A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds

42 Pages Posted: 18 Aug 2016

See all articles by Alessandro Gnoatto

Alessandro Gnoatto

University of Verona - Department of Economics

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: August 16, 2016

Abstract

This paper introduces a more general modeling world than available under the classical no-arbitrage paradigm in finance. New research questions and interesting related econometric studies emerge naturally. To explain in this paper the new approach and illustrate first important consequences, we show how to hedge a zero coupon bond with a smaller amount of initial capital than required by the classical risk neutral paradigm, whose (trivial) hedging strategy does not suggest to invest in the risky assets. Long dated zero coupon bonds we derive, invest first primarily in risky securities and when approaching more and more the maturity date they increase also more and more the fraction invested in fixed income. The conventional wisdom of financial planners suggesting investor to invest in risky securities when they are young and mostly in fixed income when they approach retirement, is here made rigorous. The main reason for the existence of less expensive zero coupon bonds is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. We provide intuition and insight on the strict supermartingale property. The less expensive zero coupon bonds provide only one first example that is indicative for the changes that the new approach offers in the much wider modeling world. The paper provides a strong warning for life insurers, pension fund managers and long term investors to take the possibility of less expensive products seriously to avoid the adverse consequences of the low interest rate regimes that many developed economies face.

Keywords: Forex, benchmark approach, benchmarked risk minimization, stochastic volatility, long term securities

JEL Classification: C6, C63, G1, G12, G13

Suggested Citation

Gnoatto, Alessandro and Grasselli, Martino and Platen, Eckhard, A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds (August 16, 2016). Available at SSRN: https://ssrn.com/abstract=2824564 or http://dx.doi.org/10.2139/ssrn.2824564

Alessandro Gnoatto

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Register to save articles to
your library

Register

Paper statistics

Downloads
50
Abstract Views
358
PlumX Metrics