Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

Mariani, Maria C.; Sengupta, Indranil; Bezdek, Pavel

doi:10.1007/s10440-012-9685-3

Cited by 15 publications

(6 citation statements)

References 15 publications

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“…) can be used in the literature of finance for the jump-diffusion models [29,30]. Observe that , ≺, , are all binary relations on the collection of vertices V(G).…”

Section: Remark 2 To Define DI F F Usion Degree Sequences D σ (Hmentioning

confidence: 99%

Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

et al. 2019

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This paper puts forward an innovative theory and method to calculate the canonical labelings of graphs that are distinct to N a u t y ’s. It shows the correlation between the canonical labeling of a graph and the canonical labeling of its complement graph. It regularly examines the link between computing the canonical labeling of a graph and the canonical labeling of its o p e n k-n e i g h b o r h o o d s u b g r a p h. It defines d i f f u s i o n d e g r e e s e q u e n c e s and e n t i r e d i f f u s i o n d e g r e e s e q u e n c e. For each node of a graph G, it designs a characteristic m _ N e a r e s t N o d e to improve the precision for calculating canonical labeling. Two theorems established here display how to compute the first nodes of M a x Q ( G ) . Another theorem presents how to determine the second nodes of M a x Q ( G ) . When computing C m a x ( G ) , if M a x Q ( G ) already holds the first i nodes u 1 , u 2 , ⋯ , u i , Diffusion and Nearest Node theorems provide skill on how to pick the succeeding node of M a x Q ( G ) . Further, it also establishes two theorems to determine the C m a x ( G ) of disconnected graphs. Four algorithms implemented here demonstrate how to compute M a x Q ( G ) of a graph. From the results of the software experiment, the accuracy of our algorithms is preliminarily confirmed. Our method can be employed to mine the frequent subgraph. We also conjecture that if there is a node v ∈ S ( G ) meeting conditions C m a x ( G - v ) ⩽ C m a x ( G - w ) for each w ∈ S ( G ) ∧ w ≠ v , then u 1 = v for M a x Q ( G ) .

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“…) can be used in the literature of finance for the jump-diffusion models [29,30]. Observe that , ≺, , are all binary relations on the collection of vertices V(G).…”

Section: Remark 2 To Define DI F F Usion Degree Sequences D σ (Hmentioning

confidence: 99%

Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

et al. 2019

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“…Now we are going to change the representation for C, the value of the option, in such a way that we can utilize "Heat Equation" section. That is, we will have a radial part in the initial condition (14). The most obvious generalization for the final condition for the European option with n-stocks can be formulated as…”

Section: Black-scholes Equationmentioning

confidence: 99%

Spherical Harmonics Applied to Differential and Integro-Differential Equations Arising in Mathematical Finance

Sengupta

Mariani

2012

Differ Equ Dyn Syst

Self Cite

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This paper is devoted to extend the spherical harmonics technique to the solution of parabolic differential equations and to integro-differential equations. The heat equation and the Black-Scholes equation are solved by using the method of spherical harmonics. We also discuss the Black-Scholes equation in annular domains, and generalized Black-Scholes equations. Finally we solve some integro-differential equation arising in financial models with jumps by using the method of spherical harmonics.

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“…We cite the recent paper by Mariani et al [12], where the authors proposed a numerical approximation scheme for European option prices in stochastic volatility models including transaction costs based on a finite-difference method.…”

Section: Introductionmentioning

confidence: 99%

American option valuation in a stochastic volatility model with transaction costs

2015

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In the present paper we analyse the American option valuation problem in a stochastic volatility model when transaction costs are taken into account. We shall show that it can be formulated as a singular stochastic optimal control problem, proving the existence and uniqueness of the viscosity solution for the associated Hamilton-Jacobi-Bellman partial differential equation. Moreover, after performing a dimensionality reduction through a suitable choice of the utility function, we shall provide a numerical example illustrating how American options prices can be computed in the present modelling framework

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Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

Cited by 15 publications

References 15 publications

Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

Spherical Harmonics Applied to Differential and Integro-Differential Equations Arising in Mathematical Finance

American option valuation in a stochastic volatility model with transaction costs

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