Abstract
Continuous-time stochastic processes have become central to many disciplines, yet the fact that they are approximations to physically realizable phenomena is often overlooked. We quantify one aspect of the approximation errors of continuous-time models by investigating the replication errors that arise from delta hedging derivative securities in discrete time. We characterize the asymptotic distribution of these replication errors and their joint distribution with other assets as the number of discrete time periods increases. We introduce the notion of temporal for continuous-time stochastic processes, which allows us to quantify the extent to which discrete-time implementations of continuous-time models can track the payoff of a derivative security. We show that granularity is a function of the contract specifications of the derivative security, and of the degree of market completeness. We derive closed form expressions for the granularity of geometric Brownian motion and of an Ornstein-Uhlenbeck process for call and put options, and perform Monte Carlo simulations that illustrate the practical relevance of granularity.
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.
