## The Mathematics of Financial Derivatives: A Student IntroductionFinance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field. |

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### Contents

An Introduction to Options and Markets | 3 |

Asset Price Random Walks | 18 |

The BlackScholes Model | 33 |

Partial Differential Equations | 58 |

The BlackScholes Formulae | 71 |

Variations on the BlackScholes Model | 90 |

American Options | 106 |

Finitedifference Methods | 135 |

Barrier Options | 206 |

A Unifying Framework for Pathdependent Options | 213 |

Asian Options | 222 |

Lookback Options | 236 |

Options with Transaction Costs | 252 |

Interest Rate Derivatives | 265 |

Convertible Bonds | 286 |

Hints to Selected Exercises | 295 |

Methods for American Options | 165 |

Binomial Methods | 180 |

Exotic and Pathdependent Options | 197 |

### Common terms and phrases

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