Discrete Delta Hedging under Stochastic Volatility and Jumps: A Monte Carlo Cost–Risk Frontier

Yue Li

doi:10.54254/2754-1169/2025.BJ28668

Advances in Economics, Management and Political SciencesOpen access

Discrete Delta Hedging under Stochastic Volatility and Jumps: A Monte Carlo Cost–Risk Frontier

Research Article

Open Access

Discrete Delta Hedging under Stochastic Volatility and Jumps: A Monte Carlo Cost–Risk Frontier

Yue Li ^1*

¹ The Ohio State University

^*Corresponding author: li.13232@buckeyemail.osu.edu

Published on 28 October 2025

AEMPS Vol.234

ISSN (Print): 2754-1177

ISSN (Online): 2754-1169

ISBN (Print): 978-1-80590-487-8

ISBN (Online): 978-1-80590-488-5

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Abstract

Delta hedging is a fundamental strategy in options risk management, relying on continuous adjustment of a replicating portfolio to eliminate risk. However, real markets exhibit features such as stochastic volatility and jumps that violate the assumptions of the Black–Scholes model, rendering perfect replication impossible and the market incomplete. In such cases, hedging can only reduce risk at best, and frequent rebalancing incurs significant transaction costs. This article investigates discrete delta hedging under stochastic volatility and jump-diffusion dynamics, quantifying the trade-off between hedging cost and risk reduction via Monte Carlo simulation. We construct a cost–risk frontier, analogous to an efficient frontier, that shows the minimal achievable risk for a given cost (and vice versa). The results demonstrate that increasing the hedge frequency (trading more often) generally lowers the variance of hedging errors but at a rapidly diminishing rate and with higher accumulated costs. Even with very frequent rebalancing, a residual risk remains due to jumps and unhedgeable volatility fluctuations. We discuss how this frontier can inform optimal hedging policies, balancing transaction costs against risk appetite, and we compare our findings with prior theoretical and empirical studies.

Keywords:

Stochastic Volatility, Transaction Costs, Jump-Diffusion.

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References

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