Stochastic lattice models for valuation of volatility options

Ma, Jingtang; Li, Wenyuan; Han, Xu

doi:10.1016/j.econmod.2015.02.015

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…It is proved by [17,18] for GBMP model and [18] for MRGP model, MRSRP model, and MRLP model that the free-boundary functions ( ) are continuously differentiable, strictly decreasing and convex on the interval ∈ [0, +∞), which are confirmed by the simulation results in [19]. Moreover we note that the free-boundary functions ( ) are bounded on the interval ( , ], where = (∞) are the early exercise boundaries of the corresponding perpetual American volatility put options, whose values satisfy the following ODEs:…”

Section: Model Descriptionsmentioning

confidence: 68%

Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing

Chen

2018

Discrete Dynamics in Nature and Society

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The aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options pricing. Firstly, the governing free-boundary PDEs are modified as a unified form of PDEs on the fixed space region; then performing Laplace-Carson transform (LCT) leads to ordinary differential equations (ODEs) which involve the unknown inverse functions of free boundaries. Secondly, the inverse free-boundary functions are approximated and optimized by solving of the free-boundary values of the perpetual American volatility options. Finally, the ODEs are solved by the finite difference methods (FDMs), and the results are restored via the numerical Laplace inversion. Numerical results confirm that the NCIMs outperform the FDMs for solving free-boundary PDEs in regard to the accuracy and computational time.

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Section: Model Descriptionsmentioning

confidence: 68%

Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing

Chen

2018

Discrete Dynamics in Nature and Society

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“…They suggest that simpler models of the second kind perform equally well with or even better than the first kind complicated models, such as the fully specified Lin and Chang model. Ma, Li and Han also use the stochastic lattice method to price the American‐style VIX options.…”

Section: Introductionmentioning

confidence: 99%

Pricing VIX options in a stochastic vol‐of‐vol model

Wang

Huang

et al. 2015

Appl Stoch Models Bus & Ind

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This paper proposes and makes a study of a new model for volatility index option pricing. Factors such as mean-reversion, jumps, and stochastic volatility are taken into consideration. In particular, the positive volatility skew is addressed by the jump and the stochastic volatility of volatility. Daily calibration is used to check whether the model fits market prices and generates positive volatility skews. Overall, the results show that the mean-reverting logarithmic jump and stochastic volatility model (called MRLRJSV in the paper) serves as the best model in all the required aspects.

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“…Applebaum (2009)). In more recent papers, Zhang and Xu (2014) introduce stochastic state variables into volatility dynamics and analyse the influence of state-variable volatile characters on investment stopping boundaries; and Ma et al (2015) use a discretised version of mean-reverting square root model for valuation of volatility options.…”

Section: Introductionmentioning

confidence: 99%

A non-parametric inference for implied volatility governed by a Lévy-driven Ornstein–Uhlenbeck process

Fard

Pourkhanali

Sy³

2018

Algorithmic Finance

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Abstract. We provide a non-parametric method for stochastic volatility modelling. Our method allows the implied volatility to be governed by a general Lévy-driven Ornstein-Uhlenbeck process, the density function of which is hidden to market participants. Using discrete-time observation we estimate the density function of the stochastic volatility process via developing a cumulant M-estimator for the Lévy measure. In contrast to other non-parametric estimators (such as kernel estimators), our estimator is guaranteed to be of the correct type. We implement this method with the aid of a support-reduction algorithm, which is an efficient iterative unconstrained optimisation method. For the empirical analysis, we use discretely observed data from two implied volatility indices, VIX and VDAX. We also present an out-of-sample test to compare the performance of our method with other parametric models.

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Stochastic lattice models for valuation of volatility options

Cited by 4 publications

References 22 publications

Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing

Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing

Pricing VIX options in a stochastic vol‐of‐vol model

A non-parametric inference for implied volatility governed by a Lévy-driven Ornstein–Uhlenbeck process

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