WHEN IS TIME CONTINUOUS?

Dimitris Bertsimas, Leonid Kogan and Andrew Lo ()
Additional contact information
Dimitris Bertsimas: Sloan School of Management, E40-147, Massachusetts Institute of Technology, Cambridge, MA 02139, United States

Chapter 3 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 71-102 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractContinuous-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 granularity 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.

Date: 2001
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789812810663_0003 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789812810663_0003 (text/html)
Ebook Access is available upon purchase.

Related works:
Journal Article: When is time continuous? (2000)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:wschap:9789812810663_0003

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().