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Original Articles

Bayesian inference approach to inverse problems in a financial mathematical model

ORCID Icon, ORCID Icon, & ORCID Icon
Pages 1967-1981 | Received 15 Mar 2019, Accepted 18 Sep 2019, Published online: 08 Oct 2019
 

Abstract

This paper investigates an inverse problem of option pricing in the extended Black–Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of an MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

2010 Mathematics Subject Classifications:

Acknowledgments

The author would like to thank the referee for carefully reading our manuscript and for giving such constructive comments which substantially helped to improve the quality of our paper.

Disclosure statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Additional information

Funding

The first author would like to acknowledge the supports from Grant-in-Aid for Scientific Research (C) 18K03439 of the Japan Society for the Promotion of Science (JSPS). The second author was supported by the National Natural Science Foundation of China [grant no. 11971121]. The third author would like to acknowledge the supports from Grant-in-Aid for Scientific Research [15K21766 and 15H057403] of the Japan Society for the Promotion of Science (JSPS).

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