Excursions in the Martingale Hypothesis

Paolo Guasoni
Additional contact information
Paolo Guasoni: Boston University, Dept. of Mathematics and Statistics, 111 Cummington St., Boston, MA 02215, USA and University of Pisa, Dipartimento di Matematica, Via Buonarroti, 2, 56127 Pisa, Italy

Chapter 4 in Stochastic Processes and Applications to Mathematical Finance, 2004, pp 73-95 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe introduce a methodology for testing the martingale-hypothesis from time-series observations of a continuous asset process. Fixing the risk premium, the tests considered return the significance level at which a sample path belongs to a continuous martingale. Conversely, if the martingale hypothesis is assumed, we obtain the significance level of the particular risk premium. Using a time-change technique, we present tests which are independent of the continuous process driving the price process. This means that results are robust to any form of heteroskedasticity in asset returns. We show that the power against mean-reverting alternatives is higher than that of variance-ratio tests, at least for levels below 20%. We address estimation issues from discretely sampled data, and apply the tests to US stock indices. We conclude that for the S&P 500 index, the martingale hypothesis cannot be rejected at 15% level for a range of equity premia between 3.3% and 6.5%.

Keywords: Stochastic Processes; Stochastic Differential Equations; Malliavin Calculus; Stochastic Control and Optimization; Functionals of Brownian Motions and Lévy Processes; Stochastic Models of Financial Market; Derivative Pricing; Hedging Problem (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789812702852_0004 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789812702852_0004 (text/html)
Ebook Access is available upon purchase.

Related works:
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:9789812702852_0004

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 ().