A first course in quantitative finance /
MAZZONI, THOMAS.
A first course in quantitative finance / - CAMBRIDGE: CUP, 2018
'A First Course in Quantitative Finance is a gentle introduction in a complicated subject. It covers most important topics - such as portfolio optimisation, derivative pricing, and fixed income products - and discusses them from the perspective of financial economics and financial mathematics. It provides the necessary mathematical background, contains the financial discussion, and is full of illustrative examples. It will be useful for anyone who wants to study the subject area on an advanced level.' Rudiger Kiesel, Universitat Duisburg-Essen 'This is a remarkably complete book on all aspects of modern finance, covering topics from the puzzles of financial economics, through modern portfolio management to the pricing of exotic options under stochastic volatility at an equally accessible yet state-of-the-art level. Quants, portfolio managers, students and teachers of finance alike will find it to be an invaluable source of insights and a must-have reference to have on their desks.' Peter Tankov, Ecole nationale de la statistique et de l'administration economique 'A First Course in Quantitative Finance is a gentle introduction in a complicated subject. It covers most important topics - such as portfolio optimisation, derivative pricing, and fixed income products - and discusses them from the perspective of financial economics and financial mathematics. It provides the necessary mathematical background, contains the financial discussion, and is full of illustrative examples. It will be useful for anyone who wants to study the subject area on an advanced level.' Rudiger Kiesel, Universitat Duisburg-Essen 'This is a remarkably complete book on all aspects of modern finance, covering topics from the puzzles of financial economics, through modern portfolio management to the pricing of exotic options under stochastic volatility at an equally accessible yet state-of-the-art level. Quants, portfolio managers, students and teachers of finance alike will find it to be an invaluable source of insights and a must-have reference to have on their desks.' Peter Tankov, Ecole nationale de la statistique et de l'administration economique
Machine generated contents note: About This Book -- 2.A Primer on Probability -- 2.1.Probability and Measure -- 2.2.Filtrations and the Flow of Information -- 2.3.Conditional Probability and Independence -- 2.4.Random Variables and Stochastic Processes -- 2.5.Moments of Random Variables -- 2.6.Characteristic Function and Fourier-Transform -- 2.7.Further Reading -- 2.8.Problems -- 3.Vector Spaces -- 3.1.Real Vector Spaces -- 3.2.Dual Vector Space and Inner Product -- 3.3.Dimensionality, Basis, and Subspaces -- 3.4.Functionals and Operators -- 3.5.Adjoint and Inverse Operators -- 3.6.Eigenvalue Problems -- 3.7.Linear Algebra -- 3.8.Vector Differential Calculus -- 3.9.Multivariate Normal Distribution -- 3.10.Further Reading -- 3.11.Problems -- 4.Utility Theory -- 4.1.Lotteries -- 4.2.Preference Relations and Expected Utility -- 4.3.Risk Aversion -- 4.4.Measures of Risk Aversion -- 4.5.Certainty Equivalent and Risk Premium -- 4.6.Classes of Utility Functions Note continued: 4.7.Constrained Optimization -- 4.8.Further Reading -- 4.9.Problems -- 5.Architecture of Financial Markets -- 5.1.The Arrow-Debreu-World -- 5.2.The Portfolio Selection Problem -- 5.3.Preference-Free Results -- 5.4.Pareto-Optimal Allocation and the Representative Agent -- 5.5.Market Completeness and Replicating Portfolios -- 5.6.Martingale Measures and Duality -- 5.7.Further Reading -- 5.8.Problems -- 6.Modern Portfolio Theory -- 6.1.The Gaussian Framework -- 6.2.Mean-Variance Analysis -- 6.3.The Minimum Variance Portfolio -- 6.4.Variance Efficient Portfolios -- 6.5.Optimal Portfolios and Diversification -- 6.6.Tobin&aposs Separation Theorem and the Market