Mirror Options

Abstract

In this work we present a new family of options (mirror options) specially crafted to satisfy the necessities of aggressive speculators. The main ideas behind mirror options are: 1) A product that can be adjusted by the holder to agree with his/her market view at any time during its life. 2) The holder's right to make an arbitrary number of those adjustments without penalizing costs. After defining mirror options as `super-versions' of standard options we derive general formulae for their value in the case where the payoff is a monotonic function of the underlying (which is the case in calls, puts, futures, spreads etc.). We briefly discuss also their valuation for general payoffs and the American case. Finally we analyze the situation where the number of allowed adjustments is restricted and we point out directions for further developments.