Alternative models for FX: pricing double barrier options in regime-switching Lévy models with memory

ArXiv ID: 2402.16724 “View on arXiv”

Authors: Unknown

Abstract

This paper is a supplement to our recent paper Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models". We introduce the class of regime-switching Lévy models with memory, which take into account the evolution of the stochastic parameters in the past. This generalization of the class of Lévy models modulated by Markov chains is similar in spirit to rough volatility models. It is flexible and suitable for application of the machine-learning tools. We formulate the modification of the numerical method in Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models", which has the same number of the main time-consuming blocks as the method for Markovian regime-switching models.

Keywords: Regime-Switching Lévy Models, Double Barrier Options, Rough Volatility, FX Markets, Numerical Methods, Foreign Exchange (FX)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper introduces advanced mathematical generalizations of Lévy models with memory, relying heavily on Fourier/Laplace transforms, Wiener-Hopf factorization, and iterative algorithms, but contains no implementation details, datasets, or backtests, focusing purely on theoretical pricing methods.

  flowchart TD
    Goal["Research Goal<br/>Price double barrier options under regime-switching<br/>Lévy models with memory (non-Markovian evolution)"]
    Inputs["Input Parameters<br/>FX market data<br/>Regime-switching Lévy model specs<br/>Double barrier option features"]
    Method["Core Methodology<br/>Adapt Markovian regime-switching algorithm<br/>to handle memory via rough volatility extension"]
    Proc["Computational Process<br/>Efficient block-based numerical solver<br/>maintains low complexity vs Markovian case"]
    Find["Key Findings & Outcomes<br/>Validated pricing framework<br/>Arbitrage-free solutions<br/>ML-ready, scalable for FX markets"]