LEADER 05393nam 2200649 a 450 001 9910829940203321 005 20170815122943.0 010 $a1-280-97434-6 010 $a9786610974344 010 $a0-470-17978-3 010 $a0-470-17977-5 035 $a(CKB)1000000000377262 035 $a(EBL)315233 035 $a(OCoLC)180192503 035 $a(SSID)ssj0000199080 035 $a(PQKBManifestationID)11186830 035 $a(PQKBTitleCode)TC0000199080 035 $a(PQKBWorkID)10185108 035 $a(PQKB)10978815 035 $a(MiAaPQ)EBC315233 035 $a(PPN)250148900 035 $a(EXLCZ)991000000000377262 100 $a20070319d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical finance$b[electronic resource] $etheory, modeling, implementation /$fChristian Fries 210 $aHoboken, N.J. $cWiley-Interscience$dc2007 215 $a1 online resource (544 p.) 300 $aDescription based upon print version of record. 311 $a0-470-04722-4 320 $aIncludes bibliographical references (p. 503-510) and index. 327 $aMathematical Finance: Theory, Modeling, Implementation; Contents; 1 Introduction; 1.1 Theory, Modeling, and Implementation; 1.2 Interest Rate Models and Interest Rate Derivatives; 1.3 About This Book; 1.3.1 How to Read This Book; 1.3.2 Abridged Versions; 1.3.3 Special Sections; 1.3.4 Notation; 1.3.5 Feedback; 1.3.6 Resources; I Foundations; 2 Foundations; 2.1 Probability Theory; 2.2 Stochastic Processes; 2.3 Filtration; 2.4 Brownian Motion; 2.5 Wiener Measure, Canonical Setup; 2.6 Ito? Calculus; 2.6.1 Ito? Integral; 2.6.2 Ito? Process; 2.6.3 Ito? Lemma and Product Rule 327 $a2.7 Brownian Motion with Instantaneous Correlation2.8 Martingales; 2.8.1 Martingale Representation Theorem; 2.9 Change of Measure; 2.10 Stochastic Integration; 2.11 Partial Differential Equations (PDEs); 2.11.1 Feynman-Kac? Theorem; 2.12 List of Symbols; 3 Replication; 3.1 Replication Strategies; 3.1.1 Introduction; 3.1.2 Replication in a Discrete Model; 3.2 Foundations: Equivalent Martingale Measure; 3.2.1 Challenge and Solution Outline; 3.2.2 Steps toward the Universal Pricing Theorem; 3.3 Excursus: Relative Prices and Risk-Neutral Measures; 3.3.1 Why relative prices? 327 $a3.3.2 Risk-Neutral MeasureII First Applications; 4 Pricing of a European Stock Option under the Black-Scholes Model; 5 Excursus: The Density of the Underlying of a European Call Option; 6 Excursus: Interpolation of European Option Prices; 6.1 No-Arbitrage Conditions for Interpolated Prices; 6.2 Arbitrage Violations through Interpolation; 6.2.1 Example 1 : Interpolation of Four Prices; 6.2.2 Example 2: Interpolation of Two Prices; 6.3 Arbitrage- Free Interpolation of European Option Prices; 7 Hedging in Continuous and Discrete Time and the Greeks; 7.1 Introduction 327 $a7.2 Deriving the Replications Strategy from Pricing Theory7.2.1 Deriving the Replication Strategy under the Assumption of a Locally Riskless Product; 7.2.2 Black-Scholes Differential Equation; 7.2.3 Derivative V(t) as a Function of Its Underlyings S i(t); 7.2.4 Example: Replication Portfolio and PDE under a Black-Scholes Model; 7.3 Greeks; 7.3.1 Greeks of a European Call-Option under the Black-Scholes Model; 7.4 Hedging in Discrete Time: Delta and Delta-Gamma Hedging; 7.4.1 Delta Hedging; 7.4.2 Error Propagation; 7.4.3 Delta-Gamma Hedging; 7.4.4 Vega Hedging 327 $a7.5 Hedging in Discrete Time: Minimizing the Residual Error (Bouchaud-Sornette Method)7.5.1 Minimizing the Residual Error at Maturity T; 7.5.2 Minimizing the Residual Error in Each Time Step; III Interest Rate Structures, Interest Rate Products, and Analytic Pricing Formulas; Motivation and Overview; 8 Interest Rate Structures; 8.1 Introduction; 8.1.1 Fixing Times and Tenor Times; 8.2 Definitions; 8.3 Interest Rate Curve Bootstrapping; 8.4 Interpolation of Interest Rate Curves; 8.5 Implementation; 9 Simple Interest Rate Products; 9.1 Interest Rate Products Part 1: Products without Optionality 327 $a9.1.1 Fix, Floating, and Swap 330 $aA balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pri 606 $aDerivative securities$xPrices$xMathematical models 606 $aSecurities$xMathematical models 606 $aInvestments$xMathematical models 615 0$aDerivative securities$xPrices$xMathematical models. 615 0$aSecurities$xMathematical models. 615 0$aInvestments$xMathematical models. 676 $a332.601 676 $a332.6015195 700 $aFries$b Christian$f1970-$01634213 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829940203321 996 $aMathematical finance$93974329 997 $aUNINA