Future Hedging Costs: Back to Basics

Abstract

The Black-Scholes model is based on replication theory which makes several unrealistic assumptions, notably that one can hedge continuously and trade without transaction costs. This paper presents a framework incorporating future hedging costs in the valuation process. It determines the trade-off between hedging costs and hedging errors due to discrete hedging for a carefully chosen utility function. It provides some equations to solve for the expectation of the hedging costs and the standard deviation of the hedging errors. The chosen utility function is based on these two quantities, allowing us to determine the optimal risk management strategy without resorting to numerical techniques. This approach could be used by regulators to define quantities relevant to the calculation of future hedging costs in the context of Prudent Value. This approach could also be used as a basis for Fair Value reserves and the pricing of the exotic deals.