Pricing via recursive quantization in stochastic volatility models

Callegaro, Giorgia; Fiorin, Lucio; Grasselli, Martino

doi:10.1080/14697688.2016.1255348

Cited by 23 publications

(21 citation statements)

References 22 publications

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“…Our results improve the option pricing performance in Ackerer et al (2018). Notable progress has recently been made on the pricing of early-exercise and path-dependent options with stochastic volatility using recursive marginal quantization as studied in Pagès and Sagna (2015); McWalter et al (2017); Callegaro et al (2017a). In the context of affine and polynomial models, this approach has been shown to perform well when combined with Fourier transform techniques as in Callegaro et al (2017b), or polynomial expansion techniques as in Callegaro et al (2017), whose results could be further improved with the new expansions presented in our paper.…”

Section: Introductionmentioning

confidence: 59%

Option Pricing with Orthogonal Polynomial Expansions

Ackerer

Filipović

2017

SSRN Journal

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We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

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Section: Introductionmentioning

confidence: 59%

Option Pricing with Orthogonal Polynomial Expansions

Ackerer

Filipović

2017

SSRN Journal

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“…The pricing of European options under local and stochastic volatility models using recursive quantization techniques has already been studied, see e.g. [19] and [4] for the local volatility case, and [5] for the stochastic volatility case. However, the method we present here is more general and is model free compared to [5] where the method depends on the structure of the model.…”

Section: Pricing Of a European Option In The Heston Modelmentioning

confidence: 99%

“…Formulas (14)- (15) are useful when, for example, we deal with the approximation of the solution of BSDEs or when we deal with the pricing of a Basket call like Equation (5). In this last situation, given a time discretization mesh t 0 = 0, .…”

Section: Introductionmentioning

confidence: 99%

Product Markovian Quantization of a Diffusion Process with Applications to Finance

Fiorin

Pagès²,

Sagna

2018

Methodol Comput Appl Probab

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We introduce a new approach to quantize the Euler scheme of an R d -valued diffusion process. This method is based on a Markovian and componentwise product quantization and allows us, from a numerical point of view, to speak of fast online quantization in dimension greater than one since the product quantization of the Euler scheme of the diffusion process and its companion weights and transition probabilities may be computed quite instantaneously. We show that the resulting quantization process is a Markov chain, then, we compute the associated companion weights and transition probabilities from (semi-) closed formulas. From the analytical point of view, we show that the induced quantization errors at the k-th discretization step t k is a cumulative of the marginal quantization error up to time t k . Numerical experiments are performed for the pricing of a Basket call option, for the pricing of a European call option in a Heston model and for the approximation of the solution of backward stochastic differential equations to show the performances of the method.

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“…, x j d d,k . Having computed all these elements, it is possible to compute the (approximate) distortion function (33), its gradient and its Hessian function and to implement the Newton-Raphson algorithm as in Callegaro et al (2015) and Callegaro et al (2016).…”

Section: Mathematical Foundation Of the Algorithmmentioning

confidence: 99%

“…Recursive marginal quantization, or fast quantization, introduced in Pagès and Sagna (2015) represents a new promising research field. Sub-optimal (stationary) quantizers of the stochastic process at fixed dates are obtained in a very fast recursive way, to the point that recursive marginal quantization has been successfully applied to many models, including local volatility models as in Callegaro et al (2015), Bormetti et al (2017), McWalter et al (2017) and stochastic volatility models as in Callegaro et al (2016), Fiorin et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Quantization Goes Polynomial

2017

Self Cite

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Quantization algorithms have been recently successfully adopted in option pricing problems to speed up Monte Carlo simulations thanks to the high convergence rate of the numerical approximation. In particular, recursive marginal quantization has been proven a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time these techniques to the family of polynomial processes, by exploiting, whenever possible, their peculiar properties. We derive theoretical results to assess the approximation errors, and we describe in numerical examples practical tools for fast exotic option pricing. JEL classification codes: C63, G13.

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Pricing via recursive quantization in stochastic volatility models

Cited by 23 publications

References 22 publications

Option Pricing with Orthogonal Polynomial Expansions

Option Pricing with Orthogonal Polynomial Expansions

Product Markovian Quantization of a Diffusion Process with Applications to Finance

Quantization Goes Polynomial

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