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.
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.
ORCID
Yasushi Ota http://orcid.org/0000-0003-0534-0031
Yu Jianghttp://orcid.org/0000-0003-4551-9335
Masaaki Uesakahttp://orcid.org/0000-0001-6377-7472