Valuation Of American Style Derivatives Within The Stochastic Volatility Model Of Heston
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The Heston Model and Its Extensions in VBA
| Author | : Fabrice D. Rouah |
| Publisher | : John Wiley & Sons |
| Total Pages | : 349 |
| Release | : 2015-03-20 |
| Genre | : Business & Economics |
| ISBN | : 1119003326 |
Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.
Derivatives in Financial Markets with Stochastic Volatility
| Author | : Jean-Pierre Fouque |
| Publisher | : Cambridge University Press |
| Total Pages | : 222 |
| Release | : 2000-07-03 |
| Genre | : Business & Economics |
| ISBN | : 9780521791632 |
This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
The Heston Model and its Extensions in Matlab and C#
| Author | : Fabrice D. Rouah |
| Publisher | : John Wiley & Sons |
| Total Pages | : 437 |
| Release | : 2013-08-01 |
| Genre | : Business & Economics |
| ISBN | : 1118695178 |
Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities
| Author | : Alexander Izmailov |
| Publisher | : |
| Total Pages | : 17 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk and Option Based Hedging Strategies”, “Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems. A Probability Density Function Approach” and “Complete Analytical Solution of the Heston Model for Option Pricing and Value-At-Risk Problems. A Probability Density Function Approach.” Please see links 'http://ssrn.com/abstract=2489601 ' http://ssrn.com/abstract= 2489601, 'http://ssrn.com/abstract=2546430 ' http://ssrn.com/abstract= 2546430, 'http://ssrn.com/abstract=2549033 ' http://ssrn.com/abstract= 2549033). In this paper we report unique analytical results for pricing American Style Options in the presence of both constant and stochastic volatility (Heston model), enabling complete analytical resolution of all problems associated with American Style Options considered within the Heston Model. Our discovery of the probability density function for American and European Style Options with constant and stochastic volatilities enables exact closed-form analytical results for their expected values (prices) for the first time without depending on approximate numerical methods. Option prices, i.e. their expected values, are just the first moments. All higher moments are as easily represented in closed form based on our probability density function, but are not calculable by extensions of other numerical methods now used to represent the first moment. Our formulation of the density functions for options with American and European Style execution rights with constant and stochastic volatility (Heston model) is expressive enough to enable derivation for the first time ever of corollary closed-form analytical results for such Value-At-Risk characteristics as the probabilities that options with different execution rights, with constant or stochastic volatility, will be below or above any set of thresholds at termination. Such assessments are absolutely out of reach of current published methods for treating options.All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Stochastic volatility and the pricing of financial derivatives
| Author | : Antoine Petrus Cornelius van der Ploeg |
| Publisher | : Rozenberg Publishers |
| Total Pages | : 358 |
| Release | : 2006 |
| Genre | : |
| ISBN | : 9051705778 |
Derivative Evaluation Using Recombining Trees Under Stochastic Volatility
| Author | : Enrico Moretto |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
Heston (1993) presents a method to derive a closed-form solution for derivative pricing when the volatility of the underlying asset follows stochastic dynamics. His approach works well for European derivatives but, unfortunately, does not readily extend to the pricing of more complex contracts. In this paper we propose an alternative stochastic volatility model which retains many features of Heston model, but is better suited for an easy discretization through recombining trees, in the spirit of Nelson and Ramaswamy (1990). After having discussed the theoretical properties of the model we construct its discretized counterpart through a recombining multinomial tree. We apply the model to the USD/EURO exchange rate market, evaluating both American and barrier options.
Pricing Models of Volatility Products and Exotic Variance Derivatives
| Author | : Yue Kuen Kwok |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2022-05-08 |
| Genre | : Mathematics |
| ISBN | : 1000584275 |
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
Pricing Derivatives in Stochastic Volatility Models Using the Finite Difference Method
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
The Heston stochastic volatility model is one extension of the Black-Scholes model which describes the money markets more accurately so that more realistic prices for derivative products are obtained. From the stochastic differential equation of the underlying financial product a partial differential equation (p.d.e.) for the value function of an option can be derived. This p.d.e. can be solved with the finite difference method (f.d.m.). The stability and consistency of the method is examined. Furthermore a boundary condition is proposed to reduce the numerical error. Finally a non uniform structured grid is derived which is fairly optimal for the numerical result in the most interesting point.
Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
| Author | : Jean-Pierre Fouque |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2011-09-29 |
| Genre | : Mathematics |
| ISBN | : 113950245X |
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
