American option pricing under stochastic volatility: an empirical evaluation

AitSahlia, Farid; Goswami, Manisha; Guha, Suchandan

doi:10.1007/s10287-008-0083-2

Cited by 7 publications

(7 citation statements)

References 28 publications

(52 reference statements)

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“…That is, we are less interested in whether the algorithm converges to a local minimum, and more interested in how well the constraints are satisfied. In all of our tests, the solution of either Equation (18) or Equation (19) yields (i) valid risk-neutral probabilities {q k } 1 k=−1 and (ii) residual errors in Equation (17) that are zero to at least four decimal places, sufficient for the purposes of this study.…”

Section: Implementation Detailsmentioning

confidence: 99%

“…For all index options considered in this study, when we find the solution (18) and insert it into (17), the residual error is zero to machine precision. We also find that β MT Θ,i;j ∈ Q, i.e., the q k 's are valid probabilities.…”

Section: Markov Treementioning

confidence: 99%

“…There are two reasons for choosing the Heston model as a representative SV model. First, the Heston model has already been subjected to pricing and hedging tests [14][15][16][17][18][19]. Comparing MT-versus-Heston results with this literature, we can gauge how the MT model would perform against many other models.…”

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confidence: 99%

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Large-Scale Empirical Tests of the Markov Tree Model

Bhat

Kumar²

2015

IJFS

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The Markov Tree model is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. In this work, we compare the empirical performance of the Markov Tree model against that of the Black-Scholes model and Heston's stochastic volatility model. Leveraging a total of five years of individual equity and index option data, and using three new methods for fitting the Markov Tree model, we find that the Markov Tree model makes smaller out-of-sample hedging errors than competing models. This comparison includes versions of Markov Tree and Black-Scholes models in which volatilities are strike-and maturity-dependent. Visualizing the errors over time, we find that the Markov Tree model yields more accurate and less risky single instrument hedges than Heston's stochastic volatility model. A statistical resampling method indicates that the Markov Tree model's superior hedging performance is due to its robustness with respect to noise in option data.

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Section: Implementation Detailsmentioning

confidence: 99%

Section: Markov Treementioning

confidence: 99%

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Large-Scale Empirical Tests of the Markov Tree Model

Bhat

Kumar²

2015

IJFS

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“…Here, we adopt Heston's approach [25] to model the volatility to satisfy a stochastic differential equation (SDE). Empirical evaluations show that Heston's model forAmerican options with stochastic volatility provides a substantial improvement for option pricing compared with the simple Black-Scholes model [3]. Extensive information on models for stochastic volatility can be found in [19].…”

Section: Introductionmentioning

confidence: 99%

Multiscale methods for the valuation of American options with stochastic volatility

Kunoth¹,

Schneider²,

Wiechers³

2012

International Journal of Computer Mathematics

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This paper deals with the efficient valuation of American options. We adopt Heston's approach for a model of stochastic volatility, leading to a generalized Black-Scholes equation called Heston's equation. Together with appropriate boundary conditions, this can be formulated as a parabolic boundary value problem with a free boundary, the optimal exercise price of the option. For its efficient numerical solution, we employ, among other multiscale methods, a monotone multigrid method based on linear finite elements in space and display corresponding numerical experiments.

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“…Typically, to make the numerical solution of SV models well-posed, conditions on the parameters (like correlation) must be laid as was shown by Lions and Musiela (2007). Pricing American options under SV models is studied for example by AitSahlia, Goswami, and Guha (2010a) with the empirical results in AitSahlia, Goswami, and Guha (2010b). The numerical influence of the stochastic volatility on the foreign equity option prices is analysed by Sun and Xu (2015).…”

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis in option pricing

Pospı́šil

Švígler

2018

International Journal of Computer Mathematics

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Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochastic volatility models, we develop a methodology for solving corresponding pricing partial integro-differential equations numerically by isogeometric analysis tools and show that a very small number of space discretization steps can be used to obtain sufficiently accurate results. Presented solution by finite element method is especially useful for practitioners dealing with derivatives where closed-form solution is not available.

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American option pricing under stochastic volatility: an empirical evaluation

Abstract: Stochastic volatility, Indirect inference, Model calibration, American option pricing, S&P 100 index, Approximate dynamic programming,

Cited by 7 publications

References 28 publications

Large-Scale Empirical Tests of the Markov Tree Model

Large-Scale Empirical Tests of the Markov Tree Model

Multiscale methods for the valuation of American options with stochastic volatility

Isogeometric analysis in option pricing

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