Equity Derivatives and Hybrids

Oliver Brockhaus is Senior Vice-President at MathFinance AG, an independent consulting company. He has 15 years of experience as front office quantitative analyst. Past positions include Head of European Equity Quantitative Analytics at Royal Bank of Scotland, Head of Equity Financial Engineering at Commerzbank, Credit Quantitative Analyst at Calyon and Hypovereinsbank, as well as Equity Quant at JP Morgan and Deutsche Bank. Brockhaus has been responsible for developing state-of-the-art pricing models and risk management tools for front office trading operations across a number of areas, including equity and credit derivatives, commodities, life insurance, and hybrid products. His academic interests range from stochastic volatility and correlation to dividend and hybrid derivatives modeling.

1 Empirical Evidence 1.1 Distribution 1.2 Drift 1.3 Autocorrelation 1.4 Jumps 2 Equity Derivatives Market 2.1 Underlyings 2.2 Dividends 2.3 Repo Rate 2.4 Delta One Products 2.5 Vanilla Options 3 Exotic Equity Derivatives 3.1 Barriers 3.2 Cliquets 3.3 Asians 3.4 Compound 3.5 Lookback 3.6 Autocallable 3.7 Volatility Products 3.8 Multi Asset Products 3.9 Dynamic Strategies 3.10 Dividend Products 4 Implied Volatility 4.1 Skew Parameterization 4.2 Tail Behaviour 4.3 Time Dependence 5 Dividends 5.1 Forward 5.2 Proportional Dividends 5.3 Deterministic Dividends 5.4 Affine Models 5.5 Dividend Discount Models 5.6 Stochastic Dividend Yield 5.7 Stochastic Hazard And Interest Rates 5.8 Variance Swap 6 Short Volatility Models 6.1 Local Volatility 6.2 Stochastic Volatility 6.3 Local Stochastic Volatility 6.4 Jump Diffusion 6.5 Non-Markovian Models 6.6 Calibration And Hedging Stochastic Volatility 7 Implied Volatility Dynamics 7.1 Implied Volatility Delta 7.2 Forward Volatility 7.3 Modelling Implied Volatility 7.4 Discrete Time Models 8 Correlation 8.1 Implied Correlation 8.2 Correlation Term Structure 8.3 Decorrelation 8.4 Langnau's Local Correlation 8.5 Stochastic Correlation 9 Copulas 9.1 Definition 9.2 Dependence Measures 9.3 Archimedean Copulas 9.4 Marshall-Olkin Copula 9.5 T-Copula 9.6 Factor Copula 9.7 Convex Combination 9.8 Model Independent Arbitrage Bounds 9.9 Gauss Copula Model 10 Fixed Income 10.1 Market 10.2 Short Rate 10.3 Heath-Jarrow-Morton 10.4 Hull-White 10.5 Cox-Ingersoll-Ross 10.6 Markov Functional 11 Equity-Interest Rate Hybrids 11.1 Constant Equity Volatility 11.2 Gauss Copula 11.3 Local Equity Volatility 11.4 Stochastic Equity Volatility 11.5 Dynamic Hedging Of Variance Swaps 12 Credit 12.1 Market 12.2 Reduced Form Models 12.3 Structural Models 12.4 Portfolio Credit Derivatives 13 Defaultable Equity 13.1 Reduced Form Models 13.2 Structural Models 14 Counterparty Credit Risk 14.1 Sources Of Credit Risk 14.2 Credit Valuation Adjustment 14.3 Wrong Way Risk 14.4 Structural Models 14.5 Reduced Form Models 14.6 Funding Valuation Adjustment 15 Foreign Exchange 15.1 Cross Currency Basis Swap 15.2 Market Smile 15.3 Vanna-Volga Approach 15.4 Models 15.5 Quanto Options 15.6 Government Intervention 16 Affine Processes 16.1 General Framework 16.2 European Options And Fourier Transform 17 Monte Carlo 17.1 Method 17.2 Random Numbers 17.3 Path Construction For Brownian Motion 17.4 Discretization 17.5 Greeks 17.6 Variance Reduction 18 Gauss 18.1 Brownian Motion 18.2 Black-Scholes 18.3 Barrier 18.4 Outside Barrier 18.5 Useful Integrals Notation References