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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Optimal Exercise Price Of American Options Near Expiry, W.-T. Chen, Song-Ping Zhu
Optimal Exercise Price Of American Options Near Expiry, W.-T. Chen, Song-Ping Zhu
Professor Song-Ping Zhu
This paper investigates American puts on a dividend-paying underlying whose volatility is a function of both time and underlying asset price. The asymptotic behaviour of the critical price near expiry is deduced by means of singular perturbation methods. It turns out that if the underlying dividend is greater than the risk-free interest rate, the behaviour of the critical price is parabolic, otherwise an extra logarithmic factor appears, which is similar to the constant volatility case. The results of this paper complement numerical approaches used to calculate the option values and the optimal exercise price at times that are not close …
A Spectral-Collocation Method For Pricing Perpetual American Puts With Stochastic Volatility, Song-Ping Zhu, Wenting Chen
A Spectral-Collocation Method For Pricing Perpetual American Puts With Stochastic Volatility, Song-Ping Zhu, Wenting Chen
Professor Song-Ping Zhu
Based on the Legendre pseudospectral method, we propose a numerical treatment for pricing perpetual American put option with stochastic volatility. In this simple approach, a nonlinear algebraic equation system is first derived, and then solved by the Gauss–Newton algorithm. The convergence of the current scheme is ensured by constructing a test example similar to the original problem, and comparing the numerical option prices with those produced by the classical Projected SOR (PSOR) method. The results of our numerical experiments suggest that the proposed scheme is both accurate and efficient, since the spectral accuracy can be easily achieved within a small …
Diffraction Of Ocean Waves Around A Hollow Cylindrical Shell Structure, Song-Ping Zhu, Lewis Mitchell
Diffraction Of Ocean Waves Around A Hollow Cylindrical Shell Structure, Song-Ping Zhu, Lewis Mitchell
Professor Song-Ping Zhu
In recent years, there has been renewed interest in problems of diffraction and radiation of ocean waves around structures, in relation to “green” power generation by Oscillating Water Column (OWC) devices. In this paper we present a first-order analytical solution for the diffraction of ocean waves around a hollow cylindrical shell structure suspended in an ocean of finite depth. By revisiting work done by Garrett (1970) on the problem of a bottomless harbor, but adopting a different and more direct method, we obtain the solution for the diffracted wave potential. Using the new approach, we analyze the dependence of the …
Selective Withdrawal From Stratified Streams, Chia-Shun Yih, Song-Ping Zhu
Selective Withdrawal From Stratified Streams, Chia-Shun Yih, Song-Ping Zhu
Professor Song-Ping Zhu
Selective withdrawal from a stratified stream is considered. The average density of the withdrawn fluid and the flow pattern are found, within the limitations on the densimetric Froude number and the withdrawal rate specified in this paper, to depend on the strength and location of the sink, and very little on any slight variation in the velocity distribution far upstream and the densimetric Froude number. The upstream density distribution is assumed linear, but many other density distributions can be similarly treated.
A Closed-Form Exact Solution For The Value Of American Put And Its Optimal Exercise Boundary, Song-Ping Zhu
A Closed-Form Exact Solution For The Value Of American Put And Its Optimal Exercise Boundary, Song-Ping Zhu
Professor Song-Ping Zhu
Searching for a closed-form exact solution for American put options under the Black-Scholes framework has been a long standing problem in the past; many researchers believe that it is impossible to find such a solution. In this paper, a closed-form exact solution, in the form of a Taylor's series expansion, of the well-known Black-Scholes equation is presented for the first time. As a result of this analytic solution, the optimal exercise boundary, which is the main difficulty of the problem, is found as an explicit function of the risk-free interest rate, the volatility and the time to expiration.
