.S. Senior Scientist Award. |

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### Contents

I | 1 |

II | 5 |

III | 13 |

IV | 15 |

V | 20 |

VI | 24 |

VII | 27 |

VIII | 29 |

XLIII | 139 |

XLIV | 142 |

XLV | 143 |

XLVII | 145 |

XLVIII | 146 |

XLIX | 152 |

L | 153 |

LI | 160 |

IX | 32 |

X | 33 |

XI | 35 |

XII | 36 |

XIII | 38 |

XIV | 42 |

XV | 52 |

XVI | 55 |

XVII | 57 |

XVIII | 63 |

XIX | 67 |

XX | 76 |

XXI | 81 |

XXII | 85 |

XXIII | 87 |

XXIV | 91 |

XXV | 95 |

XXVI | 99 |

XXVII | 102 |

XXVIII | 108 |

XXX | 110 |

XXXI | 115 |

XXXII | 118 |

XXXIII | 119 |

XXXIV | 120 |

XXXV | 121 |

XXXVI | 123 |

XXXVII | 129 |

XXXVIII | 131 |

XXXIX | 133 |

XL | 135 |

XLI | 136 |

XLII | 137 |

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### Common terms and phrases

American put option approximation arbitrage theorem Assuming bank barrier option Black-Scholes formula Brownian motion model buying cash flow sequence concave Consequently consider convex Cov(X Date Price Log denote determine dividend drift parameter end-of-day price equal Equation estimator European call option Example exercise price expected present value expected utility expected value expiration follows a geometric forward contract Gas Heating Oil geometric Brownian motion given Hence independent initial price invest in project investor loan no-arbitrage cost nominal interest rate nondecreasing normal random variable obtain option cost outcome payment payoff period portfolio possible preceding present price present value Price Log Difference probability vector rate of return result risk-neutral geometric Brownian risk-neutral price risk-neutral probabilities risk-neutral valuation Section security's price sell share simulation Solution specified standard deviation strike price Suppose tion trading days Unleaded Gas Heating utility function variable with mean variance volatility parameter yields zero