Portfolio -- 6.7.Further Reading -- 6.8.Problems -- 7.CAPM and APT -- 7.1.Empirical Problems with MPT -- 7.2.The Capital Asset Pricing Model (CAPM) -- 7.3.Estimating Betas from Market Data -- 7.4.Statistical Issues of Regression Analysis and Inference -- 7.5.The Arbitrage Pricing Theory (APT) Note continued: 7.6.Comparing CAPM and APT -- 7.7.Further Reading -- 7.8.Problems -- 8.Portfolio Performance and Management -- 8.1.Portfolio Performance Statistics -- 8.2.Money Management and Kelly-Criterion -- 8.3.Adjusting for Individual Market Views -- 8.4.Further Reading -- 8.5.Problems -- 9.Financial Econcomics -- 9.1.The Rational Valuation Principle -- 9.2.Stock Price Bubbles -- 9.3.Shiller&aposs Volatility Puzzle -- 9.4.Stochastic Discount Factor Models -- 9.5.C-CAPM and Hansen-Jagannathan-Bounds -- 9.6.The Equity Premium Puzzle -- 9.7.The Campbell-Cochrane-Model -- 9.8.Further Reading -- 9.9.Problems -- 10.Behavioral Finance -- 10.1.The Efficient Market Hypothesis -- 10.2.Beyond Rationality -- 10.3.Prospect Theory -- 10.4.Cumulative Prospect Theory (CPT) -- 10.5.CPT and the Equity Premium Puzzle -- 10.6.The Price Momentum Effect -- 10.7.Unifying CPT and Modern Portfolio Theory -- 10.8.Further Reading -- 10.9.Problems -- 11.Forwards, Futures, and Options Note continued: 11.1.Forward and Future Contracts -- 11.2.Bank Account and Forward Price -- 11.3.Options -- 11.4.Compound Positions and Option Strategies -- 11.5.Arbitrage Bounds on Options -- 11.6.Further Reading -- 11.7.Problems -- 12.The Binomial Model -- 12.1.The Coin Flip Universe -- 12.2.The Multi-Period Binomial Model -- 12.3.Valuating a European Call in the Binomial Model -- 12.4.Backward Valuation and American Options -- 12.5.Stopping Times and Snell-Envelope -- 12.6.Path Dependent Options -- 12.7.The Black-Scholes-Limit of the Binomial Model -- 12.8.Further Reading -- 12.9.Problems -- 13.The Black-Scholes-Theory -- 13.1.Geometric Brownian Motion and Ito&aposs Lemma -- 13.2.The Black-Scholes-Equation -- 13.3.Dirac&aposs sigma-Function and Tempered Distributions -- 13.4.The Fundamental Solution -- 13.5.Binary and Plain Vanilla Option Prices -- 13.6.Simple Extensions of the Black-Scholes-Model -- 13.7.Discrete Dividend Payments -- 13.8.American Exercise Right Note continued: 13.9.Discrete Hedging and the Greeks -- 13.10.Transaction Costs -- 13.11.Merton&aposs Firm Value Model -- 13.12.Further Reading -- 13.13.Problems -- 14.Exotics in the Black-Scholes-Model -- 14.1.Finite Difference Methods -- 14.2.Numerical Valuation and Coding -- 14.3.Weak Path Dependence and Early Exercise -- 14.4.Girsanov&aposs Theorem -- 14.5.The Feynman-Kac-Formula -- 14.6.Monte Carlo Simulation -- 14.7.Strongly Path Dependent Contracts -- 14.8.Valuating American Contracts with Monte Carlo -- 14.9.Further Reading -- 14.10.Problems -- 15.Deterministic Volatility -- 15.1.The Term Structure of Volatility -- 15.2.GARCH-Models -- 15.3.Duan&aposs Option Pricing Model -- 15.4.Local Volatility and the Dupire-Equation -- 15.5.Implied Volatility and Most Likely Path -- 15.6.Skew-Based Parametric Representation of the Volatility Surface -- 15.7.Brownian Bridge and GARCH-Parametrization -- 15.8.Further Reading -- 15.9.Problems -- 16.Stochastic Volatility Note continued: 16.1.The Consequence of Stochastic Volatility -- 16.2.Characteristic Functions and the Generalized Fourier-Transform -- 16.3.The Pricing Formula in Fourier-Space -- 16.4.The Heston-Nandi GARCH-Model -- 16.5.The Heston-Model -- 16.6.Inverting the Fourier-Transform -- 16.7.Implied Volatility in the SABR-Model -- 16.8.Further Reading -- 16.9.Problems -- 17.Processes with Jumps -- 17.1.Cadlag Processes, Local-, and Semimartingales -- 17.2.Simple and Compound Poisson-Process -- 17.3.GARCH-Models with Conditional Jump Dynamics -- 17.4.Merton&aposs Jump-Diffusion Model -- 17.5.Barrier Options and the Reflection Principle -- 17.6.Levy-Processes -- 17.7.Subordination of Brownian motion -- 17.8.The Esscher-Transform -- 17.9.Combining Jumps and Stochastic Volatility -- 17.10.Further Reading -- 17.11.Problems -- 18.Basic Fixed-Income Instruments -- 18.1.Bonds and Forward Rate Agreements -- 18.2.LIBOR and Floating Rate Notes Note continued: 18.3.Day-Count Conventions and Accrued Interest -- 18.4.Yield Measures and Yield Curve Construction -- 18.5.Duration and Convexity -- 18.6.Forward Curve and Bootstrapping -- 18.7.Interest Rate Swaps -- 18.8.Further Reading -- 18.9.Problems -- 19.Plain Vanilla Fixed-Income Derivatives -- 19.1.The T-Forward Measure -- 19.2.The Black-76-Model -- 19.3.Caps and Floors -- 19.4.Swaptions and the Annuity Measure -- 19.5.Eurodollar Futures -- 19.6.Further Reading -- 19.7.Problems -- 20.Term Structure Models -- 20.1.A Term Structure Toy Model -- 20.2.Yield Curve Fitting -- 20.3.Mean Reversion and the Vasicek-Model -- 20.4.Bond Option Pricing and the Jamshidian-Decomposition -- 20.5.Affine Term Structure Models -- 20.6.The Heath-Jarrow-Morton-Framework -- 20.7.Multi-Factor HJM and Historical Volatility -- 20.8.Further Reading -- 20.9.Problems -- 21.The LIBOR Market Model -- 21.1.The Transition from HJM to Market Models -- 21.2.The Change-of-Numeraire Toolkit Note continued: 21.3.Calibration to Caplet Volatilities -- 21.4.Parametric Correlation Matrices -- 21.5.Calibrating Correlations and the Swap Market Model -- 21.6.Pricing Exotics in the LMM -- 21.7.Further Reading -- 21.8.Problems -- A.1.Introduction to Complex Numbers -- A.2.Complex Functions and Derivatives -- A.3.Complex Integration -- A.4.The Residue Theorem.
A First Course in Quantitative Finance is suitable for economics, finance, econometrics and mathematics students with an interest in quantitative finance. Covering all topics from the architecture of financial markets to derivatives, it uses stereoscopic images to allow 3D visualisation of complex subjects without the need for additional tools.
9781108411431
Finance--Mathematical Models.
332.0151 / MAZ.F
A first course in quantitative finance / - CAMBRIDGE: CUP, 2018
'A First Course in Quantitative Finance is a gentle introduction in a complicated subject. It covers most important topics - such as portfolio optimisation, derivative pricing, and fixed income products - and discusses them from the perspective of financial economics and financial mathematics. It provides the necessary mathematical background, contains the financial discussion, and is full of illustrative examples. It will be useful for anyone who wants to study the subject area on an advanced level.' Rudiger Kiesel, Universitat Duisburg-Essen 'This is a remarkably complete book on all aspects of modern finance, covering topics from the puzzles of financial economics, through modern portfolio management to the pricing of exotic options under stochastic volatility at an equally accessible yet state-of-the-art level. Quants, portfolio managers, students and teachers of finance alike will find it to be an invaluable source of insights and a must-have reference to have on their desks.' Peter Tankov, Ecole nationale de la statistique et de l'administration economique 'A First Course in Quantitative Finance is a gentle introduction in a complicated subject. It covers most important topics - such as portfolio optimisation, derivative pricing, and fixed income products - and discusses them from the perspective of financial economics and financial mathematics. It provides the necessary mathematical background, contains the financial discussion, and is full of illustrative examples. It will be useful for anyone who wants to study the subject area on an advanced level.' Rudiger Kiesel, Universitat Duisburg-Essen 'This is a remarkably complete book on all aspects of modern finance, covering topics from the puzzles of financial economics, through modern portfolio management to the pricing of exotic options under stochastic volatility at an equally accessible yet state-of-the-art level. Quants, portfolio managers, students and teachers of finance alike will find it to be an invaluable source of insights and a must-have reference to have on their desks.' Peter Tankov, Ecole nationale de la statistique et de l'administration economique
