Paper: arXiv 2402.17919

Authors: Young Shin Kim, Hyun-Gyoon Kim

Abstract

In this study, we discuss a machine learning technique to price exotic options with two underlying assets based on a non-Gaussian Levy process model. We introduce a new multivariate Levy process model named the generalized normal tempered stable (gNTS) process, which is defined by time-changed multivariate Brownian motion. Since the gNTS process does not provide a simple analytic formula for the probability density function (PDF), we use the conditional real-valued non-volume preserving (CRealNVP) model, which is a type of flow-based generative network. Then, we discuss the no-arbitrage pricing on the gNTS model for pricing the quanto option, whose underlying assets consist of a foreign index and foreign exchange rate. We present the training of the CRealNVP model to learn the PDF of the gNTS process using a training set generated by Monte Carlo simulation. Next, we estimate the parameters of the gNTS model with the trained CRealNVP model using the empirical data observed in the market. Finally, we provide a method to find an equivalent martingale measure on the gNTS model and to price the quanto option using the CRealNVP model with the risk-neutral parameters of the gNTS model.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a sophisticated combination of advanced stochastic calculus (multivariate non-Gaussian Levy processes) and generative machine learning (CRealNVP normalizing flows) for exotic option pricing. While the mathematical framework and risk-neutral valuation methodology are rigorous and highly novel, full reproducibility is slightly constrained without public code availability.

Research Flowchart

  flowchart TD
    A[Research Goal: Price Quanto Options via Multivariate Non-Gaussian Lévy Process & Generative AI] --> B[1. Model Definition: Develop Generalized Normal Tempered Stable Process]
    
    subgraph Methodology & Computation
        B --> C[2. Training Generative AI: Train CRealNVP Model on Monte Carlo Simulations to Learn PDF]
        D[(Market Empirical Data: Foreign Index & FX Rate)] --> E[3. Parameter Estimation: Fit gNTS Model Parameters Using Trained CRealNVP]
        C --> E
        E --> F[4. Risk-Neutral Pricing: Find Equivalent Martingale Measure & Transform Parameters]
    end
    
    F --> G[Outcomes: Arbitrage-Free Quanto Option Pricing & Accurate Density Estimation]

Cited References (40)

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0 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.