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"Bossu, Sébastien"
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Advanced equity derivatives : volatility and correlation
\"In Advanced Equity Derivatives: Volatility and Correlation, Sebastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. Volatility and correlation are remarkably connected through the author's proxy formula which he discovered in 2004, and shares in the book. He also reveals a new derivation using linear algebra (included in Chapter 6), and the proxy formula is then exploited in the following chapters for correlation trading and correlation modeling. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging\"-- Provided by publisher.
Book
Advanced equity derivatives
In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.
eBook
An introduction to equity derivatives : theory and practice
Everything you need to get a grip on the complex world of derivatives
Written by the internationally respected academic/finance professional author team of Sebastien Bossu and Philipe Henrotte, An Introduction to Equity Derivatives is the fully updated and expanded second edition of the popular Finance and Derivatives. It covers all of the fundamentals of quantitative finance clearly and concisely without going into unnecessary technical detail. Designed for both new practitioners and students, it requires no prior background in finance and features twelve chapters of gradually increasing difficulty, beginning with basic principles of interest rate and discounting, and ending with advanced concepts in derivatives, volatility trading, and exotic products. Each chapter includes numerous illustrations and exercises accompanied by the relevant financial theory. Topics covered include present value, arbitrage pricing, portfolio theory, derivates pricing, delta-hedging, the Black-Scholes model, and more.
* An excellent resource for finance professionals and investors looking to acquire an understanding of financial derivatives theory and practice
* Completely revised and updated with new chapters, including coverage of cutting-edge concepts in volatility trading and exotic products
An accompanying website is available which contains additional resources including powerpoint slides and spreadsheets. Visit www.introeqd.com for details.
eBook
Spanning Multi-Asset Payoffs With ReLUs
We propose a distributional formulation of the spanning problem of a multi-asset payoff by vanilla basket options. This problem is shown to have a unique solution if and only if the payoff function is even and absolutely homogeneous, and we establish a Fourier-based formula to calculate the solution. Financial payoffs are typically piecewise linear, resulting in a solution that may be derived explicitly, yet may also be hard to numerically exploit. One-hidden-layer feedforward neural networks instead provide a natural and efficient numerical alternative for discrete spanning. We test this approach for a selection of archetypal payoffs and obtain better hedging results with vanilla basket options compared to industry-favored approaches based on single-asset vanilla hedges.
Paper
Implied Distributions
Perhaps the favorite activity of quantitative analysts is to decode market data into information about the future upon which a trader can base his or her decisions. This is the purpose of the implied distribution that translates option prices into probabilities for the underlying stock or stock index to reach certain levels in the future. In this chapter, we derive the implied distribution and show how it may be exploited to price and hedge certain exotic payoffs.
Book Chapter
Volatility Derivatives
Option traders who hedge their delta have long realized that their option book is exposed to many other market variables, chief of which is volatility. In fact we will see that the P&L on a delta‐hedged option position is driven by the spread between two types of volatility: the instant realized volatility of the underlying stock or stock index, and the option's implied volatility.
Thus option traders are specialists of volatility, and naturally they want to trade it directly. This prompted the creation of a new generation of derivatives: forward contracts and options on volatility itself.
Book Chapter
Exotic Derivatives
Strictly speaking, an exotic derivative is any derivative that is not a plain vanilla call or put. In this chapter we review the payoff and properties of the most widespread equity derivative exotics.
Book Chapter
Local Volatility and Beyond
The local volatility model was independently developed in the early 1990s by Derman and Kani and by Dupire. It has arguably become the benchmark model to price and hedge a wide range of equity exotics such as digitals, Asians, and barriers, but fails on certain payoffs such as forward start options, which are better approached using a stochastic volatility model.
The model can be difficult to implement since it requires a high‐quality, smooth implied volatility surface as input, and simulation of all intermediate spot prices until maturity using short time steps.
Book Chapter
Local Correlation
Local correlation models are a recent cutting‐edge development in derivatives modeling and extend the concept of local volatility to multiple assets. Indeed if the volatility of each asset is thought to depend on time and the spot price, then the same idea should probably apply to the correlation coefficient between any two assets. However there are theoretical and practical issues: on the theoretical side the entire correlation matrix must remain positive‐definite, which can be challenging; and on the practical side there are very few observable basket option prices to calibrate to. In this chapter we give evidence of non‐constant implied correlation and introduce a model that is consistent with this behavior.
Book Chapter