Machine generated contents note: About This Book -- 2.A Primer on Probability -- 2.1.Probability and Measure -- 2.2.Filtrations and the Flow of Information -- 2.3.Conditional Probability and Independence -- 2.4.Random Variables and Stochastic Processes -- 2.5.Moments of Random Variables -- 2.6.Characteristic Function and Fourier-Transform -- 2.7.Further Reading -- 2.8.Problems -- 3.Vector Spaces -- 3.1.Real Vector Spaces -- 3.2.Dual Vector Space and Inner Product -- 3.3.Dimensionality, Basis, and Subspaces -- 3.4.Functionals and Operators -- 3.5.Adjoint and Inverse Operators -- 3.6.Eigenvalue Problems -- 3.7.Linear Algebra -- 3.8.Vector Differential Calculus -- 3.9.Multivariate Normal Distribution -- 3.10.Further Reading -- 3.11.Problems -- 4.Utility Theory -- 4.1.Lotteries -- 4.2.Preference Relations and Expected Utility -- 4.3.Risk Aversion -- 4.4.Measures of Risk Aversion -- 4.5.Certainty Equivalent and Risk Premium -- 4.6.Classes of Utility Functions Note continued: 4.7.Constrained Optimization -- 4.8.Further Reading -- 4.9.Problems -- 5.Architecture of Financial Markets -- 5.1.The Arrow-Debreu-World -- 5.2.The Portfolio Selection Problem -- 5.3.Preference-Free Results -- 5.4.Pareto-Optimal Allocation and the Representative Agent -- 5.5.Market Completeness and Replicating Portfolios -- 5.6.Martingale Measures and Duality -- 5.7.Further Reading -- 5.8.Problems -- 6.Modern Portfolio Theory -- 6.1.The Gaussian Framework -- 6.2.Mean-Variance Analysis -- 6.3.The Minimum Variance Portfolio -- 6.4.Variance Efficient Portfolios -- 6.5.Optimal Portfolios and Diversification -- 6.6.Tobin&aposs Separation Theorem and the Market Portfolio -- 6.7.Further Reading -- 6.8.Problems -- 7.CAPM and APT -- 7.1.Empirical Problems with MPT -- 7.2.The Capital Asset Pricing Model (CAPM) -- 7.3.Estimating Betas from Market Data -- 7.4.Statistical Issues of Regression Analysis and Inference -- 7.5.The Arbitrage Pricing Theory (APT) Note continued: 7.6.Comparing CAPM and APT -- 7.7.Further Reading -- 7.8.Problems -- 8.Portfolio Performance and Management -- 8.1.Portfolio Performance Statistics -- 8.2.Money Management and Kelly-Criterion -- 8.3.Adjusting for Individual Market Views -- 8.4.Further Reading -- 8.5.Problems -- 9.Financial Econcomics -- 9.1.The Rational Valuation Principle -- 9.2.Stock Price Bubbles -- 9.3.Shiller&aposs Volatility Puzzle -- 9.4.Stochastic Discount Factor Models -- 9.5.C-CAPM and Hansen-Jagannathan-Bounds -- 9.6.The Equity Premium Puzzle -- 9.7.The Campbell-Cochrane-Model -- 9.8.Further Reading -- 9.9.Problems -- 10.Behavioral Finance -- 10.1.The Efficient Market Hypothesis -- 10.2.Beyond Rationality -- 10.3.Prospect Theory -- 10.4.Cumulative Prospect Theory (CPT) -- 10.5.CPT and the Equity Premium Puzzle -- 10.6.The Price Momentum Effect -- 10.7.Unifying CPT and Modern Portfolio Theory -- 10.8.Further Reading -- 10.9.Problems -- 11.Forwards, Futures, and Options Note continued: 11.1.Forward and Future Contracts -- 11.2.Bank Account and Forward Price -- 11.3.Options -- 11.4.Compound Positions and Option Strategies -- 11.5.Arbitrage Bounds on Options -- 11.6.Further Reading -- 11.7.Problems -- 12.The Binomial Model -- 12.1.The Coin Flip Universe -- 12.2.The Multi-Period Binomial Model -- 12.3.Valuating a European Call in the Binomial Model -- 12.4.Backward Valuation and American Options -- 12.5.Stopping Times and Snell-Envelope -- 12.6.Path Dependent Options -- 12.7.The Black-Scholes-Limit of the Binomial Model -- 12.8.Further Reading -- 12.9.Problems -- 13.The Black-Scholes-Theory -- 13.1.Geometric Brownian Motion and Ito&aposs Lemma -- 13.2.The Black-Scholes-Equation -- 