Smile Pricing Explained

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction to Derivatives

   • Peter Austing

   Pages 1-9

3. Stochastic Calculus

   • Peter Austing

   Pages 10-20

4. Martingale Pricing

   • Peter Austing

   Pages 21-39

5. Dynamic Hedging and Replication

   • Peter Austing

   Pages 40-46

6. Exotic Options in Black—Scholes

   • Peter Austing

   Pages 47-57

7. Smile Models

   • Peter Austing

   Pages 58-70

8. Stochastic Volatility

   • Peter Austing

   Pages 71-95

9. Numerical Techniques

   • Peter Austing

   Pages 96-120

10. Local Stochastic Volatility

    • Peter Austing

    Pages 121-148

11. Volatility Products

    • Peter Austing

    Pages 149-171

12. Multi-Asset

    • Peter Austing

    Pages 172-197

13. Afterword

    • Peter Austing

    Pages 198-199

14. Back Matter

    Pages 200-221

    PDF

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.

• Volatility smile
• Implied volatility
• local volatility model
• Stochastic volatility model
• Derivatives pricing
• Black-Scholes
• Stochastic calculus
• Brownian motion
• Martingale
• Girsanov theorem
• Dynamic hedging
• Exotic options
• Heston model
• SABR model
• Regime switching
• Monte Carlo
• PDE approach
• Local stochastic volatility model
• Arbitrage
• Variance swap

'This appealing little book is skillfully written by Dr. Peter Austing, a well-known authority on options pricing. It is easy to understand and covers a lot of ground on theory and practice of smile pricing. It will be helpful to both seasoned and aspiring quants, as well as other financial practitioners and academics.' - Alexander Lipton, MD, Quantitative Solutions Executive, Bank of America

'A gem of a book, 'Smile Pricing Explained' oozes with the enthusiasm that its author Dr Austing, a seasoned practitioner and expert on multi-asset smile modelling, has for the subject. The book takes us on a concise but very exciting journey from the carefully yet succinctly explained basics of arbitrage pricing to the cutting edge of correlation smile, a journey that is fuelled by generous measures of intuition and practical advice. There is no doubt that students and practicing quants alike will enjoy this book immensely and will learn a lot from it too.' - Vladimir Piterbarg, Managing Director and Head of Quantitative Analytics, Barclays

'Smile Pricing Explained takes the reader on a sophisticated journey starting with the elements of arbitrage pricing theory and ending right at the frontier of quant practice with impressively succinct explanations of local stochastic volatility and local correlation models. Students and experienced practitioners alike will find this concise but self-contained book both a pleasure to read and an invaluable reference.' - Jim Gatheral, Presidential Professor, Baruch College, CUNY and author of The Volatility Surface

'Finally a book that explains Ito's lemma in exact and yet tangibly applied terms. I was elated!' - Peter Jäckel, Managing Director of OTC Analytics, Deputy Head of VTB Capital Quantitative Research, and author of Monte Carlo Methods in Finance

'This is a very interesting book on smile modelling written with passion by Dr Peter Austing, a researcher at Imperial College London with important industry experience on using models in practical contexts and day to day situations. It is rare finding authors with this combination of skills working as full time academics, and the book reflects this peculiar background. The approach in the book is not just using rigorous mathematics for smile modelling, but also letting the reader understand why this is important and how the models can then be implemented. I found the chapter on local stochastic volatility and the final chapter on the multivariate setting particularly appealing. Eclectic, rigorous, practical, written with passion, this book is recommended to both the advanced expert and the newcomer.' - Professor Damiano Brigo, Dept. of Mathematics, Imperial College London, co-originator of the no-arbitrage mixture dynamics approach to smile modelling

'A super book which describes the state of the art for skew option pricing, specifically in FX markets. It brings together both theory and practice, including accessiblemathematical derivations, practical market considerations and implementation techniques. Models described in detail include both local and stochastic volatility, the synthesis of the two, and the author's own ground-breaking work on multi-asset skew pricing. Well-written and filled with enthusiasm for all aspects of the subject.' - Martin Baxter, Head of Quantitative Research, Nomura, (co-author of the best selling Financial Calculus)

'Aristotle realized that the earth is not flat in 330 BC, but it was not until the crash of 1987 that option market makers drew the same conclusion for the implied vol surface. This friendly book explores two widely accepted extensions of the Black Scholes paradigm called local vol and stochastic vol. The reader of this book will have a good understanding of these concepts in the continuous-time continuous sample-path setting that is widely used in practice'. - Peter Carr, PhD., Global Head of Market Modeling, Morgan Stanley and Executive Director of NYU Math Finance Program

• Imperial College, London, UK

  Peter Austing

In Smile Pricing Explained, Peter Austing draws on a decade of experience building the mathematical models for derivatives trading at major investment banks, most recently Barclays Capital where he was a Director in Quantitative Analytics.

Before moving to finance, Dr Austing held research positions in theoretical physics studying candidate theories of quantum gravity. It was at Oxford University, while teaching mathematics at St John's College, that he developed his love for teaching and accessible style.

A seasoned quantitative practitioner, and regular conference speaker, Peter Austing is best known for his work on multi-asset derivative pricing with correlation smile. He is currently engaged in research at Imperial College, London.

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