## Financial Engineering and Computation: Principles, Mathematics, AlgorithmsNowadays students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practiced in today's capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from very basic ideas in finance and gradually builds up the theory. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. Along with the theory, the author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more. Each instrument is treated in a short, self-contained chapter for ready reference use. Many of these algorithms are coded in Java as programs for the Web, available from the book's home page (www.csie.ntu.edu/~lyuu/Capitals/capitals.htm) |

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### Contents

Analysis of Algorithms | 7 |

Bond Price Volatility | 32 |

Term Structure of Interest Rates | 45 |

Option Basics | 75 |

Arbitrage in Option Pricing | 84 |

Option Pricing Models | 92 |

Sensitivity Analysis of Options | 123 |

Extensions of Options Theory | 131 |

Time Series Analysis | 284 |

Interest Rate Derivative Securities | 295 |

Term Structure Fitting | 321 |

Introduction to Term Structure Modeling | 328 |

Foundations of Term Structure Modeling | 345 |

Equilibrium Term Structure Models | 361 |

NoArbitrage Term Structure Models | 375 |

FixedIncome Securities | 399 |

Forwards Futures Futures Options Swaps | 155 |

Stochastic Processes and Brownian Motion | 177 |

ContinuousTime Financial Mathematics | 190 |

ContinuousTime Derivatives Pricing | 206 |

Hedging | 224 |

Trees | 234 |

Numerical Methods | 249 |

Matrix Computation | 268 |

Introduction to MortgageBacked Securities | 415 |

Analysis of MortgageBacked Securities | 427 |

Collateralized Mortgage Obligations | 451 |

Modern Portfolio Theory | 458 |

Software | 480 |

553 | |

Glossary of Useful Notations | 585 |

### Common terms and phrases

arbitrage Assume binomial interest rate binomial model binomial tree binomial tree algorithm Black-Scholes bond price Brownian motion callable callable bond cash flow computed continuously compounded convexity coupon bond coupon rate delta denote derivative discount dividend yield dollars duration equals European call European options example Exercise expiration factor Figure fixed-rate floating-rate formula forward contract forward rate function futures contract futures price geometric Brownian motion hedge Hence implies interest rate swap interest rate tree investor Journal lemma LIBOR linear loan martingale matrix method Monte Carlo mortgage node option pricing option value payment payoff pays period portfolio prepayment Programming Assignment put-call parity random variable rate of return risk risk-neutral probability riskless securities short rate spot rate curve stock price strike price swap term structure Theorem tranche Treasury underlying asset variance Verify volatility yield curve yield to maturity zero zero-coupon bond