Valuation of Perpetual Strangles: A Quasi-Analytical Approach

Abstract

A strangle is the simultaneous purchase of an out-of-the-money call and an out-of-the-money put with the same expiration dates. If the options are both European, only one can be in the money at expiration, and the strangle is valued simply as the sum of the call and the put. An American call on a non-dividend-paying stock should not be exercised before maturity, so as maturity extends to infinity, the call value asymptotically approaches the value of the underlying stock. An infinitely lived European put should have zero value, but a perpetual American put can and should be exercised early. In practice, however, a perpetual strangle contract is not just the sum of a perpetual American call and put, because it entails the restriction that exercise of one of the options cancels the other. This obviously reduces the strangle value and makes the early exercise decision of some interest. In this article, Chuang develops a quasi-analytical approach for pricing a perpetual strangle based on the properties of the perpetual case’s early exercise frontier.