Hedging in Jump Diffusion Model with Transaction Costs

ArXiv ID: 2408.10785 “View on arXiv”

Authors: Unknown

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.

Keywords: Jump-Diffusion Model, Conditional Least Square Hedging, European Call Option, Transaction Costs, Recursive Hedging, Equity Derivatives / Options

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents dense, advanced mathematics including stochastic calculus, conditional moments, and explicit derivations for hedging strategies in jump-diffusion models, placing it in the high math complexity range. However, the summary and excerpt focus on theoretical formulations and closed-form solutions without mention of actual backtests, code, datasets, or implementation details, indicating low empirical rigor.

  flowchart TD
    A["Research Goal<br>Optimal Hedging in Jump-Diffusion<br>with Transaction Costs"] --> B["Methodology<br>Conditional Least Squares &<br>Recursive Hedging Strategies"]
    B --> C{"Inputs & Model Parameters"}
    C --> D["Jump-Diffusion Asset Model<br>Stochastic Differential Equation"]
    C --> E["Transaction Cost Structure"]
    C --> F["European Call Option<br>Payoff Function"]
    D & E & F --> G["Computational Process<br>Derive Closed-Form<br>Hedging Formulas"]
    G --> H{"Analysis & Validation"}
    H --> I["Decision Trees<br>& Value Tables"]
    H --> J["Graphical Plots of<br>Hedging Performance"]
    I & J --> K["Key Findings<br>Closed-form hedging strategy<br>Explicit pricing under costs<br>Impact of jump intensity<br>on optimal hedge"]