A Numerical Model For Multiphase Flow Based On The Gmpps Formulation, Part I Kinematics, Song-Ping Zhu, Frank Bierbrauer
A Numerical Model For Multiphase Flow Based On The Gmpps Formulation, Part I Kinematics, Song-Ping Zhu, Frank Bierbrauer
Professor Song-Ping Zhu
The CFD modeling of two dimensional multiphase ows is a useful tool in industry, although accurate modeling itself remains a difficult task. One of the difficulties is to track the complicated topological deformations of the interfaces between di erent phases. This paper describes a marker-particle method designed to track fluid interfaces for fluid ows of at least three phases. The interface-tracking scheme presented in this paper is the first part of a series of papers presenting our complete model based on a one-field Godunov marker-particle projection scheme (GMPPS). In this part, we shall focus on the presentation of the interface-tracking …
Simulating Ultrasonic Sensing With The Lattice Gas Model, Phillip J. Mckerrow, S. M. Zhu, S. New
Simulating Ultrasonic Sensing With The Lattice Gas Model, Phillip J. Mckerrow, S. M. Zhu, S. New
Professor Song-Ping Zhu
People have difficulty understanding ultrasonic sensing because they cannot see sound. The purpose of simulation is to overcome this problem by visualizing the scattering of ultrasonic waves off objects. The lattice gas model calculates wave behavior with finite difference equations to produce data suitable for grayscale visualization. This visualization is useful when designing ultrasonic sensing systems for navigating mobile robots. Situations that result in the sensor failing to detect an object can be studied with the simulator.
Pricing Convertible Bonds Based On A Multi-Stage Compound Option Model, P. Gong, Z. He, Song-Ping Zhu
Pricing Convertible Bonds Based On A Multi-Stage Compound Option Model, P. Gong, Z. He, Song-Ping Zhu
Professor Song-Ping Zhu
In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds. Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the Finite Difference Method (FDM) to solve the Black-Scholes equation for each stage actually resulted in a better numerical efficiency. By comparing our results with those obtained by solving the Black-Scholes equation directly, we can show that the new approach does provide an approximation approach for the valuation of convertible bonds and demonstrate that it offers a great potential for a further …
A Closed-Form Analytical Solution For The Valuation Of Convertible Bonds With Constant Dividend Yield, Song-Ping Zhu
A Closed-Form Analytical Solution For The Valuation Of Convertible Bonds With Constant Dividend Yield, Song-Ping Zhu
Professor Song-Ping Zhu
In this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented. To the au- thor’s best knowledge, never has a closed-form analytical formula been found for American-style convertible bonds (CBs) of finite maturity time although there have been quite a few approximate solutions and numerical approaches proposed. The solution presented here is written in the form of a Taylor’s series expansion, which 1 contains infinitely many terms, and thus is completely analytical and in a closed form. Although it is only for simplest CBs without call or put features, …
A Third-Order Boussinesq Model Applied To Nonlinear Evolution Of Shallow-Water Waves, Y. L. Zhang, Song-Ping Zhu
A Third-Order Boussinesq Model Applied To Nonlinear Evolution Of Shallow-Water Waves, Y. L. Zhang, Song-Ping Zhu
Professor Song-Ping Zhu
The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin's (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin's experimental data is found.
A Closed-Form Analytical Solution For The Valuation Of Convertible Bonds With Constant Dividend Yield, Song-Ping Zhu
A Closed-Form Analytical Solution For The Valuation Of Convertible Bonds With Constant Dividend Yield, Song-Ping Zhu
Professor Song-Ping Zhu
In this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented. To the au- thor’s best knowledge, never has a closed-form analytical formula been found for American-style convertible bonds (CBs) of finite maturity time although there have been quite a few approximate solutions and numerical approaches proposed. The solution presented here is written in the form of a Taylor’s series expansion, which 1 contains infinitely many terms, and thus is completely analytical and in a closed form. Although it is only for simplest CBs without call or put features, …
Pricing Convertible Bonds Based On A Multi-Stage Compound Option Model, P. Gong, Z. He, Song-Ping Zhu
Pricing Convertible Bonds Based On A Multi-Stage Compound Option Model, P. Gong, Z. He, Song-Ping Zhu
Professor Song-Ping Zhu
In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds. Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the Finite Difference Method (FDM) to solve the Black-Scholes equation for each stage actually resulted in a better numerical efficiency. By comparing our results with those obtained by solving the Black-Scholes equation directly, we can show that the new approach does provide an approximation approach for the valuation of convertible bonds and demonstrate that it offers a great potential for a further …
A Flat Ship Theory On Bow And Stern Flows, Song-Ping Zhu, Y. L. Zhang
A Flat Ship Theory On Bow And Stern Flows, Song-Ping Zhu, Y. L. Zhang
Professor Song-Ping Zhu
An analytical solution of a two dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell’s thin ship theory and leads to a mixed initial boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener Hopf technique and closed form farfield results are obtained for an arbitrary hull shape. Apart …