ELS pricing and hedging in a fractional Brownian motion environment

An equity-linked security (ELS) is a debt instrument with several payments and maturities linked to equity markets. This paper is a study of the pricing and hedging of the ELS when the underlying asset price moves in a geometric fractional Brownian motion environment. We develop two different methods for calibrating fractional implied volatility, obtain an empirical result on the Hurst exponent, and introduce a new Greek called Eta to find the sensitivity of the ELS price to the Hurst parameter. We propose three Delta hedging strategies and compare them with each other and the classical Black-Scholes Delta hedging strategy. Their performance is shown to depend on market circumstance (bull or bear). Our results with constant volatility and Hurst exponent provide a building basis for more stable hedging strategies in the non-Markov environment.