A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model PDF Download
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Author: Natalia Beliaeva
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Languages : en
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In a recent paper, NBZ [2010] present a multidimensional transform for generating path-independent trees for pricing American options under low dimensional stochastic volatility models. For this class of models, this approach has higher accuracy than the GARCH tree method of Ritchken and Trevor [1999], and is computationally more efficient than the Monte Carlo regression method of Longstaff and Schwartz [2001] as well as the lattice method of Leisen [2000]. In this paper, we give an explicit demonstration of the NBZ transform using the specific example of the Heston [1993] stochastic volatility model. This approach obtains highly accurate American option prices within a fraction of a second using the control variate method.
Author: Natalia Beliaeva
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Languages : en
Pages :
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Book Description
In a recent paper, NBZ [2010] present a multidimensional transform for generating path-independent trees for pricing American options under low dimensional stochastic volatility models. For this class of models, this approach has higher accuracy than the GARCH tree method of Ritchken and Trevor [1999], and is computationally more efficient than the Monte Carlo regression method of Longstaff and Schwartz [2001] as well as the lattice method of Leisen [2000]. In this paper, we give an explicit demonstration of the NBZ transform using the specific example of the Heston [1993] stochastic volatility model. This approach obtains highly accurate American option prices within a fraction of a second using the control variate method.
Author: Peter Ruckdeschel
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Languages : en
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Book Description
We introduce a refined tree method to compute option prices using the stochastic volatility model of Heston. In a first step, we model the stock and variance process as two separate trees and with transition probabilities obtained by matching marginal tree moments up to order two against the Heston model ones. The correlation between the driving Brownian motions is then incorporated by a node-wise adjustment of the probabilities. This adjustment, leaving the marginals fixed, optimizes the match between tree and model correlation. In some nodes, we are even able to further match moments of higher order. Numerically this gives convergence orders faster than 1/N, where N is the number of discretization steps. Accuracy of our method is checked for European option prices against a semi closed-form, and our prices for both European and American options are compared to alternative approaches.
Author: Fabrice D. Rouah
Publisher: John Wiley & Sons
ISBN: 1118695178
Category : Business & Economics
Languages : en
Pages : 437
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Book Description
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.
Author: Jonathan Ziveyi
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Languages : en
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Book Description
In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes as proposed in Christoffersen, Heston and Jacobs (2009). We consider the associated partial differential equation (PDE) for the option price and its solution. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. For the particular form of the underlying dynamics we are able to solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach provides quite good accuracy.
Author: Fabrice D. Rouah
Publisher: John Wiley & Sons
ISBN: 1119003326
Category : Business & Economics
Languages : en
Pages : 349
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Book Description
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.
Author: Manisha Goswami
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Languages : en
Pages :
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Book Description
The approximate method to price American options makes use of the fact that accurate pricing of these options does not require exact determination of the early exercise boundary. Thus, the procedure mixes the two models of constant and stochastic volatility. The idea is to obtain early exercise boundary through constant volatility model using the approximation methods of AitSahlia and Lai or Ju and then utilize this boundary to price the options under stochastic volatility models. The data on S & P 100 Index American options is used to analyze the pricing performance of the mixing of the two models. The performance is studied with respect to percentage pricing error and absolute pricing errors for each money-ness maturity group.
Author: Steven L. Heston
Publisher:
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Languages : en
Pages :
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Book Description
This paper shows a relationship between bond pricing models and option pricing models with stochastic volatility. It exploits this relationship to find a new stochastic volatility model with a closed-form solution for European option prices. The model allows nonzero correlation between volatility and spot asset returns. When the correlation is unity the model contains the Black-Scholes [1973] model and Cox's [1975] constant elasticity of variance model as special cases. The option formula preserves the Black-Scholes property that changes in volatility are equivalent to changes in option expiration.
Author: Carl Chiarella
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston's stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.
Author: Boda Kang
Publisher:
ISBN:
Category :
Languages : en
Pages : 49
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Book Description
This paper analyzes the importance of asset and volatility jumps in American option pricing models. Using the Heston (1993) stochastic volatility model with asset and volatility jumps and the Hull and White (1987) short rate model, American options are numerically evaluated by the Method of Lines. The calibration of these models to S&P 100 American options data reveals that jumps, especially asset jumps, play an important role in improving the models' ability to fit market data. Further, asset and volatility jumps tend to lift the free boundary, an effect that augments during volatile market conditions, while the additional volatility jumps marginally drift down the free boundary. As markets turn more volatile and exhibit jumps, American option holders become more prudent with their exercise decisions, especially as maturity of the options approaches.
Author: Zhe Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 198
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