SQF3: The SABR Model
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SQF3: The SABR Model

An Implementation Guide

About the Book

This book serves as an implementation guide to the SABR model, with pricing quants as the aimed readers. It lists various approximation formulas without explaining how they are obtained (hence the subtitle, "An Implementation Guide"). With the goal of "coding it up", this book also provides some general facts on implied volatility and derives an estimation of convergence rate for one of the approximation formulas, to ensure numerical accuracy.

The text is based on the following references:

[1] Shalom Benaim, Peter Friz and Roger Lee. On Black-Scholes Implied Volatility at Extreme Strikes. In Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling, Rama Cont (editor). John Wiley & Sons, 2012.

[2] Patrick S. Hagan, Deep Kumar, Andrew S. Lesniewski, and Diana E. Woodward. Managing smile risk. Wilmott Magazine, page 84-108, 2002.

[3] Richard Jordan and Charles Tier. Asymptotic approximation to CEV and SABR models. Preprint, 2011. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1850709

[4] Roger Lee. The moment formula for implied volatility at extreme strikes. Mathematical Finance, Volume 14, Issue 3, pages 469-480. July 2004.

[5] Jan Obloj. Fine-tune your smile: Correction to Hagan et al. Wilmott Magazine, May 2008.

[6] Louis Paulot. Asymptotic implied volatility at the second order with application to the SABR model. SSRN working paper, 2009.

About the Author

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