| 1. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility
- 2017
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Ingår i: INCPAA 2016 Proceedings. - : Author(s). - 9780735414648 ; , s. 020035-1-020035-10
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Konferensbidrag (refereegranskat)abstract
- After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes model was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced non-constant volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multi-factor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented an approximate formula for pricing American option.The huge calculation involved in the Chiarella and Ziveyi approach motivated us to investigate another approach to compute European option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present chapter we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.
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| 2. |
- Engström, Christopher, 1987-, et al.
(författare)
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Calculating PageRank in a changing network with added or removed edges
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020052-1-020052-8
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Konferensbidrag (refereegranskat)abstract
- PageRank was initially developed by S. Brinn and L. Page in 1998 to rank homepages on the Internet using the stationary distribution of a Markov chain created using the web graph. Due to the large size of the web graph and many other real worldnetworks fast methods to calculate PageRank is needed and even if the original way of calculating PageRank using a Power iterations is rather fast, many other approaches have been made to improve the speed further. In this paper we will consider the problem of recalculating PageRank of a changing network where the PageRank of a previous version of the network is known. In particular we will consider the special case of adding or removing edges to a single vertex in the graph or graph component
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| 3. |
- Guariglia, Emanuel, 1982-, et al.
(författare)
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A functional equation for the Riemann zeta fractional derivative
- 2017
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Ingår i: Proceedings of INCPAA 2016, 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020063-1-020063-10
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Konferensbidrag (refereegranskat)abstract
- In this paper a functional equation for the fractional derivative of the Riemann zeta function is presented. The fractional derivative of the zeta function is computed by a generalization of the Grunwald-Letnikov fractional operator, which satisfies the generalized Leibniz rule. It is applied to the asymmetric functional equation of the Rieman zeta function in order to obtain the result sought. Moreover, further properties of this fractional derivative are proposed and discussed.
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| 4. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases
- 2017
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Ingår i: AIP Conference Proceedings. - : American Institute of Physics (AIP). - 0094-243X. - 9780735414648 ; , s. 020094-1-020094-7
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Konferensbidrag (refereegranskat)abstract
- In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process.
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| 5. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020093-1-020093-10
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Konferensbidrag (refereegranskat)abstract
- A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning dischargecurrents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate itsnon-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents’ modelling is illustrated through anessential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape.
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| 6. |
- Metri, Prashant G, 1987-, et al.
(författare)
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Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020097-1-020097-10
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Konferensbidrag (refereegranskat)abstract
- In this paper, we examine the hydromagnetic boundary layer flow and heat transfer characteristics of a laminar nano liquid film over an unsteady stretching sheet is presented. The highly nonlinear partial dierential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric power series functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed analytically.
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| 7. |
- Metri, Prashant G, 1987-, et al.
(författare)
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Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020096-1-020096-10
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Konferensbidrag (refereegranskat)abstract
- An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two-dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow permeated by a uniform transverse magnetic field. The governing partial dierential equations are reduced to a system of ordinarydierential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations.The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary dierential equation corresponding to momentum equation and second order dierential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the eects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source/sink, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.
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| 8. |
- Narayana, Mahesha, et al.
(författare)
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Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet
- 2017
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Ingår i: Proceedings of ICNPAA 2016 world congress. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020109-1-020109-10
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Konferensbidrag (refereegranskat)abstract
- The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nano liquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nano liquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) – water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results which form special case of the present study are in excellent agreement with the results reported in the literature
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| 9. |
- Ni, Ying, 1976-, et al.
(författare)
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Approximation Methods of European Option Pricing in Multiscale Stochastic Volatility Model
- 2017
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Ingår i: INCPAA 2016 Proceedings. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020112-1-020112-10
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Konferensbidrag (refereegranskat)abstract
- In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model , in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown by Christoffersen, Heston and Jacobs. We consider one specific type of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this chapter is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi using method of characteristics, Fourier and bivariate Laplace transforms.
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| 10. |
- Qi, Xiaomin, 1987-, et al.
(författare)
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Data classification with support vector machine and generalized support vector machine
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : Author(s). - 9780735414648 ; , s. 020126-1-020126-9
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Konferensbidrag (refereegranskat)abstract
- In the paper, we study the theory of support vector machine and the using for linear and nonlinear classification of data. And we also used the notion of generalized support vector machine for data classifications. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions.
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