How Much Is Your Strangle Worth? On the Relative Value of the Strangle under the Black-Scholes Pricing Model

Abstract

Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. We propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes-Merton option pricing model. This new measure accounts for the price of the strangle, relative to the Present Value of the spread between the two strikes, all expressed, after a natural re-parameterization, in terms of delta and a volatility parameter. We show that under the standard BSM model, this measure of relative value is bounded by a simple function of delta only and is independent of the time to expiry, the price of the underlying security or the prevailing volatility used in the pricing model. We demonstrate how this bound can be used as a quick benchmark to assess, regardless the market volatility, the duration of the contract or the price of the underlying security, the market (relative) value of the strangle in comparison to its BSM (relative) price. In fact, the explicit and simple expression for this measure and bound allows us to also study in detail the strangle’s exit strategy and the corresponding optimal choice for a value of delta.