Efficient hedging in general Black-Scholes model

TL;DR

This paper extends the concept of efficient hedging for European call options from the standard Black-Scholes model to more general models with time-varying parameters and fractional Brownian motion, providing broader applicability.

Contribution

It introduces efficient hedging strategies for European call options in general and fractional Black-Scholes models, accounting for time-varying and fractional stochastic processes.

Findings

Derived hedging strategies for models with time-varying coefficients.

Extended efficient hedging to fractional Black-Scholes models.

Demonstrated reduced capital requirements with effective risk mitigation.

Abstract

An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes model with constant drift and volatility coefficients. In this paper we considered the efficient hedging for European call option in general Black-Scholes model $dX_t=X_t(m(t)dt+\sigma (t)dw(t))$ with time-varying drift and volatility coefficients and in fractional Black-Scholes model $dX_t=X_t(\sigma B_H(t)+mdt)$ with constant coefficients.