## Quantitative Modeling of Derivative Securities: From Theory To PracticeQuantitative Modeling of Derivative Securities demonstrates how to take the basic ideas of arbitrage theory and apply them - in a very concrete way - to the design and analysis of financial products. Based primarily (but not exclusively) on the analysis of derivatives, the book emphasizes relative-value and hedging ideas applied to different financial instruments. Using a "financial engineering approach," the theory is developed progressively, focusing on specific aspects of pricing and hedging and with problems that the technical analyst or trader has to consider in practice. More than just an introductory text, the reader who has mastered the contents of this one book will have breached the gap separating the novice from the technical and research literature. |

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### Contents

The Binomial Option Pricing Model | 21 |

Analysis of the BlackScholes Formula | 41 |

Refinements of the Binomial Model | 57 |

References and Further Reading | 76 |

References and Further Reading | 88 |

References and Further Reading | 106 |

References and Further Reading | 122 |

Ito Processes ContinuousTime Martingales | 161 |

### Common terms and phrases

American option approximation arbitrage Arbitrage Pricing Theory assume barrier options binomial model binomial tree Black-Scholes formula bond option boundary conditions Brownian motion Brownian paths calculation call option caplet cash-flows chapter compute contingent claim corresponding coupon defined Delta derivative security discount factors distribution dividend dollar dynamics e~rT equivalent fact FIGURE Finance fixed-income floating rate forward price forward-rate curve function future Gamma Gaussian given hedging Ho-Lee Ho-Lee model implied volatility instantaneous forward rates interest rate interest-rate investor Ito processes Lemma LIBOR log-normal martingale mathematical matrix maturity no-arbitrage nodes Notice obtain option prices parameters payments payoff portfolio position probability measure PROPOSITION random variables represents risk risk-neutral measure risk-neutral probabilities riskless satisfies solution spot price square-root state-prices stochastic differential equation stochastic integral strike swaptions theorem traded securities trading period trinomial underlying asset variance vector yield curve zero zero-coupon bond

### Popular passages

Page 312 - Martingale Methods in Financial Modelling, Applications of Mathematics, vol. 36, Springer- Verlag, Berlin.