Author: Steven L. Heston Publisher: ISBN: Category : Languages : en Pages :
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: Fabrice D. Rouah Publisher: John Wiley & Sons ISBN: 1118695178 Category : Business & Economics Languages : en Pages : 437
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: Natalia Beliaeva Publisher: ISBN: Category : Languages : en Pages :
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: Moawia Alghalith Publisher: ISBN: Category : Languages : en Pages : 8
Book Description
We overcome the limitations of the previous literature in the European options pricing. In doing so, we provide a closed-form formula that doesn't require any numerical/computational methods. The formula is as simple as the classical Black-Scholes pricing formula. In addition, we simultaneously include jumps and stochastic volatility.
Author: Lorenzo Bergomi Publisher: CRC Press ISBN: 1482244071 Category : Business & Economics Languages : en Pages : 520
Book Description
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author: Bogdan Negrea Publisher: ISBN: Category : Languages : en Pages : 52
Book Description
The Black and Scholes (1973) option pricing model was developed starting from the hypothesis of constant volatility. However, many empirical studies, have argued that the mentioned hypothesis is subject to debate. A few authors, among who - Stein and Stein (1991), Heston (1993), Bates (1996) and Bakshi et al.(1997, 2000) - suggested the use of the Fourier transform for the density of the underlying return or for the risk-neutral probabilities, in order to evaluate the fair price of an option. In this paper we propose a stochastic valuation model using the Fourier transform for option price. This model can be used for the valuation of European options, characterized by two state variables: the price of the underlying asset and its volatility. We model the stochastic processes described by the two variables and we obtain a partial derivatives equation of which the solution is the price of the derivative. We propose a solution to this partial derivatives equation using the Fourier transform. When we apply the Fourier transform, we demonstrate that a second order partial derivatives equation is solved as an ordinary differential equation. We consider a correlation between the underlying asset price and its volatility and two sources of risk: return and volatility. The first part of the paper describes the hypotheses of the model. After describing the Fourier transforms, we propose a formula for the valuation of European options with stochastic volatility. In the second part, we present a few empirical results on the pricing of CAC 40 index call options.
Author: Steven L. Heston
Author: Fabrice D. Rouah
Author: Alan L. Lewis
Author: Natalia Beliaeva
Author: Moawia Alghalith
Author: Lorenzo Bergomi
Author: Bogdan Negrea
Author: Christian Hafner
Author: Libo Xie
Author: Stephen Chin