Smile Pricing Explained [electronic resource] /
Austing, Peter.author.
Smile Pricing Explained provides a clear and thorough explanation of the concepts of smile modelling that are at the forefront of modern derivatives pricing. The key models used in practice are covered, together with numerical techniques and calibration.
Description based upon print version of record.
Cover; Half-Title; Title; Copyright; Dedication; Contents; List of Symbols; Acknowledgements; Preface; 1 Introduction to Derivatives; 1.1 Hedging with Forward Contracts; 1.2 Speculation with Forward Contracts; 1.3 Arbitrage; 1.4 Vanilla Options; 1.5 Interest Rates; 1.6 Valuing a Forward Contract; 1.7 Key Points; 1.8 Further Reading; 2 Stochastic Calculus; 2.1 Brownian Motion; 2.2 Stochastic Model for Stock Price Evolution; 2.3 Ito's Lemma; 2.4 The Product Rule; 2.5 Log-Normal Stock Price Evolution; 2.6 The Markov Property; 2.7 Term Structure; 2.8 Ito's Lemma in More than One Dimension
2.9 Key Points2.10 Further Reading; 3 Martingale Pricing; 3.1 Setting the Scene; 3.2 Tradeable Assets; 3.3 Zero Coupon Bond; 3.4 Rolling Money Market Account; 3.5 Choosing a Numeraire; 3.6 Changing the Measure; 3.7 Girsanov's Theorem; 3.8 Martingales; 3.9 Continuous Martingales; 3.10 Black-Scholes Formula for a Call Option; 3.11 At-the-Money Options; 3.12 The Black-Scholes Equation; 3.13 An Elegant Derivation of the Black-Scholes Formula; 3.14 Key Points; 3.15 Further Reading; 4 Dynamic Hedging and Replication; 4.1 Dynamic Hedging in the Absence of Interest Rates
4.2 Dynamic Hedging with Interest Rates4.3 Delta Hedging; 4.4 The Greeks; 4.5 Gamma, Vega and Time Decay; 4.6 Vega and Volatility Trading; 4.7 Key Points; 4.8 Further Reading; 5 Exotic Options in Black-Scholes; 5.1 European Options; 5.2 Asian Options; 5.3 Continuous Barrier Options; 5.3.1 The Reflection Principle; 5.3.2 The Reflection Principle with Log-Normal Dynamic; 5.3.3 Valuing Barrier Options in Black-Scholes; 5.3.4 Discretely Monitored Barrier Options; 5.4 Key Points; 5.5 Further Reading; 6 Smile Models; 6.1 The Volatility Smile; 6.2 Smile Implied Probability Distribution
6.3 The Forward Kolmogorov Equation6.4 Local Volatility; 6.5 Key Points; 6.6 Further Reading; 7 Stochastic Volatility; 7.1 Properties of Stochastic Volatility Models; 7.2 The Heston Model; 7.2.1 What Makes the Heston Model Special; 7.2.2 Solving for Vanilla Prices; 7.2.3 The Feller Boundary Condition; 7.3 The SABRModel; 7.4 The Ornstein-Uhlenbeck Process; 7.5 Mixture Models; 7.6 Regime Switching Model; 7.7 Calibrating Stochastic Volatility Models; 7.8 Key Points; 7.9 Further Reading; 8 Numerical Techniques; 8.1 Monte Carlo; 8.1.1 Monte Carlo in One Dimension
8.1.2 Monte Carlo in More than One Dimension8.1.3 Variance Reduction in Monte Carlo; 8.1.4 Limitations ofMonte Carlo; 8.2 The PDE Approach; 8.2.1 Stable and Unstable Schemes; 8.2.2 Choice of Scheme; 8.2.3 OtherWays of Improving Accuracy; 8.2.4 More Complex Contracts in PDE; 8.2.5 Solving Higher Dimension PDEs; 8.3 Key Points; 8.4 Further Reading; 9 Local Stochastic Volatility; 9.1 The Fundamental Theorem of On-smile Pricing; 9.2 Arbitrage in Implied Volatility Surfaces; 9.3 Two Extremes of Smile Dynamic; 9.3.1 Sticky Strike Dynamic; 9.3.2 Sticky Delta Dynamic; 9.4 Local Stochastic Volatility
9.5 Simplifying Models
Includes bibliographical references and index.
Smile Pricing Explained provides a clear and thorough explanation of the concepts of smile modelling that are at the forefront of modern derivatives pricing. The key models used in practice are covered, together with numerical techniques and calibration.
Investment banking.
Securities.
Financial engineering.
Capital market.
Economic theory.
Business enterprises-Finance.
Management.
Investments and Securities.
Financial Engineering.
Capital Markets.
Economic Theory/Quantitative Economics/Mathematical Methods.
Business Finance.
Management.