LEADER 06256nam 22007212 450 001 9910819394403321 005 20160224090748.0 010 $a1-107-22565-5 010 $a1-283-34216-2 010 $a1-139-15982-8 010 $a9786613342164 010 $a1-139-16082-6 010 $a1-139-15526-1 010 $a1-139-15701-9 010 $a1-139-15877-5 010 $a1-139-02053-6 035 $a(CKB)2550000000061479 035 $a(EBL)807167 035 $a(OCoLC)763159208 035 $a(SSID)ssj0000612366 035 $a(PQKBManifestationID)11379569 035 $a(PQKBTitleCode)TC0000612366 035 $a(PQKBWorkID)10567295 035 $a(PQKB)10513182 035 $a(UkCbUP)CR9781139020534 035 $a(Au-PeEL)EBL807167 035 $a(CaPaEBR)ebr10514263 035 $a(CaONFJC)MIL334216 035 $a(MiAaPQ)EBC807167 035 $a(PPN)261330160 035 $a(EXLCZ)992550000000061479 100 $a20141103d2011|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMultiscale stochastic volatility for equity, interest rate, and credit derivatives /$fJean-Pierre Fouque [and others]$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2011. 215 $a1 online resource (xiii, 441 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-139-15323-4 311 $a0-521-84358-8 320 $aIncludes bibliographical references and index. 327 $aCover; MULTISCALE STOCHASTIC VOLATILITY FOR EQUITY, INTEREST RATE, AND CREDIT DERIVATIVES; Title; Copyright; To our families and students; Contents; Introduction; 1 The Black-Scholes Theory of Derivative Pricing; 1.1 Market Model; 1.2 Derivative Contracts; 1.3 Replicating Strategies; 1.4 Risk-Neutral Pricing; 1.5 Risk-Neutral Expectations and Partial Differential Equations; 1.6 American Options and Free Boundary Problems; 1.7 Path-Dependent Derivatives; 1.8 First-Passage Structural Approach to Default; 1.9 Multidimensional Stochastic Calculus; 1.10 Complete Market 327 $a2 Introduction to Stochastic Volatility Models2.1 Implied Volatility Surface; 2.2 Local Volatility; 2.3 Stochastic Volatility Models; 2.4 Derivative Pricing; 2.5 General Results on Stochastic Volatility Models; 2.6 Summary and Conclusions; 3 Volatility Time Scales; 3.1 A Simple Picture of Fast and Slow Time Scales; 3.2 Ergodicity and Mean-Reversion; 3.3 Examples of Mean-Reverting Processes; 3.4 Time Scales in Synthetic Returns Data; 3.5 Time Scales in Market Data; 3.6 Multiscale Models; 4 First-Order Perturbation Theory; 4.1 Option Pricing under Multiscale Stochastic Volatility 327 $a4.2 Formal Regular and Singular Perturbation Analysis4.3 Parameter Reduction; 4.4 First-Order Approximation: Summary and Discussion; 4.5 Accuracy of First-Order Approximation; 5 Implied Volatility Formulas and Calibration; 5.1 Approximate Call Prices and Implied Volatilities; 5.2 Calibration Procedure; 5.3 Illustration with S&P 500 Data; 5.4 Maturity Cycles; 5.5 Higher-Order Corrections; 6 Application to Exotic Derivatives; 6.1 European Binary Options; 6.2 Barrier Options; 6.3 Asian Options; 7 Application to American Derivatives; 7.1 American Options Valuation under Stochastic Volatility 327 $a7.2 Stochastic Volatility Correction for American Put7.3 Parameter Reduction; 7.4 Summary; 8 Hedging Strategies; 8.1 Black-Scholes Delta Hedging; 8.2 The Strategy and its Cost; 8.3 Mean Self-Financing Hedging Strategy; 8.4 A Strategy with Frozen Parameters; 8.5 Strategies Based on Implied Volatilities; 8.6 Martingale Approach to Pricing; 8.7 Non-Markovian Models of Volatility; 9 Extensions; 9.1 Dividends and Varying Interest Rates; 9.2 Probabilistic Representation of the Approximate Prices; 9.3 Second-Order Correction from Fast Scale; 9.4 Second-Order Corrections from Slow and Fast Scales 327 $a9.5 Periodic Day Effect9.6 Markovian Jump Volatility Models; 9.7 Multidimensional Models; 10 Around the Heston Model; 10.1 The Heston Model; 10.2 Approximations to the Heston Model; 10.3 A Fast Mean-Reverting Correction to the Heston Model; 10.4 Large Deviations and Short Maturity Asymptotics; 11 Other Applications; 11.1 Application to Variance Reduction in Monte Carlo Computations; 11.2 Portfolio Optimization under Stochastic Volatility; 11.3 Application to CAPM Forward-Looking Beta Estimation; 12 Interest Rate Models; 12.1 The Vasicek Model; 12.2 The Bond Price and its Expansion 327 $a12.3 The Quadratic Model 330 $aBuilding upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics. 517 3 $aMultiscale Stochastic Volatility for Equity, Interest Rate, & Credit Derivatives 606 $aDerivative securities$xEconometric models 615 0$aDerivative securities$xEconometric models. 676 $a332.642015195 700 $aFouque$b Jean-Pierre$0133104 701 $aFouque$b Jean-Pierre$0133104 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910819394403321 996 $aMultiscale stochastic volatility for equity, interest rate, and credit derivatives$94049599 997 $aUNINA