13.3.Dirac&aposs sigma-Function and Tempered Distributions -- 13.4.The Fundamental Solution -- 13.5.Binary and Plain Vanilla Option Prices -- 13.6.Simple Extensions of the Black-Scholes-Model -- 13.7.Discrete Dividend Payments -- 13.8.American Exercise Right Note continued: 13.9.Discrete Hedging and the Greeks -- 13.10.Transaction Costs -- 13.11.Merton&aposs Firm Value Model -- 13.12.Further Reading -- 13.13.Problems -- 14.Exotics in the Black-Scholes-Model -- 14.1.Finite Difference Methods -- 14.2.Numerical Valuation and Coding -- 14.3.Weak Path Dependence and Early Exercise -- 14.4.Girsanov&aposs Theorem -- 14.5.The Feynman-Kac-Formula -- 14.6.Monte Carlo Simulation -- 14.7.Strongly Path Dependent Contracts -- 14.8.Valuating American Contracts with Monte Carlo -- 14.9.Further Reading -- 14.10.Problems -- 15.Deterministic Volatility -- 15.1.The Term Structure of Volatility -- 15.2.GARCH-Models -- 15.3.Duan&aposs Option Pricing Model -- 15.4.Local Volatility and the Dupire-Equation -- 15.5.Implied Volatility and Most Likely Path -- 15.6.Skew-Based Parametric Representation of the Volatility Surface -- 15.7.Brownian Bridge and GARCH-Parametrization -- 15.8.Further Reading -- 15.9.Problems -- 16.Stochastic Volatility Note continued: 16.1.The Consequence of Stochastic Volatility -- 16.2.Characteristic Functions and the Generalized Fourier-Transform -- 16.3.The Pricing Formula in Fourier-Space -- 16.4.The Heston-Nandi GARCH-Model -- 16.5.The Heston-Model -- 16.6.Inverting the Fourier-Transform -- 16.7.Implied Volatility in the SABR-Model -- 16.8.Further Reading -- 16.9.Problems -- 17.Processes with Jumps -- 17.1.Cadlag Processes, Local-, and Semimartingales -- 17.2.Simple and Compound Poisson-Process -- 17.3.GARCH-Models with Conditional Jump Dynamics -- 17.4.Merton&aposs Jump-Diffusion Model -- 17.5.Barrier Options and the Reflection Principle -- 17.6.Levy-Processes -- 17.7.Subordination of Brownian motion -- 17.8.The Esscher-Transform -- 17.9.Combining Jumps and Stochastic Volatility -- 17.10.Further Reading -- 17.11.Problems -- 18.Basic Fixed-Income Instruments -- 18.1.Bonds and Forward Rate Agreements -- 18.2.LIBOR and Floating Rate Notes Note continued: 18.3.Day-Count Conventions and Accrued Interest -- 18.4.Yield Measures and Yield Curve Construction -- 18.5.Duration and Convexity -- 18.6.Forward Curve and Bootstrapping -- 18.7.Interest Rate Swaps -- 18.8.Further Reading -- 18.9.Problems -- 19.Plain Vanilla Fixed-Income Derivatives -- 19.1.The T-Forward Measure -- 19.2.The Black-76-Model -- 19.3.Caps and Floors -- 19.4.Swaptions and the Annuity Measure -- 19.5.Eurodollar Futures -- 19.6.Further Reading -- 19.7.Problems -- 20.Term Structure Models -- 20.1.A Term Structure Toy Model -- 20.2.Yield Curve Fitting -- 20.3.Mean Reversion and the Vasicek-Model -- 20.4.Bond Option Pricing and the Jamshidian-Decomposition -- 20.5.Affine Term Structure Models -- 20.6.The Heath-Jarrow-Morton-Framework -- 20.7.Multi-Factor HJM and Historical Volatility -- 20.8.Further Reading -- 20.9.Problems -- 21.The LIBOR Market Model -- 21.1.The Transition from HJM to Market Models -- 21.2.The Change-of-Numeraire Toolkit Note continued: 21.3.Calibration to Caplet Volatilities -- 21.4.Parametric Correlation Matrices -- 21.5.Calibrating Correlations and the Swap Market Model -- 21.6.Pricing Exotics in the LMM -- 21.7.Further Reading -- 21.8.Problems -- A.1.Introduction to Complex Numbers -- A.2.Complex Functions and Derivatives -- A.3.Complex Integration -- A.4.The Residue Theorem.
A First Course in Quantitative Finance is suitable for economics, finance, econometrics and mathematics students with an interest in quantitative finance. Covering all topics from the architecture of financial markets to derivatives, it uses stereoscopic images to allow 3D visualisation of complex subjects without the need for additional tools.
9781108411431
Finance--Mathematical Models.
332.0151 / MAZ.F