Market practice in financial modelling

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Intro Contents Preface Foreword Acknowledgements 1. Introduction 1.1 The Theory 1.1.1 Itoâ#x80 #x99 s Lemma 1.1.2 The Blackâ#x80 #x93 Scholes Partial Differential Equation (PDE) 1.1.3 Martingale Representation Theorem 1.1.4 Radonâ#x80 #x93 Nikodym Transform 1.1.5 Girsanov Theorem 1.1.6 Feynmanâ#x80 #x93 Kac Theorem 1.1.7 Reflection Principle 1.2 Market Quantities 1.2.1 Interest Rates 1.2.2 Spot Quantities 1.2.3 Asset Forward Prices 1.2.4 Volatilities 1.2.5 Correlations 1.2.6 Calibration 1.3 Consolidation 1.3.1 Summary 1.3.2 Exercises 2. Standard Market Instruments 2.1 Linear Interest Rates. 2.1.1 Deposits, Futures, and SwapsDeposits Futures Swaps 2.1.2 The Yield Curve 2.1.3 Overnight Index Swaps and Basis Swaps 2.2 Interest Rate Options 2.2.1 Caplets 2.2.2 Swaptions 2.3 Foreign Exchange 2.3.1 Forwards and the Cross-Currency Swap 2.3.2 Options, Strangles, and Risk Reversals At-the-money options Strangles Risk reversals 2.3.3 Barriers and One-Touches 2.4 Equities 2.4.1 Forwards and Futures 2.4.2 Exchange Traded Options 2.4.3 Put-Call Parity 2.5 Consolidation 2.5.1 Summary 2.5.2 Exercises 3. Replication 3.1 Static Replication 3.1.1 The Digital Option. 3.1.2 The Libor-in-Arrears3.1.3 The Constant Maturity Swap 3.1.4 Payment Delay 3.1.5 The Linear Swap Rate Model 3.1.6 Auto-Quantoes 3.1.7 Variance Swaps 3.2 Replication as a Framework 3.2.1 Barriers Under Deterministic Volatility 3.2.2 Barriers Given Volatility Dynamics 3.3 Consolidation 3.3.1 Summary 3.3.2 Exercises 4. Correlation Between Two Underlyings 4.1 Copulae 4.1.1 Marginal Distributions 4.1.2 Gaussian Copulae 4.1.3 Archimedean Copulae 4.2 Financial Products 4.2.1 CMS Spread Options 4.2.2 Quantoes 4.2.3 â#x80 #x98 Best-ofâ#x80 #x99 Products 4.3 Consolidation 4.3.1 Summary. 4.3.2 Exercises5. Local Volatility 5.1 The Theory 5.1.1 Fokkerâ#x80 #x93 Planck Equation 5.1.2 Dupireâ#x80 #x99 s Formula 5.1.3 Presence of Stochastic Interest Rates or Volatility 5.2 Dynamics 5.2.1 Evolution of Smile Over Time 5.2.2 Smile Dynamics With Respect to Underlying Moves 5.3 Parametric Local Volatility 5.3.1 Normal 5.3.2 Lognormal 5.3.3 Blended 5.3.4 CEV 5.4 Consolidation 5.4.1 Summary 5.4.2 Exercises 6. Stochastic Volatility 6.1 General Dynamics of Stochastic Volatility 6.1.1 Dynamics vis-a-vis Underlying Moves 6.1.2 Persistence of Smile. 6.2 The Stochastic Alpha Beta Rho (SABR) Model6.2.1 The Asymptotic Expansion 6.2.2 SABR Dynamics 6.2.3 Smile, Skew, and Backbone 6.2.4 Issues with SABR 6.3 Heston Model 6.3.1 The Effect of Mean Reversion 6.3.2 Heston Dynamics 6.3.3 Characteristic Function Method for Pricing 6.3.4 The Heston Partial Differential Equation (PDE) 6.3.5 Simulating the Heston Process 6.4 Approximating Stochastic Volatility 6.4.1 Discrete Multi-State Volatility 6.4.2 Limitations of Multi-State Volatility 6.5 Moments Explosion 6.5.1 An Illustration of Moments Explosion 6.6 Consolidation 6.6.1 Summary.