A General Framework For Pricing Asian Options Under Stochastic Volatility On Parallel Architectures
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| Author | : Stefania Corsaro |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 2019 |
| Genre | : |
| ISBN | : |
In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.
| Author | : George Yin |
| Publisher | : Springer |
| Total Pages | : 593 |
| Release | : 2019-07-16 |
| Genre | : Mathematics |
| ISBN | : 3030254984 |
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
| Author | : Justin Kirkby |
| Publisher | : |
| Total Pages | : 39 |
| Release | : 2020 |
| Genre | : |
| ISBN | : |
Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines Continuous-Time Markov Chain (CTMC) approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, alpha-Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a unified approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.
| Author | : Oleg Bondarenko |
| Publisher | : |
| Total Pages | : 29 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
We present a generalization of Cochrane and Saá-Requejo's good-deal bounds which allows to include in a flexible way the implications of a given stochastic discount factor model. Furthermore, a useful application to stochastic volatility models of option pricing is provided where closed-form solutions for the bounds are obtained. A calibration exercise demonstrates that our benchmark good-deal pricing results in much tighter bounds. Finally, a discussion of methodological and economic issues is also provided.
| Author | : Johannes Ruppert |
| Publisher | : |
| Total Pages | : 76 |
| Release | : 2016 |
| Genre | : |
| ISBN | : |
"In this thesis, we look at the general affine pricing model introduced in [11]. This model allows to price geometric Asian options, which are of big interest due to their lower volatility in comparison to, for example, European options. Because of their structure and in order to be able to price these options, we look at the basic theory of Lévy processes and stochastic calculus. Furthermore, we provide the detailed description of the parameters of the pricing formulas for some popular specific single-factor stochastic volatility models with jumps and generalize the approach of [11] to multi-factor models"--Abstract, page iii.
| Author | : Alexander Izmailov |
| Publisher | : |
| Total Pages | : 11 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
The first ever explicit formulation of the concept of the 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.The first ever explicit formulation of the concept of the options' probability density functions within the framework of stochastic volatility (Heston model) has been introduced in our publications “Complete Analytical Solution of the Heston Model for Option Pricing and Value-at-Risk Problems: A Probability Density Function Approach”, “Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities: A Probability Density Function Approach” and “A Complete Analytical Resolution of the Double Barrier Option's Pricing Within the Heston Model. A Probability Density Approach.” See links:'http://ssrn.com /abstract=2549033' http://ssrn.com/abstract=2549033 and 'http://ssrn.com/abstract=2554038' http://ssrn.com/abstract=2554038 and 'http://ssrn.com/abstract=2605948' http://ssrn.com/abstract=2605948.In this paper we report complete analytical closed-form results for the European style Asian Options considered within the Heston model for Stochastic Volatility (SV). Our discovery of the probability density function of the European style Asian Options with SV enables exact closed-form representation of its expected value (price) for the first time ever. Our formulation of the probability density function for the European style Asian Options with SV is expressive enough to enable derivation for the first time ever of corollary analytical closed-form results for such Value-At-Risk characteristics as the probabilities that an Asian Option with SV will be below or above any threshold at any future time before or at termination. Such assessments are absolutely out of reach of the current published methods for treating Asian Options even in the framework of constant volatility.All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
| Author | : 翟雲飛 |
| Publisher | : |
| Total Pages | : 198 |
| Release | : 2012 |
| Genre | : Options (Finance) |
| ISBN | : |
| Author | : Ying Lok Cheung |
| Publisher | : |
| Total Pages | : 104 |
| Release | : 2004 |
| Genre | : Options (Finance) |
| ISBN | : |
| Author | : Pingping Zeng |
| Publisher | : |
| Total Pages | : 31 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. By extending the conditioning variable approach, we derive the lower bound on the Asian option price and construct an upper bound based on the sharp lower bound. We also consider the general partially exact and bounded (PEB) approximations, which include the sharp lower bound and partially conditional moments matching approximation as special cases. The PEB approximations are known to lie between a sharp lower bound and an upper bound. Our numerical tests show that the PEB approximations to discrete arithmetic Asian option prices can produce highly accurate approximations when compared to other approximation methods. Our proposed approximation methods can be readily applied to pricing Asian options under the most common types of underlying asset price processes, like the Heston stochastic volatility model nested in time-changed Lévy processes with leverage effect.
| Author | : Gianluca Fusai |
| Publisher | : |
| Total Pages | : 37 |
| Release | : 2016 |
| Genre | : |
| ISBN | : |
We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases.
