A hybrid option pricing model using a neural network for estimating volatility

The Black–Scholes (BS) model is the standard approach used for pricing financial options. However, although being theoretically strong, option prices valued by the model often differ from the prices observed in the financial markets. This paper applies a hybrid neural network which preprocesses financial input data for improving the estimation of option market prices. This model is comprised of two parts. The first part is a neural network developed to estimate volatility. The second part is an additional neural network developed to value the difference between the BS model results and the actual market option prices. The resulting option price is then a summation between the BS model and the network response. The hybrid system with a neural network for estimating volatility provides better performance in terms of pricing accuracy than either the BS model with historical volatility (HV), or the BS model with volatility valued by the neural network.     

A software architecture framework for on-line option pricing

The problem of growing computational complexity in the finance industry demands manageable, high-speed and real-time solutions in solving complex mathematical problems such as option pricing. In current option trading scenarios, determining a fair price for options “any time” and “anywhere” has become vital yet difficult computational problem. In this study, we have designed, implemented, and deployed an architecture for pricing options on-line using a hand-held device that is J2ME-based Mobile computing-enabled and is assisted by web mining tools. In our architecture, the client is a MIDP user interface, and the back end servlet runs on a standalone server bound to a known port address. In addition, the server uses table-mining techniques to mine real-time data from reliable web sources upon the mobile trader’s directive. The server performs all computations required for pricing options since mobile devices have limited battery power, low bandwidth, and low memory. We have parallelized and implemented various computational techniques such as binomial lattice and finite differencing. To the best of our knowledge, this is one of the first studies that facilitate the mobile-enabled-trader to compute the price of an option in ubiquitous fashion. This architecture aims at providing the trader with various computational techniques to avail (to provide results from approximate to accurate results) while on-the-go and to make important and effective trading decisions using the results that will ensure higher returns on investments in options.

一类非线性LC电路的分析与模拟

给出一类非线性LC电路的状态分析和数值模拟：将电容的电荷表示为相位角的简谐函数,电路的响应频率表示为相位角关于时间的变化率;以电路的响应频率为未知函数,对状态方程进行近似求解;算出时间随相位角变化的近似关系式;给出电路的相图、电容的电荷以及电感的磁通链随时间变化关系式及数值模拟,结果与数值积分法吻合良好。     

Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model

In this paper, we discuss the numerical analysis and the pricing and hedging of European Spread options on correlated assets when, in contrast to the standard framework and consistent with a market with imperfect liquidity, the option trader's trading in the stock market has a direct impact on one of the stocks price. We consider a first-order feedback model which leads to a linear partial differential equation. The Peaceman–Rachford scheme is applied as an alternating direction implicit method to solve the equation numerically. We also discuss the stability and convergence of this numerical scheme. Finally, we provide a numerical analysis of the effect of the illiquidity in the underlying asset market on the replication of an European Spread option; compared to the Black–Scholes case, a trader generally buys less stock to replicate a call option.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

Modeling nonlinear waves in a numerical wave tank with localized meshless RBF method

This paper presents the numerical simulation of free surface waves in a 2D domain which represents a wave tank, using a localized approach of the meshless radial basis function (RBF) method. Instead of global collocation, the local approach breaks down the problem domain into subdomains, leading to a sparse global system matrix which is particularly advantageous in tackling the time consuming simulation process. Mixed Eulerian–Lagrangian approach is adopted for free surface tracking and fourth order Adams–Bashforth–Moulton scheme (ABM4) is used for time stepping. Both linear and nonlinear Stokes waves are simulated and compared to analytical solutions.     

A class of nonlinear stochastic volatility models and its implications for pricing currency options

A class of stochastic volatility (SV) models is proposed by applying the Box-Cox transformation to the volatility equation. This class of nonlinear SV (N-SV) models encompasses all standard SV models, including the well-known lognormal (LN) SV model. It allows to empirically compare and test all standard specifications in a very convenient way and provides a measure of the degree of departure from the classical models. A likelihood-based technique is developed for analyzing the model. Daily dollar/pound exchange rate data provide some evidence against LN model and strong evidence against all the other classical specifications. An efficient algorithm is proposed to study the economic importance of the proposed model on pricing currency options.     

A new adaptive scheme for a class of discrete-time nonlinear systems

A new adaptive control scheme for discrete-time systems is proposed. The objective is the tracking of the trajectory. Global boundedness convergence and boundedness are obtained for a certain subclass of nonlinear systems.     

A stochastic approximation algorithm for option pricing model calibration with a switchable market

This paper is concerned with option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, finite-state Markov chain. At any given instance, the price follows either a geometric Brownian motion model or a mean-reversion model, depending on its market mode. Stochastic approximation/optimization algorithms are developed for model calibration. Convergence of the algorithm is proved; rate of convergence is also provided. Option market data are used to predict the future market mode.     

NICE—An explicit numerical scheme for efficient integration of nonlinear constitutive equations

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for the integration of a system of algebraic and differential equations in general, the scheme is primarily developed for use with the direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed explicit scheme, where no iteration is required, the implementation simplicity of the forward-Euler scheme and the accuracy of the backward-Euler scheme are successfully combined. The properties of the proposed NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, are compared with the properties of the classical forward-Euler scheme and backward-Euler scheme. For this purpose two highly nonlinear examples, with the von Mises and GTN material model considered, have been studied. The accuracy of the new scheme is demonstrated to be at least of the same level as experienced by the backward-Euler scheme, if we compare them on the condition of the same CPU time consumption. Besides, the simplicity of the NICE scheme, which is due to implementation similarity with the classical forward-Euler scheme, is its great Advantage.     

