Hedging strategies with a put option and their failure rates

TL;DR

This paper develops a new approach for stock hedging using put options, relaxing common assumptions and evaluating failure rates through simulations to improve risk management effectiveness.

Contribution

It introduces a formula for failure probability, relaxes key assumptions, and compares hedging strategies via simulations to enhance risk control.

Findings

Proposed method is more prudent than traditional approaches.

Relaxing assumptions improves hedging risk assessment.

Simulation results validate the effectiveness of the new approach.

Abstract

The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss exceeds a predetermined level of Value-at-Risk, which is used to find the optimal strike price and optimal hedge ratio. The assumptions that the chosen put option finishes in-the-money and the constraint of hedging budget is binding are relaxed in this paper. A hypothesis test is proposed to determine whether the failure rate of hedging strategy is greater than the predetermined level of risk. The performances of the proposed method and the method with those two assumptions are compared through simulations. The results of simulated investigations indicate that the proposed method is much more prudent than the method with those two assumptions.