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Full-Text Articles in Physical Sciences and Mathematics
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 …