The Premium Reduction of European, American, and Perpetual Log Return Options
19 Pages Posted: 22 Oct 2019 Last revised: 5 Aug 2020
Date Written: October 12, 2019
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: Suggested Citation