How much is your Strangle worth? On the relative value of the $\delta-$Symmetric Strangle under the Black-Scholes model

TL;DR

This paper introduces a new measure for evaluating the relative value of delta-Symmetric Strangles under the Black-Scholes model, providing a simple, delta-dependent benchmark that aids in assessing market value and optimizing exit strategies.

Contribution

It proposes a novel, delta-dependent measure of the relative value of delta-Symmetric Strangles, independent of other market parameters, and demonstrates its use as a quick benchmark and for optimizing exit strategies.

Findings

The measure is bounded by a simple function of delta only.

It is independent of time to expiry, underlying price, and volatility.

The measure facilitates quick market value assessment and optimal exit decisions.

Abstract

Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. In this paper we propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes 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 BS option pricing 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 {\it 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 $\delta-$strangle in comparison to its BS (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 {\it optimal} choice for a value of delta.