The Premium Reduction of European, American, and Perpetual Log Return Options

16 Pages Posted: 22 Oct 2019

See all articles by Stephen Michael Taylor

Stephen Michael Taylor

New Jersey Institute of Technology

Jan Vecer

Charles University in Prague - Faculty of Mathematics and Physics

Date Written: October 12, 2019

Abstract

Traditional plain vanilla options can be regarded as options on a simple return. These options have convex payoffs and as a consequence of Jensen’s inequality, their prices are increasing as a function of maturity in the absence of interest rate. This makes long dated call options as excessively expensive in relationship to the fraction of the insured portfolio. We show that replacing a simple return payoff with the log return call option payoff leads to substantial savings while providing the same protection type. The call options on log return have a favorable price for very long maturities in the scale of decades, making them attractive for long term investment funds, such as pension funds.

Keywords: Long Term Portfolio Protection, Option Pricing, Hedging

JEL Classification: G12, G13, G22

Suggested Citation

Taylor, Stephen Michael and Vecer, Jan, The Premium Reduction of European, American, and Perpetual Log Return Options (October 12, 2019). Available at SSRN: https://ssrn.com/abstract=3467150 or http://dx.doi.org/10.2139/ssrn.3467150

Stephen Michael Taylor (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

Jan Vecer

Charles University in Prague - Faculty of Mathematics and Physics ( email )

Sokolovska 83
Prague, 186 75
Czech Republic

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