A Terminal Condition in Linear Bond-pricing Under Symmetry Invariance

被引：0
作者：
Rivoningo Maphanga
Sameerah Jamal
机构：
[1] University of the Witwatersrand,School of Mathematics
来源：
Journal of Nonlinear Mathematical Physics | 2023年 / 30卷
关键词：
Bond-pricing; Lie symmetries; Heat equation; Boundary conditions; 35K05; 35K15; 37C79;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we examine a general bond-pricing model with respect to its solutions that satisfy a given terminal condition. Firstly, we obtain reversible transformations that change the model to a classical and well known partial differential equation, the one dimensional heat equation. We further show that the terminal condition is transformed into a nonsmooth initial condition. The important result that emerges is that the Lie symmetries are adopted to solve the equation subject to its unique configuration of initial conditions.
引用
收藏
页码：1295 / 1304
页数：9
相关论文
共 40 条
[1]  
Bachelier L(1900)Theorie de la speculation Ann. Scient. de l’Ecole Normale Superieure. 3 21-86
[2]  
Merton RC(1971)Optimum consumption and portfolio rules in a continuous time model J. Econ. Thr. 3 373-413
[3]  
Black F(1973)The pricing of options and corporate liabilities J. Political Econ. 81 637-654
[4]  
Scholes M(1977)An equilibrium characterization of the term structure J. Finan. Econ. 5 177-188
[5]  
Vasicek O(1978)On the term structure of interest rates J. Finan. Econ. 6 59-69
[6]  
Dothan L(1985)An intertemporal general equilibrium model of asset prices Econometrica 53 363-384
[7]  
Cox JC(1980)Analyzing convertible bonds J. Finan. Quant. Anal. 15 907-929
[8]  
Ingersoll JE(2018)Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance Open Phys. 16 766-779
[9]  
Ross SA(1998)Lie symmetry analysis of differential equations in finance Nonlinear Dyn. 17 387-407
[10]  
Brennan MJ(2018)Exact solutions via invariant approach for Black-Scholes model with time-dependent parameters Math. Methods Appl. Sci. 41 4417-4427
1234