Incorporating Views on Market Dynamics in Options Hedging

TL;DR

This paper develops a method to incorporate market movement views into options hedging by adjusting the hedge ratio over a fixed holding period, accounting for market dynamics and implied volatility changes.

Contribution

It introduces an analytical adjustment to the standard delta hedge to include market views and volatility dynamics during the holding period.

Findings

Derived an analytical expression for adjusted hedge ratio.

Numerical results demonstrate the effectiveness of the approach.

Abstract

We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we explore whether it is possible to adjust the number of shares needed to effectively hedge our position to account for views on market dynamics from present until the end of our interval, to account for the time-dependence of the options' sensitivity to the underlying. We derive an analytical expression for the number of shares needed by adjusting the standard Black-Scholes-Merton $\Delta$ quantity, in the case of an arbitrary process for implied volatility, and we present numerical results.