Abstract
AbstractThe invariant approach is employed to solve the Cauchy problem for the bond-pricing partial differential equation (PDE) of mathematical finance. We first briefly review the invariant criteria for a scalar second-order parabolic PDE in two independent variables and then utilize it to reduce the bond-pricing equation to different Lie canonical forms. We show that the invariant approach aids in transforming the bond-pricing equation to the second Lie canonical form and that with a proper parametric selection, the bond-pricing PDE can be converted to the first Lie canonical form which is the classical heat equation. Different cases are deduced for which the original equation reduces to the first and second Lie canonical forms. For each of the cases, we work out the transformations which map the bond-pricing equation into the heat equation and also to the second Lie canonical form. We construct the fundamental solutions for the bond-pricing model via these transformations by utilizing the fundamental solutions of the classical heat equation as well as solution to the second Lie canonical form. Finally, the closed-form analytical solutions of the Cauchy initial value problems for the bond-pricing model with proper choice of terminal conditions are obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
