IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2405.12988.html
   My bibliography  Save this paper

Prediction of Cryptocurrency Prices through a Path Dependent Monte Carlo Simulation

Author

Listed:
  • Ayush Singh
  • Anshu K. Jha
  • Amit N. Kumar

Abstract

In this paper, our focus lies on the Merton's jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of methodologies. We adopt an approach that involves implementing different drift, volatility, and jump terms within the model through various machine learning techniques, traditional methods, and statistical methods on price-volume data. Additionally, we introduce a path-dependent Monte Carlo simulation to model cryptocurrency prices, taking into account the volatility and unexpected jumps in prices.

Suggested Citation

  • Ayush Singh & Anshu K. Jha & Amit N. Kumar, 2024. "Prediction of Cryptocurrency Prices through a Path Dependent Monte Carlo Simulation," Papers 2405.12988, arXiv.org.
  • Handle: RePEc:arx:papers:2405.12988
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2405.12988
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Selmi, Refk & Mensi, Walid & Hammoudeh, Shawkat & Bouoiyour, Jamal, 2018. "Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold," Energy Economics, Elsevier, vol. 74(C), pages 787-801.
    2. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Junwei Chen, 2023. "Analysis of Bitcoin Price Prediction Using Machine Learning," JRFM, MDPI, vol. 16(1), pages 1-25, January.
    5. Sun, Xiaolei & Liu, Mingxi & Sima, Zeqian, 2020. "A novel cryptocurrency price trend forecasting model based on LightGBM," Finance Research Letters, Elsevier, vol. 32(C).
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Mariusz Tarnopolski, 2017. "Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach," Papers 1707.03746, arXiv.org, revised Aug 2017.
    8. Nicola Uras & Lodovica Marchesi & Michele Marchesi & Roberto Tonelli, 2020. "Forecasting Bitcoin closing price series using linear regression and neural networks models," Papers 2001.01127, arXiv.org.
    9. Basak, Suryoday & Kar, Saibal & Saha, Snehanshu & Khaidem, Luckyson & Dey, Sudeepa Roy, 2019. "Predicting the direction of stock market prices using tree-based classifiers," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 552-567.
    10. Ahmad Chokor & Élise Alfieri, 2021. "Long and short-term impacts of regulation in the cryptocurrency market," Post-Print hal-03275473, HAL.
    11. Chokor, Ahmad & Alfieri, Elise, 2021. "Long and short-term impacts of regulation in the cryptocurrency market," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 157-173.
    12. Fahad Mostafa & Pritam Saha & Mohammad Rafiqul Islam & Nguyet Nguyen, 2021. "GJR-GARCH Volatility Modeling under NIG and ANN for Predicting Top Cryptocurrencies," JRFM, MDPI, vol. 14(9), pages 1-22, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessio Brini & Jimmie Lenz, 2024. "A comparison of cryptocurrency volatility-benchmarking new and mature asset classes," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-38, December.
    2. Ren, Yi-Shuai & Ma, Chao-Qun & Kong, Xiao-Lin & Baltas, Konstantinos & Zureigat, Qasim, 2022. "Past, present, and future of the application of machine learning in cryptocurrency research," Research in International Business and Finance, Elsevier, vol. 63(C).
    3. Alessio Brini & Jimmie Lenz, 2024. "A Comparison of Cryptocurrency Volatility-benchmarking New and Mature Asset Classes," Papers 2404.04962, arXiv.org.
    4. Hau, Liya & Zhu, Huiming & Shahbaz, Muhammad & Sun, Wuqin, 2021. "Does transaction activity predict Bitcoin returns? Evidence from quantile-on-quantile analysis," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    5. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    6. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    7. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    8. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    9. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    10. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    11. Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    12. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    13. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.
    14. Zhang, Jian-Xun & Hu, Chang-Hua & He, Xiao & Si, Xiao-Sheng & Liu, Yang & Zhou, Dong-Hua, 2017. "Lifetime prognostics for deteriorating systems with time-varying random jumps," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 338-350.
    15. Chen, Fen-Ying & Yang, Sharon S. & Huang, Hong-Chih, 2022. "Modeling pandemic mortality risk and its application to mortality-linked security pricing," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 341-363.
    16. Tung-Lung Wu, 2020. "Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 13-24, March.
    17. Aurelio F. Bariviera & Ignasi Merediz‐Solà, 2021. "Where Do We Stand In Cryptocurrencies Economic Research? A Survey Based On Hybrid Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 377-407, April.
    18. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    19. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2405.12988. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.