## A Course in Financial CalculusFinance provides a dramatic example of the successful application of mathematics to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus. Key concepts are introduced in the discrete time framework: proofs in the continuous-time world follow naturally. The second half of the book is devoted to financially sophisticated models and instruments. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts are applied to realistic financial questions. |

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### Contents

z Binomial trees and discrete parameter martingales | 21 |

Brownian motion | 51 |

Stochastic calculus | 102 |

The BlackScholes model | 112 |

Different payoffs | 139 |

Bigger models | 159 |

189 | |

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### Common terms and phrases

American put option arbitrage binary model binomial Black-Scholes equation Black-Scholes model Black-Scholes price bounded variation calculate Chapter conditional expectation constant continuous define Definition denote derivative discounted asset price discounted stock price dividend dollar equivalent European call option European options Example expiry follows forward contract function geometric Brownian motion Girsanov Theorem hedging portfolio interest rate interval Ito's formula jumps Lemma market models martingale measure Martingale Representation Theorem maturity measure Q normally distributed notation obtain option with strike P-Brownian P-martingale parameter partial differential equation payoff Poisson portfolio consisting price vector pricing and hedging pricing formula probability measure proof put option quadratic variation random variable random walk replicating portfolio result risk-free riskless cash bond self-financing solution solves standard Brownian motion Sterling stochastic differential equation stochastic integral stochastic process strategy strike price Suppose tradable asset tree units of stock variance write zero