Investigating Time-Efficient Methods to Price Compound Options in the Heston Model PDF Download
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Author: Carl Chiarella
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston's stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using the Green's function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing.
Author: Carl Chiarella
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston's stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using the Green's function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing.
Author: Roger Lord
Publisher: Rozenberg Publishers
ISBN: 9051709099
Category :
Languages : en
Pages : 211
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Book Description
Author: Alexander Izmailov
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
• 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" and "Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems. A Probability Density Function Approach." (See links 'http://ssrn.com/abstract=2489601' http://ssrn.com/abstract=2489601 and 'http://ssrn.com/abstract=2546430' http://ssrn.com/abstract=2546430). • In this paper we report similar unique results for pricing options in the presence of stochastic volatility (Heston model), enabling complete analytical resolution of all problems associated with options considered within the Heston Model. • Our discovery of the probability density function for options with stochastic volatility enables exact closed-form analytical results for their expected values (prices) for the first time without depending on approximate numerical methods and a Fourier transform that only abbreviates complex numerical integration procedure. • Expected value is the first moment. 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, such as a Fourier transform, now used to represent the first moment. • Our formulation of the density function for options with stochastic volatility within the 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 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 within the Heston model.• All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Author: Fabrice Rouah
Publisher:
ISBN:
Category : C# (Computer program language)
Languages : en
Pages : 432
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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. Note: The ebook version does not provide access to the companion files.
Author: Fabrice D. Rouah
Publisher: Wiley
ISBN: 9781118695135
Category : Business & Economics
Languages : en
Pages : 432
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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: 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: Conall O'Sullivan
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown to significantly reduce the severity of the stability constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the simplicity of the chosen underlying explicit method. For European and American put options under Heston's stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude that STS is a powerful tool for the numerical pricing of options and propose them as the method-of-choice for exotic financial instruments in two and multi-factor models.
Author: Jeffrey Owen Katz
Publisher: McGraw-Hill
ISBN: 9780071626446
Category : Business & Economics
Languages : en
Pages : 452
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Book Description
"Advanced Option Pricing Models" details specific conditions under which current option pricing models fail to provide accurate price estimates and then shows option traders how to construct improved models for better pricing in a wider range of market conditions. Model-building steps cover options pricing under conditional or marginal distributions, using polynomial approximations and "curve fitting," and compensating for mean reversion. The authors also develop effective prototype models that can be put to immediate use, with real-time examples of the models in action.
Author: Christian Bayer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We provide an efficient and accurate simulation scheme for the rough Heston model in the standard (H > 0) as well as the hyper-rough regime (H > -1/2). The scheme is based on low-dimensional Markovian approximations of the rough Heston process derived in [Bayer and Breneis, arXiv:2309.07023], and provides weak approximation to the rough Heston process. Numerical experiments show that the new scheme exhibits second order weak convergence, while the computational cost increases linear with respect to the number of time steps. In comparison, existing schemes based on discretization of the underlying stochastic Volterra integrals such as Gatheral's HQE scheme show a quadratic dependence of the computational cost. Extensive numerical tests for standard and path-dependent European options and Bermudan options show the method's accuracy and efficiency.
Author: Peter Ruckdeschel
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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.
