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Quantization goes Polynomial
TL;DR: This paper applies recursive marginal quantization techniques to the family of polynomial processes, by exploiting, whenever possible, their peculiar properties, and derives theoretical results to assess the approximation errors.
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Abstract: Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time quantization techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the induced approximation errors, and we describe in numerical examples practical tools for fast vanilla and exotic option pricing.
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Markov cubature rules for polynomial processes
TL;DR: Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial processes.
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Polynomial Jump-Diffusion Models
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References
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Foundations of Quantization for Probability Distributions
Siegfried Graf,Harald Luschgy +1 more
- 16 May 2000
TL;DR: In this article, asymptotic quantization for nonsingular probability distributions and singular probability distributions is studied. But quantization of singular distributions is not a special case of the problem of non-singular distributions.
A quantization tree method for pricing and hedging multidimensional american options
TL;DR: The quantization method is presented, which is well‐adapted for the pricing and hedging of American options on a basket of assets and results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids are provided.
245
Parametric properties of semi-nonparametric distributions, with applications to option valuation
TL;DR: This paper derived the statistical properties of the semi-nonparametric (SNP) densities of Gallant and Nychka (1987) and showed that these densities are more flexible than truncated Gram-Charlier expansions with positivity restrictions.
A General Valuation Framework for SABR and Stochastic Local Volatility Models
TL;DR: A general framework for the valuation of options in stochastic local volatility models with a general correlation structure, which includes the Stochastic alpha beta structure, is proposed.
100
The Jacobi stochastic volatility model
TL;DR: In this article, the authors introduced a stochastic volatility model where the squared volatility of the asset return follows a Jacobi process, and they showed that the joint density of any finite sequence of log returns admits a Gram-Charlier A with closed-form coefficients.
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