On the numerical solution of initial value problems for nonlinear trapezoidal formulas with different types

In this paper, the local truncation errors of the trapezoidal formulas such as arithmetic mean (AM), geometric mean (GM), heronian mean (HeM), harmonic mean (HaM), contraharmonic mean (CoM), root mean square (RMS), logarithmic mean (LM) and centroidal mean (CeM) are investigated and the stability analysis of these formulas are found. Finally, it is applied to various initial value problems.     

A viral infection model with periodic immune response and nonlinear CTL response

This paper investigates a viral infection model with periodic immune response and nonlinear cytotoxic T lymphocyte (CTL) response. Using the periodic rhythms of human immune system, the model can avoid the unreasonable equilibrium in the basic viral model with nonlinear CTL response introduced by Nowak et al. We obtain the global stability of the infection-free equilibrium and the immune-exhausted equilibrium. Numerical simulations show that the oscillation of immune system can affect the pattern of the viral dynamical behaviors. Period doubling bifurcations of the system are observed via simulations. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV and HCV infection patients.     

A novel scheme for large deflection analysis of suspended cables made of linear or nonlinear elastic materials

This paper presents a new approach to investigate the static response of horizontal and inclined suspended cables with deformable cross-section, made of general linear or nonlinear elastic materials, and subjected to vertical concentrated and distributed loads. The proposed technique also includes large sag and extensibility effects, and is based on an original finite difference scheme combined to a nonlinear least squares numerical solution. The mathematical formulation is developed for various loading cases, and an innovative computational strategy is used to transform the resulting nonlinear system of equations into a scaled nonlinear least squares problem. The numerical scheme is programmed and its application illustrated through examples highlighting the effects of coupling between the tension in a cable and the deformation of its cross-section as well as the use of cables made of neo-Hookean materials. The results obtained are in excellent agreement with analytical solutions when available. The proposed technique can be easily programmed and constitutes a valuable tool for large deflection analysis of suspended cables made of nonlinear elastic materials.     

A second-order explicit scheme for the numerical solution of a fox-rabies model

A second-order, unconditionally-stable, finite-difference scheme is developed for the numerical solution of the SI model of fox-rabies dynamics. The local stability of the scheme, by direct inspection of the eigenvalues dependent on the time step size and on two parameters, is shown to be unconditionally stable.     

A numerical algorithm for avascular tumor growth model

Avascular tumor growth model for multicellular spheroids is considered. The model is a moving boundary problem and consists of three types of cells. The governing equations are nonlinear hyperbolic and/or parabolic differential equations. Comparisons of the numerical solutions with the solution of the recent studies are done. The effect of the necrotic region on the tumor growth is discussed.     

Numerical study of an evolutive model for magnetostrictive materials

A finite difference approximation method for the numerical study of the evolution equations for magnetoelastic materials is proposed and results concerning the numerical stability are established. Experiments on a specific test problem are carried out mainly to investigate on some evolutive phenomena such as the development and propagation of singular solutions.     

一类非线性系统的直接自适应控制器

针对带一类非线性参数系统的状态反馈自适应跟踪控制问题,通过设计一种新的李亚普诺夫函数--加权控制李亚普诺夫函数,由它作用于控制器和参数调整律,使之达到全局渐近跟踪从而满足控制指标。     

A recursive,numerically stable,and efficient simulation algorithm for serial robots

Traditionally, the dynamic model, i.e., the equations of motion, of a robotic system is derived from Euler–Lagrange (EL) or Newton–Euler (NE) equations. The EL equations begin with a set of generally independent generalized coordinates, whereas the NE equations are based on the Cartesian coordinates. The NE equations consider various forces and moments on the free body diagram of each link of the robotic system at hand, and, hence, require the calculation of the constrained forces and moments that eventually do not participate in the motion of the coupled system. Hence, the principle of elimination of constraint forces has been proposed in the literature. One such methodology is based on the Decoupled Natural Orthogonal Complement (DeNOC) matrices, reported elsewhere. It is shown in this paper that one can also begin with the EL equations of motion based on the kinetic and potential energies of the system, and use the DeNOC matrices to obtain the independent equations of motion. The advantage of the proposed approach is that a computationally more efficient forward dynamics algorithm for the serial robots having slender rods is obtained, which is numerically stable. The typical six-degree-of-freedom PUMA robot is considered here to illustrate the advantages of the proposed algorithm.     

On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input–output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tomlin and Sastry (Systems Control Lett. 35(3) (1998) 145) is applicable for a wider class of nonlinear systems.     

A computationally attractive nonlinear predictive control scheme with guaranteed stability for stable systems

We introduce in this paper a nonlinear model predictive control scheme for open-loop stable systems subject to input and state constraints. Closed-loop stability is guaranteed by an appropriate choice of the finite prediction horizon, independent of the specification of the desired control performance. In addition, this control scheme is likely to allow ‘real time’ implementation, because of its computational attractiveness. The theoretical results are demonstrated and discussed with a CSTR control application.