Abstract
In the present report, a review of discrete calculus on directed graphs is presented. It is found that the binary tree is a special directed graph that contains both the exterior calculus and stochastic calculus as different continuum limits are taken. In the latter case, we arrive at something that may be referred to as “discrete stochastic calculus.” The resulting discrete stochastic calculus may be applied to any stochastic financial model and is guaranteed to produce results that converge in the continuum limit. Discrete stochastic calculus is applied to the Black-Scholes model for an illustration. The resulting algorithm generated by discrete stochastic calculus agrees with that of the Cox-Ross-Rubinstein model, as it should. The results presented here are preliminary and are intended to encourage others to learn discrete stochastic calculus and apply it to more complicated financial models.
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.
