Hedging in Jump Diffusion Model with Transaction Costs

TL;DR

This paper develops a closed-form hedging strategy for jump-diffusion models with transaction costs, providing explicit formulas and recursive methods for European options within a Black-Scholes framework.

Contribution

It introduces a novel closed-form conditional least squares hedging strategy for jump-diffusion models considering transaction costs, with explicit solutions for European options.

Findings

Explicit closed-form hedging formulas derived

Recursive hedging strategies formulated

Numerical results and decision trees provided

Abstract

We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the Black-Scholes framework with interpretations related to investor priorities and transaction costs. We investigate the explicit form of this result for the particular case of the European call option under transaction costs and formulate recursive hedging strategies. Finally, we present a decision tree, table of values, and figures to support our results.