Equity Derivatives and Hybrids

Since the development of the Black-Scholes model, research on equity derivatives has evolved rapidly to the point where it is now difficult to cut through the myriad of literature to find relevant material. Written by a quant with many years of experience in the field this book provides an up-to-date account of equity and equity-hybrid (equity-rates, equity-credit, equity-foreign exchange) derivatives modeling from a practitioner's perspective. The content reflects the requirements of practitioners in financial institutions: Quants will find a survey of state-of-the-art models and guidance on how to efficiently implement them with regards to market data representation, calibration, and sensitivity computation. Traders and structurers will learn about structured products, selection of the most appropriate models, as well as efficient hedging methods while risk managers will better understand market, credit, and model risk and find valuable information on advanced correlation concepts. Equity Derivatives and Hybrids provides exhaustive coverage of both market standard and new approaches, including: -Empirical properties of stock returns including autocorrelation and jumps -Dividend discount models -Non-Markovian and discrete-time volatility processes -Correlation skew modeling via copula as well as local and stochastic correlation factors -Hybrid modeling covering local and stochastic processes for interest rate, hazard rate, and volatility as well as closed form solutions -Credit, debt, and funding valuation adjustment (CVA, DVA, FVA) -Monte Carlo techniques for sensitivities including algorithmic differentiation, path recycling, as well as multilevel. Written in a highly accessible manner with examples, applications, research, and ideas throughout, this book provides a valuable resource for quantitative-minded practitioners and researchers.

'This deep, on-the-money account of equity derivatives and hybrids will appeal to finance professionals and finance professors alike.'

-Peter Carr, PhD, Managing Director, Market Modeling, Morgan Stanley; Executive Director, Masters in Math Finance, NYU Courant Institute

"Oliver Brockhaus is to be commended for his thoughtfully curated compendium of key results for equity and hybrid quants. The choice of topics bears the mark of the author's experience as a professional quant, including for example a sophisticated treatment of dividend modeling techniques and clear explanations of CVA, DVA, and FVA. Both students and practitioners will find this book invaluable.'

-Jim Gatheral, Presidential Professor, Baruch College, CUNY; author of The Volatility Surface

'Oliver Brockhaus is a long established and recognized authority on financial mathematics and derivatives pricing models, and his expertise is abundantly visible in this book. The presentation isclear, the subject matter highly relevant, and the coverage is comprehensive yet focused. In summary: an excellent addition to any practitioner's library for both graduates at entry level as well as senior professionals more interested in advanced aspects of financial engineering.'

-Peter Jäckel, PhD, Deputy Head of Quantitative Research, VTB Capital; Managing Director, OTC Analytics

Auteur
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.

Contenu

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