On volatility of prices in arbitrage-free markets

Ayman Hindy
Additional contact information
Ayman Hindy: Graduate School of Business, Stanford University, Stanford, CA 94305, USA

Economic Theory, 1995, vol. 6, issue 3, 438 pages

Abstract: This paper addresses the question of what one can learn about the dynamics of an economy from observing cross-sectional and time series variations in the volatility of prices in an arbitrage-free securities market. We introduce the notions of stochastic derivatives, marginal risk-adjusted growth rates, and marginal risk exposure in a single factor economy. We show that future variations in the state of the economy are due to two independent sources: the marginal risk-adjusted growth rate and the changes in marginal risk exposure. Using the martingale characterization of arbitrage-free prices, together with a martingale representation formula due to Haussmann (1978), we show that cross sectional variations in price volatility of assets with linear payoffs can be used to identify the sum of these two sources. Measurements of price volatility for assets with linear payoffs are not sufficient for complete identification of the independent determinants of possible future variations in the economy. However, using the volatility of prices of options on the state variable, we can identify the stochastic derivative and hence compute the price volatility of any path independent contingent claim.

Date: 1997-11-09
Note: Received: February 8, 1993; revised version April 14, 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:joecth:v:6:y:1995:i:3:p:421-438

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/199/PS2

Access Statistics for this article

Economic Theory is currently edited by Nichoals Yanneils

More articles in Economic Theory from Springer, Society for the Advancement of Economic Theory (SAET) Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().