# Option Pricing Models and Volatility Using Excel-VBA

Language: English

Pages: 441

ISBN: 0471794643

Format: PDF / Kindle (mobi) / ePub

This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book.

**Praise for Option Pricing Models & Volatility Using Excel-VBA**

"Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers."

—**Peter Christoffersen**, Associate Professor of Finance, Desautels Faculty of Management, McGill University

"This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library."

—**Espen Gaarder Haug**, option trader, philosopher, and author of *Derivatives Models on Models*

"I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH."

—**Steven L. Heston**, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland

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Once these three prices are obtained it is easy to write functions for the variance, skewness and kurtosis, in accordance with equations (12.9), (12.10), and (12.11). This is achieved with the VBA functions BMFVar(), BMFSkew(), and BMFKurt(), respectively. Function BMFVar(CallK, CallP, PutK, PutP, S, r, tau) Dim V As Double, W As Double, X As Double V = BV(CallK, CallP, PutK, PutP, S, r, tau) W = BW(CallK, CallP, PutK, PutP, S, r, tau) X = BX(CallK, CallP, PutK, PutP, S, r, tau) er = Exp(r

implied volatility loss function is the closest to the model-free approach for skewness and kurtosis, but overestimates the volatility compared to the dollar and relative root mean squared error loss functions. Another interesting way of examining the model fit to the implied moments is by examining the implied volatility curves induced by each of the parameters, and comparing these curves to the actual implied volatility curve. The Excel file Chapter12GoogleIV contains these implied

approximation uses the entire interval, and the other uses the sum of the approximations from each subinterval. If the difference between these approximations is larger than some tolerance level, the smaller subintervals are used; otherwise, [a, b] is used. Improper Integrals and Open Rules When an integration rule uses all the abscissas x0, x1, …, xn in its formulation, the rule is said to be a closed rule. When the endpoints x0 = a and xn = b, are excluded, however, the rule is an open

cells H7:H22 for values of the x-axis, and cells G7:G22 for values of the y-axis. Deterministic Volatility Functions The parabolic shape of the volatility smile, and its dependence on moneyness and maturity, has motivated researchers to model implied volatility as a quadratic function of moneyness and maturity. Dumas, Fleming, and Whaley (1998) describe this as the deterministic volatility function (DVF) approach to modeling implied volatility. They consider four specifications for the

available in closed form. For the binomial and trinomial trees of Chapter 3, some of the Greeks can be approximated by considering the price of the option at different nodes of the tree. Others must be approximated by finite differences—inducing a small perturbation in the value of an input variable and calculating the change in option price relative to the perturbation. For the Heston (1993) model of Chapter 5 and the Heston and Nandi (2000) model of Chapter 6, the Greeks are also available in