Break-Even Volatility

Abstract

A profit or loss (P&L) of a dynamically hedged option depends on the implied volatility used to price the option and implement the hedges. Break-even volatility is a method of solving for the volatility which yields no profit or loss based on replicating the hedging procedure of an option on a historical share price time series. This dissertation investigates the traditional break-even volatility method on simulated data, how the break-even formula is derived and details the implementation with reference to MATLAB. We extend the methodology to the Heston model by changing the reference model in the hedging process. Resultantly, the need to employ characteristic function pricing methods arises to calculate the Heston model sensitivities. The break-even volatility solution is then found by means of an optimisation of the continuously delta hedged P&L over the Heston model parameters.