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Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence

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  • 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.

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  • Young Shin Kim & Hyun-Gyoon Kim, 2024. "Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence," Papers 2402.17919, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2402.17919
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    References listed on IDEAS

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    1. Young Kim & Jeong Lee, 2007. "The relative entropy in CGMY processes and its applications to finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 327-338, October.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Naaman, Michael, 2021. "On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 173(C).
    4. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    5. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    6. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
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