Option Pricing Under GARCH Processes Using PDE Methods

Breton, Michèle; Frutos, Javier de

doi:10.1287/opre.1100.0822

Cited by 17 publications

(23 citation statements)

References 31 publications

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“…Finally the proposed factorization has potential and immediate applications to the study of properties of discrete time Markov Chains as well, a very important topic in operational research for modeling queuing sequences and many other practical systems, see [29]. Extension to other processes, as normal mixture distribution, see [5], and options with multiple risk factors, such as stochastic volatility models or multi-assets contracts, as in [9,24,33], are also amenable to the presented technique, and will be treated in a follow-up paper.…”

Section: Resultsmentioning

confidence: 99%

Pricing exotic derivatives exploiting structure

Sesana

Marazzina

Fusai

2014

European Journal of Operational Research

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractIn this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs, and the underlying evolves according to a Markov one-dimensional stochastic processes. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion. The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process for pricing different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options for which up to date no efficient procedures are available. Extensive numerical experiments confirm the theoretical results. The MATLAB code used to perform the computation is available online at

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Section: Resultsmentioning

confidence: 99%

Pricing exotic derivatives exploiting structure

Sesana

Marazzina

Fusai

2014

European Journal of Operational Research

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“…where π o denotes the optimal trading strategy solving (4). Therefore, the optimal value function can be computed as the solution of (14)- (15) in (α 1 , α 2 ) × [0, T ] subject to the boundary conditions:…”

Section: Methodsmentioning

confidence: 99%

“…Both pictures are in the same scale and we can observe that the error reduces for increasing value of N θ . 4] where v N was computed with the Chebyshev method with N θ = 256 (left) and N θ = 2048 (right).…”

Section: Value Of the Function In V(0 T)mentioning

confidence: 99%

A spectral method for an Optimal Investment problem with transaction costs under Potential Utility

Frutos

Gatón

2017

Journal of Computational and Applied Mathematics

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This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In [12], the problem is reformulated as a non-linear parabolic double obstacle problem posed in one spatial variable and defined in an unbounded domain where several explicit properties and formulas are obtained. The restatement of the problem in polar coordinates allows to pose the problem in one spatial variable in a finite domain, avoiding some of the technical difficulties of the numerical solution of the previous statement of the problem. If high precision is required, the spectral numerical method proposed becomes more efficient than simpler methods as finite differences for example.

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“…which, taking into account the model parameters, is an 8-variable function. For this model, there is no known closed form solution and several numerical methods can be employed, being Monte-Carlo based methods ( [13], [30]), Lattice methods ( [25], [28]), Finite Elements ([1]) or Spectral methods ( [6]) some of them.…”

Section: Option Pricing and Garch Modelsmentioning

confidence: 99%

“…In this work, the numerical method employed for computing the option prices in the Chebyshev nodes will be the spectral method developed in [6] and will be referred as B-F method. This numerical method gives enough precision with few grid points, and the employment of FFT techniques makes it a low-time consuming method.…”

Section: Option Pricing and Garch Modelsmentioning

confidence: 99%

Chebyshev reduced basis function applied to option valuation

Frutos

Gatón

2017

Comput Manag Sci

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We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. In the paper we consider, as an example, a GARCH model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. In particular the method is applied to the problem of model calibration. The method is easily generalizable to be used with other models or problems.

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Option Pricing Under GARCH Processes Using PDE Methods

Cited by 17 publications

References 31 publications

Pricing exotic derivatives exploiting structure

Pricing exotic derivatives exploiting structure

A spectral method for an Optimal Investment problem with transaction costs under Potential Utility

Chebyshev reduced basis function applied to option valuation

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